CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 8
Liberty University
Question 1
Question
A solution is prepared by dissolving 0.050 moles of hydrochloric acid (HCl) in
enough water to make 500 mL of solution. Calculate the pH of the resulting
solution.
Solution
Step 1: Calculate the molarity of the HCl solution Given that the solution
contains 0.050 moles of HCl and a volume of 500 mL (which is 0.500 L), we can
calculate the molarity using the formula:
Molarity (M) = moles
volume (L)
Molarity (M) = 0.050 mol
0.500 L = 0.100 M
Step 2: Calculate the concentration of hydrogen ions (H) in the solution
Since HCl is a strong acid, it fully dissociates in water to form H and Cl ions.
Therefore, the concentration of H ions is equal to the molarity of the HCl solu-
tion:
[H] = 0.100 M
Step 3: Calculate the pH of the solution The pH is defined as the negative
logarithm of the hydrogen ion concentration:
pH = −log[H] = −log(0.100)
pH = −log1.0×10−1=−(−1) = 1
Therefore, the pH of the resulting solution is 1.
Question 2
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given concentration into the pH formula:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9
pH = −log(3.2) + log10−9
pH = −(log(3.2) −9)
pH ≈ −(−0.494 −9)
pH ≈ −(−9.494)
pH ≈9.494
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−9M is approximately 9.494.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−7
M.
Solution
Step 1: Recall the relationship between hydroxide ion concentration and pOH:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula
to find the pOH:
pOH =−log1.5×10−7
2
Step 3: Calculate the pOH:
pOH =−log1.5×10−7= 6.82
Step 4: Recall that pH and pOH are related by:
pH +pOH = 14
Step 5: Calculate the pH using the pOH value obtained:
pH = 14 −pOH = 14 −6.82 = 7.18
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−7M is 7.18.
Question 4
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−5M.
Solution
Step 1: Calculate the pOH of the solution using the formula: pOH =−log[OH−].
Given: [OH−]=2.5×10−5M
Calculate: pOH =−log2.5×10−5
Step 2: Calculate the pH of the solution using the relationship: pH +pOH =
14.
Given: pOH =−log2.5×10−5
Calculate: pH = 14 −pOH
Question 5
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−3
M.
3
Solution
Step 1: Recall the definition of pH:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3
pH = −log2.5×10−3
pH ≈ −(−2.60)
pH ≈2.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−3M is 2.60.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, we need to convert
the hydronium ion concentration to pH.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log3.5×10−4
pH = −log(3.5) + log10−4
pH = −(log(3.5) + 4)
pH ≈ −(0.544 068 044 4 + 4)
pH ≈ −4.5440680444
Step 4: Round the pH value to two decimal places:
pH ≈ −4.54
Therefore, the pH of the solution with a hydronium ion concentration of
3.5×10−4M is approximately 4.54.
4
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−4
M.
Solution
Step 1: The pH of a solution is defined as −log[H+], where [H+] is the hydrogen
ion concentration. Given [H+] = 2.5×10−4M, we can calculate the pH as
follows:
pH = −log2.5×10−4
Step 2: Substitute the value of [H+] into the formula to find the pH:
pH = −log2.5×10−4=−log(2.5) + log10−4
Step 3: Simplify the expression by using the properties of logarithms:
pH = −(0.3979) −4
Step 4: Calculate the final value of pH:
pH = −4.3979
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−4M is 4.3979.
Question 8
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as pH = -log[H+], where [H+] represents the
concentration of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = -log(3.2 ×10−5).
Step 3: Calculate the pH using a calculator: pH = -log(3.2 ×10−5) =
-(-4.49485) 4.49.
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately 4.49.
5
Question 9
Question
A 0.025 M solution of hydrochloric acid (HCl) has a pH of 1.75. Calculate the
pOH of the solution.
Solution
Step 1: Use the formula pH =−log[H+] to determine the concentration of
hydrogen ions:
pH = −log[H+]
1.75 = −log[H+]
[H+] = 10−1.75
Step 2: Calculate the concentration of hydroxide ions using the equation
Kw= [H+][OH−]:
Kw= [H+][OH−]
1.0×10−14 = (10−1.75)([OH−])
[OH−] = 1.0×10−14
10−1.75
Step 3: Find the pOH of the solution using the relationship pOH =−log[OH−]:
pOH =−log[OH−]
pOH =−log 1.0×10−14
10−1.75
Step 4: Simplify the expression and calculate the final value of pOH.
Question 10
Question
Calculate the pH of a solution with a pOH of 2.8.
Solution
Step 1: Recall the relationship between pH and pOH:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation above to find the
pH:
pH + 2.8 = 14
Step 3: Solve for pH:
pH = 14 −2.8 = 11.2
Therefore, the pH of the solution is 11.2.
6
Question 11
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that the pH is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.5×10−5
Step 3: Use the properties of logarithms to simplify:
pH = −log(3.5) −log10−5
pH = −log(3.5) + 5
Step 4: Use a calculator to find the value of −log(3.5):
pH ≈ − log(3.5) + 5 ≈ −0.5441 + 5
Step 5: Calculate the final pH value:
pH ≈4.456
Therefore, the pH of the solution is approximately 4.456.
Question 12
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+],pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH using the formula:
pH = −log2.5×10−9
7
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5)−log10−9=−log(2.5)−(−9) = −log(2.5)+9
Step 4: Use a calculator to find the pH:
pH ≈9.60
Step 5: Since we know that [H+]×[OH−] = 1.0×10−14 M2at 25
°
C, we can
find the pOH using the relationship:
pOH = −log[OH−]=−log 1.0×10−14
2.5×10−9
Step 6: Calculate the pOH:
pOH = −log 1.0×10−14
2.5×10−9=−log4.0×105
Step 7: Use a calculator to find the pOH:
pOH ≈5.40
Therefore, the pH of the solution is approximately 9.60 and the pOH is
approximately 5.40.
Question 13
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we can calculate
the pH using the given concentration of H3O+.
pH = −log3.2×10−5
Step 2: Substitute the given concentration into the equation and solve for
pH.
pH = −log3.2×10−5=−(log 3.2 + log 10−5) = −(log 3.2−5)
Step 3: Use the property of logarithms (log ab = log a+ log b) to simplify
the expression further.
pH = −(0.5052 −5)
Step 4: Calculate the final pH value.
pH ≈4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
8
Question 14
Question
Calculate the pH of a solution that has a hydronium ion concentration of 3.5×
10−4M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. We are given that the hydro-
nium ion concentration is 3.5×10−4M. Therefore, we can calculate the pH as
follows:
pH = −log3.5×10−4
Step 2: Use the property of logarithms that log(ab) = log(a) + log(b) to
simplify the calculation:
pH = −log(3.5) −log10−4
Step 3: Simplify further by using the property that log(10n) = nfor any
real number n:
pH = −log(3.5) −(−4)
Step 4: Calculate the log of 3.5 using a calculator:
pH = −0.5441 −(−4)
Step 5: Simplify the expression by subtracting the negative values:
pH = 4 + 0.5441
Step 6: Therefore, the pH of a solution with hydronium ion concentration
of 3.5×10−4M is approximately 4.5441 .
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−9
9
Step 3: Calculate the pH:
pH = −log2.5×10−9
pH = −(log 2.5 + log 10−9)
pH = −(0.3979 + 9)
pH = −9.3979
pH ≈9.40
Therefore, the pH of the solution is approximately 9.40.
Question 16
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall the definition of pH: The pH of a solution is defined as the
negative base 10 logarithm of the hydrogen ion concentration:
pH = −log[H+]
Step 2: Given the hydrogen ion concentration is 2.5×10−8M, we can
substitute this value into the pH formula:
pH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) + log10−8=−(log(2.5) −8)
Step 4: Using the properties of logarithms, we can simplify the expression
further:
pH = −(0.3979 −8) = −7.6021 ≈ −7.6
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.6.
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
10
Solution
Step 1: Use the relationship between pOH and OH−concentration:
pOH = −log[OH−]
Step 2: Calculate the pOH of the solution:
pOH = −log2.5×10−3=−log(2.5)+log10−3=−log(2.5)−3=0.398−3 = −2.602
Step 3: Use the relationship between pH and pOH:
pH + pOH = 14
Step 4: Calculate the pH of the solution:
pH = 14 −pOH = 14 −(−2.602) = 16.602
Therefore, the pH of the solution is 16.602.
Question 18
Question
A solution is prepared by mixing 50.0 mL of 0.20 M hydrochloric acid (HCl)
with 75.0 mL of 0.15 M sodium hydroxide (NaOH). Calculate the pH of the
resulting solution. Given Kw= 1.0×10−14 at 25◦C.
Solution
Step 1: Write the balanced chemical equation for the neutralization reaction
between HCl and NaOH:
HCl + NaOH →NaCl + H2O
Step 2: Determine the limiting reactant to find the moles of each reactant
that reacts. In this case, HCl and NaOH react in a 1:1 molar ratio, so the
limiting reactant is the one that is initially present in lower amount.
Calculate the moles of HCl:
Moles of HCl = Volume of HCl(L)×Molarity of HCl(mol/L)
Moles of HCl = 0.050 L ×0.20 mol/L = 0.010 mol
Calculate the moles of NaOH:
Moles of NaOH = Volume of NaOH(L)×Molarity of NaOH(mol/L)
Moles of NaOH = 0.075 L ×0.15 mol/L = 0.01125 mol
11
Since HCl is the limiting reactant, 0.010 mol of HCl reacts.
Step 3: Calculate the concentration of H+ions in the resulting solution.
Since 0.010 mol of HCl reacts, it produces 0.010 mol of H+ions. Calculate the
total volume of the solution:
Vtotal =VHCl +VNaOH = 50.0 mL + 75.0 mL = 125.0 mL = 0.125 L
Calculate the concentration of H+ions:
[H+] = moles of H+
volume of solution =0.010 mol
0.125 L = 0.080 M
Step 4: Calculate the pH of the resulting solution using the equation pH =
−log[H+]:
pH = −log(0.080) = −(−1.096) = 1.096
Therefore, the pH of the resulting solution is 1.096.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−9
M.
Solution
Step 1: Recall that the pH is calculated using the formula pH =−log[H+],
where [H+] is the hydrogen ion concentration.
Given [H+] = 3.5×10−9M, we can calculate the pH as follows:
Step 2: Substitute the given hydrogen ion concentration into the formula for
pH:
pH =−log3.5×10−9
Step 3: Calculate the pH using the calculator:
pH =−log3.5×10−9
pH ≈ − log(3.5) −log10−9
pH ≈ −0.5441 −(−9)
pH ≈8.456
Therefore, the pH of the solution with a hydrogen ion concentration of 3.5×
10−9M is approximately 8.456.
12
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.6×10−5
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.6×10−5
Step 3: Calculate the pH:
pH = −log3.6×10−5=−log(3.6) + log10−5=−0.5563 −(−5) = 4.4437
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.6×10−5M is approximately 4.44.
Question 21
Question
Calculate the pH of a solution that has a pOH of 2.75.
Solution
Step 1: Recall that the pH and pOH of a solution are related by the equation:
pH + pOH = 14
Step 2: Given that the pOH of the solution is 2.75, we can find the pH by
subtracting the pOH from 14:
pH = 14 −2.75
Step 3: Perform the subtraction to find the pH:
pH = 11.25
Step 4: Therefore, the pH of the solution is 11.25.
13
Question 22
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the definition of pH. The pH of a solution is defined as the
negative logarithm of the hydronium ion concentration. Mathematically, pH =
−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula.
Given [H3O+]=3.2×10−5M, we can plug this value into the formula: pH =
−log3.2×10−5.
Step 3: Calculate the pH. Using a calculator, we find: pH =−log3.2×10−5≈
−log(3.2) −log10−5≈ −0.5052 −(−5) ≈4.4948.
Step 4: Write the final answer. Therefore, the pH of the solution with a
hydronium ion concentration of 3.2×10−5M is approximately 4.49.
Question 23
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl). The
dissociation constant of HCl is 1.3×10−4. (Hint: pH =−log[H+])
Solution
Step 1: Write the dissociation of hydrochloric acid:
HCl →H++ Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely.
So the concentration of H+is equal to the initial concentration of HCl, which
is 0.025 M.
Step 3: Calculate the pH using the formula pH =−log[H+]:
pH =−log(0.025) = −log2.5×10−2
Step 4: Using the property of logarithms log(ab) = log(a) + log(b), we can
rewrite the expression as:
pH =−log(2.5) −log10−2
Step 5: Recall that −log(2.5) ≈ −0.3979 and −log10−2= 2. Therefore:
pH ≈ −0.3979 −2
14
Step 6: Add the two values to find the pH:
pH ≈ −2.3979
Step 7: Thus, the pH of a 0.025 M hydrochloric acid solution is approxi-
mately 2.40.
Question 24
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−6
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm of the hydrogen
ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.5×10−6
Step 3: Use the property of logarithms (log(xy) = log(x)+log(y)) to simplify
the expression:
pH = −[log(3.5) + log10−6]
Step 4: Recall that log10−6=−6:
pH = −[log(3.5) −6]
Step 5: Use a calculator to find the value of log(3.5), then subtract 6 and
change the sign to get the final pH value:
pH ≈ −[0.5441 −6] = −[−5.4559] = 5.4559
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.5×10−6M is approximately 5.46.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
15
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+]×[OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to calculate the hydrogen
ion concentration.
[OH−]=1.5×10−10 M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−10 = 6.67 ×10−5M
Step 3: Calculate the pH of the solution.
pH = −log[H+]=−log6.67 ×10−5=−(−4.18) = 4.18
Therefore, the pH of the solution is 4.18.
Question 26
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 3.6×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
where [H+] is the hydrogen ion concentration and [OH−] is the hydroxide ion
concentration. In a neutral solution, [H+] = [OH−]=1.0×10−7M.
Step 2: Given that the hydrogen ion concentration is 3.6×10−9M, we can
calculate pH as follows:
pH = −log3.6×10−9
Step 3: Calculate the pH:
pH = −log3.6×10−9=−log(3.6) −log10−9
Step 4: Simplify the expression:
pH ≈ − log(3.6) + 9 = −0.5563 + 9
16
Step 5: Calculate the pH:
pH ≈8.4437
Step 6: Using the relationship between pH and pOH:
pH + pOH = 14
Step 7: Calculate the pOH:
pOH = 14 −pH
Step 8: Substituting the calculated pH value:
pOH = 14 −8.4437
Step 9: Calculate the pOH:
pOH ≈5.5563
Therefore, the pH of the solution is approximately 8.4437 and the pOH is
approximately 5.5563.
Question 27
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×
10−10 M.
Solution
Step 1: Recall that the hydroxide ion concentration (OH−) is related to the pH
by the formula: pOH =−log[OH−]. We also know that pH +pOH = 14 for
any aqueous solution at 25
°
C.
Step 2: Given that [OH−]=1.5×10−10 M, we can calculate the pOH:
pOH = −log1.5×10−10=−log 1.5−log 10−10 =−(log 1.5+10 log 10) ≈ −(log 1.5+10) ≈ −(0.176+10) ≈ −10.176 ≈10.176
Step 3: Now, we can find the pH using the relationship pH +pOH = 14:
pH = 14 −pOH = 14 −10.176 = 3.824
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−10 M is approximately 3.824.
17
Question 28
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, to find the pH of the
solution, we first need to determine the hydrogen ion concentration.
Given: [H+]=3.5×10−5M
Step 2: Substitute the given hydrogen ion concentration into the pH formula
to find the pH.
pH = −log3.5×10−5
Step 3: Calculate the pH using a calculator.
pH = −log3.5×10−5
pH = −log(3.5) + log10−5
pH = −log(3.5) −5
pH ≈ −(−0.45593) −5
pH ≈0.45593 −5
pH ≈4.54407
Therefore, the pH of the solution with a hydrogen ion concentration of 3.5×
10−5M is approximately 4.54.
Question 29
Question
Calculate the pH of a solution with a hydrogen ion concentration of 1.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration in moles per liter.
Step 2: Given that the hydrogen ion concentration is 1.5×10−4M, we can
calculate the pH using the formula:
pH = −log1.5×10−4
18
Step 3: Substitute the given hydrogen ion concentration value into the for-
mula:
pH = −log1.5×10−4
Step 4: Use a calculator to find the logarithm of 1.5×10−4:
pH = −log1.5×10−4≈ − log(0.00015) ≈ −(−3.82391) ≈3.82391
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 1.5×10−4M is approximately 3.82.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Recall the relationship between pH, pOH, and the ion concentrations
in a solution:
pH +pOH = 14
Step 2: Calculate the pOH of the solution using the given hydroxide ion
concentration:
pOH = −log[OH−] = −log1.5×10−4
Step 3: Calculate the pOH value:
pOH = −log1.5×10−4=−log(1.5) + log10−4= 0.1761 + 4 = 4.1761
Step 4: Use the relationship between pH, pOH to find the pH of the solution:
pH = 14 −pOH = 14 −4.1761 = 9.8239
Therefore, the pH of the solution is approximately 9.82.
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we can calculate
the pH using the concentration given. Step 2: Substitute the given hydronium
ion concentration into the formula for pH. Step 3: Calculate the pH. Step 4:
Round the answer to the appropriate number of significant figures.
19
Step 1:
The pH of a solution can be calculated using the formula −log[H3O+].
Step 2:
Given that the hydronium ion concentration is 3.2×10−6M, we have [H3O+] =
3.2×10−6M.
Step 3:
Substitute the hydronium ion concentration into the formula:
pH = −log3.2×10−6
Step 4:
Calculating the pH:
pH = −log3.2×10−6=−log(3.2) + log10−6=−(0.5051) −6 = −6.5051
Therefore, the pH of the solution is 6.51.
Question 32
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−8
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. We are given [H+] = 3.2×10−8
M.
Step 2: Substitute [H+]=3.2×10−8into the pH formula:
pH = −log3.2×10−8
Step 3: Calculate log3.2×10−8:
log3.2×10−8≈ −7.49485
Step 4: Calculate the negative of log3.2×10−8to find the pH:
pH ≈7.49485
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−8M is approximately 7.49.
20
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−11
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Given that the hydroxide ion concentration is 3.2×10−11 M, we
can calculate the hydrogen ion concentration using the fact that in water,
[H+][OH−]=1.0×10−14:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
3.2×10−11
Step 3: Simplifying the expression gives:
[H+] = 1.0
3.2×10−14−(−11) = 3.125 ×10−4M
Step 4: Now, we can calculate the pH:
pH = −log3.125 ×10−4=−log 3.125 −log 10−4
Step 5: Further simplification gives us:
pH = −(−0.505) −(−4) = 0.505 + 4 = 4.505
Therefore, the pH of the solution is 4.505.
Question 34
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
21
where [H+] represents the concentration of hydrogen ions in the solution. Since
we are given the concentration of hydroxide ions ([OH−]), we can use the fact
that [H+][OH−]=1.0×10−14 at 25
°
C to find [H+].
Step 2: First, calculate the concentration of hydrogen ions using the concen-
tration of hydroxide ions:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
3.2×10−4
Step 3: Calculate the pH by taking the negative logarithm of the hydrogen
ion concentration:
pH = −log[H+] = −log 1.0×10−14
3.2×10−4
Question 35
Question
The pH of a 0.005 M hydrochloric acid (HCl) solution is calculated to be 2.30.
Calculate the pOH of the solution.
Solution
Step 1: Recall the relationship between pH and pOH:
pH + pOH = 14
Step 2: Given that the pH of the HCl solution is 2.30, we can find the
hydrogen ion concentration by taking the antilog of the negative of the pH
value.
[H+] = 10−pH = 10−2.30
Step 3: Calculate the hydrogen ion concentration:
[H+] = 10−2.30 = 0.00501 M
Step 4: The pOH can be calculated by taking the negative logarithm base
10 of the hydroxide ion concentration ([OH-]).
pOH = −log[OH-]
Step 5: Since the solution is a strong acid (HCl dissociates completely), the
hydroxide ion concentration is the same as the hydrogen ion concentration:
[OH-] = [H+]=0.00501 M
Step 6: Calculate the pOH of the solution:
pOH = −log(0.00501) = 2.30
Therefore, the pOH of the 0.005 M HCl solution is 2.30.
22
Question 2
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given concentration into the pH formula:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9
pH = −log(3.2) + log10−9
pH = −(log(3.2) −9)
pH ≈ −(−0.494 −9)
pH ≈ −(−9.494)
pH ≈9.494
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−9M is approximately 9.494.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−7
M.
Solution
Step 1: Recall the relationship between hydroxide ion concentration and pOH:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula
to find the pOH:
pOH =−log1.5×10−7
2
Step 3: Calculate the pOH:
pOH =−log1.5×10−7= 6.82
Step 4: Recall that pH and pOH are related by:
pH +pOH = 14
Step 5: Calculate the pH using the pOH value obtained:
pH = 14 −pOH = 14 −6.82 = 7.18
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−7M is 7.18.
Question 4
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−5M.
Solution
Step 1: Calculate the pOH of the solution using the formula: pOH =−log[OH−].
Given: [OH−]=2.5×10−5M
Calculate: pOH =−log2.5×10−5
Step 2: Calculate the pH of the solution using the relationship: pH +pOH =
14.
Given: pOH =−log2.5×10−5
Calculate: pH = 14 −pOH
Question 5
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−3
M.
3
Solution
Step 1: Recall the definition of pH:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3
pH = −log2.5×10−3
pH ≈ −(−2.60)
pH ≈2.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−3M is 2.60.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, we need to convert
the hydronium ion concentration to pH.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log3.5×10−4
pH = −log(3.5) + log10−4
pH = −(log(3.5) + 4)
pH ≈ −(0.544 068 044 4 + 4)
pH ≈ −4.5440680444
Step 4: Round the pH value to two decimal places:
pH ≈ −4.54
Therefore, the pH of the solution with a hydronium ion concentration of
3.5×10−4M is approximately 4.54.
4
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−4
M.
Solution
Step 1: The pH of a solution is defined as −log[H+], where [H+] is the hydrogen
ion concentration. Given [H+] = 2.5×10−4M, we can calculate the pH as
follows:
pH = −log2.5×10−4
Step 2: Substitute the value of [H+] into the formula to find the pH:
pH = −log2.5×10−4=−log(2.5) + log10−4
Step 3: Simplify the expression by using the properties of logarithms:
pH = −(0.3979) −4
Step 4: Calculate the final value of pH:
pH = −4.3979
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−4M is 4.3979.
Question 8
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as pH = -log[H+], where [H+] represents the
concentration of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = -log(3.2 ×10−5).
Step 3: Calculate the pH using a calculator: pH = -log(3.2 ×10−5) =
-(-4.49485) 4.49.
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately 4.49.
5
Question 9
Question
A 0.025 M solution of hydrochloric acid (HCl) has a pH of 1.75. Calculate the
pOH of the solution.
Solution
Step 1: Use the formula pH =−log[H+] to determine the concentration of
hydrogen ions:
pH = −log[H+]
1.75 = −log[H+]
[H+] = 10−1.75
Step 2: Calculate the concentration of hydroxide ions using the equation
Kw= [H+][OH−]:
Kw= [H+][OH−]
1.0×10−14 = (10−1.75)([OH−])
[OH−] = 1.0×10−14
10−1.75
Step 3: Find the pOH of the solution using the relationship pOH =−log[OH−]:
pOH =−log[OH−]
pOH =−log 1.0×10−14
10−1.75
Step 4: Simplify the expression and calculate the final value of pOH.
Question 10
Question
Calculate the pH of a solution with a pOH of 2.8.
Solution
Step 1: Recall the relationship between pH and pOH:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation above to find the
pH:
pH + 2.8 = 14
Step 3: Solve for pH:
pH = 14 −2.8 = 11.2
Therefore, the pH of the solution is 11.2.
6
Question 11
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that the pH is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.5×10−5
Step 3: Use the properties of logarithms to simplify:
pH = −log(3.5) −log10−5
pH = −log(3.5) + 5
Step 4: Use a calculator to find the value of −log(3.5):
pH ≈ − log(3.5) + 5 ≈ −0.5441 + 5
Step 5: Calculate the final pH value:
pH ≈4.456
Therefore, the pH of the solution is approximately 4.456.
Question 12
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+],pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH using the formula:
pH = −log2.5×10−9
7
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5)−log10−9=−log(2.5)−(−9) = −log(2.5)+9
Step 4: Use a calculator to find the pH:
pH ≈9.60
Step 5: Since we know that [H+]×[OH−] = 1.0×10−14 M2at 25
°
C, we can
find the pOH using the relationship:
pOH = −log[OH−]=−log 1.0×10−14
2.5×10−9
Step 6: Calculate the pOH:
pOH = −log 1.0×10−14
2.5×10−9=−log4.0×105
Step 7: Use a calculator to find the pOH:
pOH ≈5.40
Therefore, the pH of the solution is approximately 9.60 and the pOH is
approximately 5.40.
Question 13
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we can calculate
the pH using the given concentration of H3O+.
pH = −log3.2×10−5
Step 2: Substitute the given concentration into the equation and solve for
pH.
pH = −log3.2×10−5=−(log 3.2 + log 10−5) = −(log 3.2−5)
Step 3: Use the property of logarithms (log ab = log a+ log b) to simplify
the expression further.
pH = −(0.5052 −5)
Step 4: Calculate the final pH value.
pH ≈4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
8
Question 14
Question
Calculate the pH of a solution that has a hydronium ion concentration of 3.5×
10−4M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. We are given that the hydro-
nium ion concentration is 3.5×10−4M. Therefore, we can calculate the pH as
follows:
pH = −log3.5×10−4
Step 2: Use the property of logarithms that log(ab) = log(a) + log(b) to
simplify the calculation:
pH = −log(3.5) −log10−4
Step 3: Simplify further by using the property that log(10n) = nfor any
real number n:
pH = −log(3.5) −(−4)
Step 4: Calculate the log of 3.5 using a calculator:
pH = −0.5441 −(−4)
Step 5: Simplify the expression by subtracting the negative values:
pH = 4 + 0.5441
Step 6: Therefore, the pH of a solution with hydronium ion concentration
of 3.5×10−4M is approximately 4.5441 .
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−9
9
Step 3: Calculate the pH:
pH = −log2.5×10−9
pH = −(log 2.5 + log 10−9)
pH = −(0.3979 + 9)
pH = −9.3979
pH ≈9.40
Therefore, the pH of the solution is approximately 9.40.
Question 16
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall the definition of pH: The pH of a solution is defined as the
negative base 10 logarithm of the hydrogen ion concentration:
pH = −log[H+]
Step 2: Given the hydrogen ion concentration is 2.5×10−8M, we can
substitute this value into the pH formula:
pH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) + log10−8=−(log(2.5) −8)
Step 4: Using the properties of logarithms, we can simplify the expression
further:
pH = −(0.3979 −8) = −7.6021 ≈ −7.6
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.6.
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
10
Solution
Step 1: Use the relationship between pOH and OH−concentration:
pOH = −log[OH−]
Step 2: Calculate the pOH of the solution:
pOH = −log2.5×10−3=−log(2.5)+log10−3=−log(2.5)−3=0.398−3 = −2.602
Step 3: Use the relationship between pH and pOH:
pH + pOH = 14
Step 4: Calculate the pH of the solution:
pH = 14 −pOH = 14 −(−2.602) = 16.602
Therefore, the pH of the solution is 16.602.
Question 18
Question
A solution is prepared by mixing 50.0 mL of 0.20 M hydrochloric acid (HCl)
with 75.0 mL of 0.15 M sodium hydroxide (NaOH). Calculate the pH of the
resulting solution. Given Kw= 1.0×10−14 at 25◦C.
Solution
Step 1: Write the balanced chemical equation for the neutralization reaction
between HCl and NaOH:
HCl + NaOH →NaCl + H2O
Step 2: Determine the limiting reactant to find the moles of each reactant
that reacts. In this case, HCl and NaOH react in a 1:1 molar ratio, so the
limiting reactant is the one that is initially present in lower amount.
Calculate the moles of HCl:
Moles of HCl = Volume of HCl(L)×Molarity of HCl(mol/L)
Moles of HCl = 0.050 L ×0.20 mol/L = 0.010 mol
Calculate the moles of NaOH:
Moles of NaOH = Volume of NaOH(L)×Molarity of NaOH(mol/L)
Moles of NaOH = 0.075 L ×0.15 mol/L = 0.01125 mol
11
Since HCl is the limiting reactant, 0.010 mol of HCl reacts.
Step 3: Calculate the concentration of H+ions in the resulting solution.
Since 0.010 mol of HCl reacts, it produces 0.010 mol of H+ions. Calculate the
total volume of the solution:
Vtotal =VHCl +VNaOH = 50.0 mL + 75.0 mL = 125.0 mL = 0.125 L
Calculate the concentration of H+ions:
[H+] = moles of H+
volume of solution =0.010 mol
0.125 L = 0.080 M
Step 4: Calculate the pH of the resulting solution using the equation pH =
−log[H+]:
pH = −log(0.080) = −(−1.096) = 1.096
Therefore, the pH of the resulting solution is 1.096.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−9
M.
Solution
Step 1: Recall that the pH is calculated using the formula pH =−log[H+],
where [H+] is the hydrogen ion concentration.
Given [H+] = 3.5×10−9M, we can calculate the pH as follows:
Step 2: Substitute the given hydrogen ion concentration into the formula for
pH:
pH =−log3.5×10−9
Step 3: Calculate the pH using the calculator:
pH =−log3.5×10−9
pH ≈ − log(3.5) −log10−9
pH ≈ −0.5441 −(−9)
pH ≈8.456
Therefore, the pH of the solution with a hydrogen ion concentration of 3.5×
10−9M is approximately 8.456.
12
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.6×10−5
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.6×10−5
Step 3: Calculate the pH:
pH = −log3.6×10−5=−log(3.6) + log10−5=−0.5563 −(−5) = 4.4437
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.6×10−5M is approximately 4.44.
Question 21
Question
Calculate the pH of a solution that has a pOH of 2.75.
Solution
Step 1: Recall that the pH and pOH of a solution are related by the equation:
pH + pOH = 14
Step 2: Given that the pOH of the solution is 2.75, we can find the pH by
subtracting the pOH from 14:
pH = 14 −2.75
Step 3: Perform the subtraction to find the pH:
pH = 11.25
Step 4: Therefore, the pH of the solution is 11.25.
13
Question 22
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the definition of pH. The pH of a solution is defined as the
negative logarithm of the hydronium ion concentration. Mathematically, pH =
−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula.
Given [H3O+]=3.2×10−5M, we can plug this value into the formula: pH =
−log3.2×10−5.
Step 3: Calculate the pH. Using a calculator, we find: pH =−log3.2×10−5≈
−log(3.2) −log10−5≈ −0.5052 −(−5) ≈4.4948.
Step 4: Write the final answer. Therefore, the pH of the solution with a
hydronium ion concentration of 3.2×10−5M is approximately 4.49.
Question 23
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl). The
dissociation constant of HCl is 1.3×10−4. (Hint: pH =−log[H+])
Solution
Step 1: Write the dissociation of hydrochloric acid:
HCl →H++ Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely.
So the concentration of H+is equal to the initial concentration of HCl, which
is 0.025 M.
Step 3: Calculate the pH using the formula pH =−log[H+]:
pH =−log(0.025) = −log2.5×10−2
Step 4: Using the property of logarithms log(ab) = log(a) + log(b), we can
rewrite the expression as:
pH =−log(2.5) −log10−2
Step 5: Recall that −log(2.5) ≈ −0.3979 and −log10−2= 2. Therefore:
pH ≈ −0.3979 −2
14
Step 6: Add the two values to find the pH:
pH ≈ −2.3979
Step 7: Thus, the pH of a 0.025 M hydrochloric acid solution is approxi-
mately 2.40.
Question 24
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−6
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm of the hydrogen
ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.5×10−6
Step 3: Use the property of logarithms (log(xy) = log(x)+log(y)) to simplify
the expression:
pH = −[log(3.5) + log10−6]
Step 4: Recall that log10−6=−6:
pH = −[log(3.5) −6]
Step 5: Use a calculator to find the value of log(3.5), then subtract 6 and
change the sign to get the final pH value:
pH ≈ −[0.5441 −6] = −[−5.4559] = 5.4559
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.5×10−6M is approximately 5.46.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
15
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+]×[OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to calculate the hydrogen
ion concentration.
[OH−]=1.5×10−10 M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−10 = 6.67 ×10−5M
Step 3: Calculate the pH of the solution.
pH = −log[H+]=−log6.67 ×10−5=−(−4.18) = 4.18
Therefore, the pH of the solution is 4.18.
Question 26
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 3.6×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
where [H+] is the hydrogen ion concentration and [OH−] is the hydroxide ion
concentration. In a neutral solution, [H+] = [OH−]=1.0×10−7M.
Step 2: Given that the hydrogen ion concentration is 3.6×10−9M, we can
calculate pH as follows:
pH = −log3.6×10−9
Step 3: Calculate the pH:
pH = −log3.6×10−9=−log(3.6) −log10−9
Step 4: Simplify the expression:
pH ≈ − log(3.6) + 9 = −0.5563 + 9
16
Step 5: Calculate the pH:
pH ≈8.4437
Step 6: Using the relationship between pH and pOH:
pH + pOH = 14
Step 7: Calculate the pOH:
pOH = 14 −pH
Step 8: Substituting the calculated pH value:
pOH = 14 −8.4437
Step 9: Calculate the pOH:
pOH ≈5.5563
Therefore, the pH of the solution is approximately 8.4437 and the pOH is
approximately 5.5563.
Question 27
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×
10−10 M.
Solution
Step 1: Recall that the hydroxide ion concentration (OH−) is related to the pH
by the formula: pOH =−log[OH−]. We also know that pH +pOH = 14 for
any aqueous solution at 25
°
C.
Step 2: Given that [OH−]=1.5×10−10 M, we can calculate the pOH:
pOH = −log1.5×10−10=−log 1.5−log 10−10 =−(log 1.5+10 log 10) ≈ −(log 1.5+10) ≈ −(0.176+10) ≈ −10.176 ≈10.176
Step 3: Now, we can find the pH using the relationship pH +pOH = 14:
pH = 14 −pOH = 14 −10.176 = 3.824
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−10 M is approximately 3.824.
17
Question 28
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, to find the pH of the
solution, we first need to determine the hydrogen ion concentration.
Given: [H+]=3.5×10−5M
Step 2: Substitute the given hydrogen ion concentration into the pH formula
to find the pH.
pH = −log3.5×10−5
Step 3: Calculate the pH using a calculator.
pH = −log3.5×10−5
pH = −log(3.5) + log10−5
pH = −log(3.5) −5
pH ≈ −(−0.45593) −5
pH ≈0.45593 −5
pH ≈4.54407
Therefore, the pH of the solution with a hydrogen ion concentration of 3.5×
10−5M is approximately 4.54.
Question 29
Question
Calculate the pH of a solution with a hydrogen ion concentration of 1.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration in moles per liter.
Step 2: Given that the hydrogen ion concentration is 1.5×10−4M, we can
calculate the pH using the formula:
pH = −log1.5×10−4
18
Step 3: Substitute the given hydrogen ion concentration value into the for-
mula:
pH = −log1.5×10−4
Step 4: Use a calculator to find the logarithm of 1.5×10−4:
pH = −log1.5×10−4≈ − log(0.00015) ≈ −(−3.82391) ≈3.82391
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 1.5×10−4M is approximately 3.82.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Recall the relationship between pH, pOH, and the ion concentrations
in a solution:
pH +pOH = 14
Step 2: Calculate the pOH of the solution using the given hydroxide ion
concentration:
pOH = −log[OH−] = −log1.5×10−4
Step 3: Calculate the pOH value:
pOH = −log1.5×10−4=−log(1.5) + log10−4= 0.1761 + 4 = 4.1761
Step 4: Use the relationship between pH, pOH to find the pH of the solution:
pH = 14 −pOH = 14 −4.1761 = 9.8239
Therefore, the pH of the solution is approximately 9.82.
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we can calculate
the pH using the concentration given. Step 2: Substitute the given hydronium
ion concentration into the formula for pH. Step 3: Calculate the pH. Step 4:
Round the answer to the appropriate number of significant figures.
19
Step 1:
The pH of a solution can be calculated using the formula −log[H3O+].
Step 2:
Given that the hydronium ion concentration is 3.2×10−6M, we have [H3O+] =
3.2×10−6M.
Step 3:
Substitute the hydronium ion concentration into the formula:
pH = −log3.2×10−6
Step 4:
Calculating the pH:
pH = −log3.2×10−6=−log(3.2) + log10−6=−(0.5051) −6 = −6.5051
Therefore, the pH of the solution is 6.51.
Question 32
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−8
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. We are given [H+] = 3.2×10−8
M.
Step 2: Substitute [H+]=3.2×10−8into the pH formula:
pH = −log3.2×10−8
Step 3: Calculate log3.2×10−8:
log3.2×10−8≈ −7.49485
Step 4: Calculate the negative of log3.2×10−8to find the pH:
pH ≈7.49485
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−8M is approximately 7.49.
20
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−11
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Given that the hydroxide ion concentration is 3.2×10−11 M, we
can calculate the hydrogen ion concentration using the fact that in water,
[H+][OH−]=1.0×10−14:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
3.2×10−11
Step 3: Simplifying the expression gives:
[H+] = 1.0
3.2×10−14−(−11) = 3.125 ×10−4M
Step 4: Now, we can calculate the pH:
pH = −log3.125 ×10−4=−log 3.125 −log 10−4
Step 5: Further simplification gives us:
pH = −(−0.505) −(−4) = 0.505 + 4 = 4.505
Therefore, the pH of the solution is 4.505.
Question 34
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
21
where [H+] represents the concentration of hydrogen ions in the solution. Since
we are given the concentration of hydroxide ions ([OH−]), we can use the fact
that [H+][OH−]=1.0×10−14 at 25
°
C to find [H+].
Step 2: First, calculate the concentration of hydrogen ions using the concen-
tration of hydroxide ions:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
3.2×10−4
Step 3: Calculate the pH by taking the negative logarithm of the hydrogen
ion concentration:
pH = −log[H+] = −log 1.0×10−14
3.2×10−4
Question 35
Question
The pH of a 0.005 M hydrochloric acid (HCl) solution is calculated to be 2.30.
Calculate the pOH of the solution.
Solution
Step 1: Recall the relationship between pH and pOH:
pH + pOH = 14
Step 2: Given that the pH of the HCl solution is 2.30, we can find the
hydrogen ion concentration by taking the antilog of the negative of the pH
value.
[H+] = 10−pH = 10−2.30
Step 3: Calculate the hydrogen ion concentration:
[H+] = 10−2.30 = 0.00501 M
Step 4: The pOH can be calculated by taking the negative logarithm base
10 of the hydroxide ion concentration ([OH-]).
pOH = −log[OH-]
Step 5: Since the solution is a strong acid (HCl dissociates completely), the
hydroxide ion concentration is the same as the hydrogen ion concentration:
[OH-] = [H+]=0.00501 M
Step 6: Calculate the pOH of the solution:
pOH = −log(0.00501) = 2.30
Therefore, the pOH of the 0.005 M HCl solution is 2.30.
22
Question 2
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given concentration into the pH formula:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9
pH = −log(3.2) + log10−9
pH = −(log(3.2) −9)
pH ≈ −(−0.494 −9)
pH ≈ −(−9.494)
pH ≈9.494
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−9M is approximately 9.494.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−7
M.
Solution
Step 1: Recall the relationship between hydroxide ion concentration and pOH:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula
to find the pOH:
pOH =−log1.5×10−7
2
Step 3: Calculate the pOH:
pOH =−log1.5×10−7= 6.82
Step 4: Recall that pH and pOH are related by:
pH +pOH = 14
Step 5: Calculate the pH using the pOH value obtained:
pH = 14 −pOH = 14 −6.82 = 7.18
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−7M is 7.18.
Question 4
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−5M.
Solution
Step 1: Calculate the pOH of the solution using the formula: pOH =−log[OH−].
Given: [OH−]=2.5×10−5M
Calculate: pOH =−log2.5×10−5
Step 2: Calculate the pH of the solution using the relationship: pH +pOH =
14.
Given: pOH =−log2.5×10−5
Calculate: pH = 14 −pOH
Question 5
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−3
M.
3
Solution
Step 1: Recall the definition of pH:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3
pH = −log2.5×10−3
pH ≈ −(−2.60)
pH ≈2.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−3M is 2.60.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, we need to convert
the hydronium ion concentration to pH.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log3.5×10−4
pH = −log(3.5) + log10−4
pH = −(log(3.5) + 4)
pH ≈ −(0.544 068 044 4 + 4)
pH ≈ −4.5440680444
Step 4: Round the pH value to two decimal places:
pH ≈ −4.54
Therefore, the pH of the solution with a hydronium ion concentration of
3.5×10−4M is approximately 4.54.
4
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−4
M.
Solution
Step 1: The pH of a solution is defined as −log[H+], where [H+] is the hydrogen
ion concentration. Given [H+] = 2.5×10−4M, we can calculate the pH as
follows:
pH = −log2.5×10−4
Step 2: Substitute the value of [H+] into the formula to find the pH:
pH = −log2.5×10−4=−log(2.5) + log10−4
Step 3: Simplify the expression by using the properties of logarithms:
pH = −(0.3979) −4
Step 4: Calculate the final value of pH:
pH = −4.3979
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−4M is 4.3979.
Question 8
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as pH = -log[H+], where [H+] represents the
concentration of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = -log(3.2 ×10−5).
Step 3: Calculate the pH using a calculator: pH = -log(3.2 ×10−5) =
-(-4.49485) 4.49.
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately 4.49.
5
Question 9
Question
A 0.025 M solution of hydrochloric acid (HCl) has a pH of 1.75. Calculate the
pOH of the solution.
Solution
Step 1: Use the formula pH =−log[H+] to determine the concentration of
hydrogen ions:
pH = −log[H+]
1.75 = −log[H+]
[H+] = 10−1.75
Step 2: Calculate the concentration of hydroxide ions using the equation
Kw= [H+][OH−]:
Kw= [H+][OH−]
1.0×10−14 = (10−1.75)([OH−])
[OH−] = 1.0×10−14
10−1.75
Step 3: Find the pOH of the solution using the relationship pOH =−log[OH−]:
pOH =−log[OH−]
pOH =−log 1.0×10−14
10−1.75
Step 4: Simplify the expression and calculate the final value of pOH.
Question 10
Question
Calculate the pH of a solution with a pOH of 2.8.
Solution
Step 1: Recall the relationship between pH and pOH:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation above to find the
pH:
pH + 2.8 = 14
Step 3: Solve for pH:
pH = 14 −2.8 = 11.2
Therefore, the pH of the solution is 11.2.
6
Question 11
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that the pH is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.5×10−5
Step 3: Use the properties of logarithms to simplify:
pH = −log(3.5) −log10−5
pH = −log(3.5) + 5
Step 4: Use a calculator to find the value of −log(3.5):
pH ≈ − log(3.5) + 5 ≈ −0.5441 + 5
Step 5: Calculate the final pH value:
pH ≈4.456
Therefore, the pH of the solution is approximately 4.456.
Question 12
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+],pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH using the formula:
pH = −log2.5×10−9
7
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5)−log10−9=−log(2.5)−(−9) = −log(2.5)+9
Step 4: Use a calculator to find the pH:
pH ≈9.60
Step 5: Since we know that [H+]×[OH−] = 1.0×10−14 M2at 25
°
C, we can
find the pOH using the relationship:
pOH = −log[OH−]=−log 1.0×10−14
2.5×10−9
Step 6: Calculate the pOH:
pOH = −log 1.0×10−14
2.5×10−9=−log4.0×105
Step 7: Use a calculator to find the pOH:
pOH ≈5.40
Therefore, the pH of the solution is approximately 9.60 and the pOH is
approximately 5.40.
Question 13
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we can calculate
the pH using the given concentration of H3O+.
pH = −log3.2×10−5
Step 2: Substitute the given concentration into the equation and solve for
pH.
pH = −log3.2×10−5=−(log 3.2 + log 10−5) = −(log 3.2−5)
Step 3: Use the property of logarithms (log ab = log a+ log b) to simplify
the expression further.
pH = −(0.5052 −5)
Step 4: Calculate the final pH value.
pH ≈4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
8
Question 14
Question
Calculate the pH of a solution that has a hydronium ion concentration of 3.5×
10−4M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. We are given that the hydro-
nium ion concentration is 3.5×10−4M. Therefore, we can calculate the pH as
follows:
pH = −log3.5×10−4
Step 2: Use the property of logarithms that log(ab) = log(a) + log(b) to
simplify the calculation:
pH = −log(3.5) −log10−4
Step 3: Simplify further by using the property that log(10n) = nfor any
real number n:
pH = −log(3.5) −(−4)
Step 4: Calculate the log of 3.5 using a calculator:
pH = −0.5441 −(−4)
Step 5: Simplify the expression by subtracting the negative values:
pH = 4 + 0.5441
Step 6: Therefore, the pH of a solution with hydronium ion concentration
of 3.5×10−4M is approximately 4.5441 .
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−9
9
Step 3: Calculate the pH:
pH = −log2.5×10−9
pH = −(log 2.5 + log 10−9)
pH = −(0.3979 + 9)
pH = −9.3979
pH ≈9.40
Therefore, the pH of the solution is approximately 9.40.
Question 16
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall the definition of pH: The pH of a solution is defined as the
negative base 10 logarithm of the hydrogen ion concentration:
pH = −log[H+]
Step 2: Given the hydrogen ion concentration is 2.5×10−8M, we can
substitute this value into the pH formula:
pH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) + log10−8=−(log(2.5) −8)
Step 4: Using the properties of logarithms, we can simplify the expression
further:
pH = −(0.3979 −8) = −7.6021 ≈ −7.6
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.6.
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
10
Solution
Step 1: Use the relationship between pOH and OH−concentration:
pOH = −log[OH−]
Step 2: Calculate the pOH of the solution:
pOH = −log2.5×10−3=−log(2.5)+log10−3=−log(2.5)−3=0.398−3 = −2.602
Step 3: Use the relationship between pH and pOH:
pH + pOH = 14
Step 4: Calculate the pH of the solution:
pH = 14 −pOH = 14 −(−2.602) = 16.602
Therefore, the pH of the solution is 16.602.
Question 18
Question
A solution is prepared by mixing 50.0 mL of 0.20 M hydrochloric acid (HCl)
with 75.0 mL of 0.15 M sodium hydroxide (NaOH). Calculate the pH of the
resulting solution. Given Kw= 1.0×10−14 at 25◦C.
Solution
Step 1: Write the balanced chemical equation for the neutralization reaction
between HCl and NaOH:
HCl + NaOH →NaCl + H2O
Step 2: Determine the limiting reactant to find the moles of each reactant
that reacts. In this case, HCl and NaOH react in a 1:1 molar ratio, so the
limiting reactant is the one that is initially present in lower amount.
Calculate the moles of HCl:
Moles of HCl = Volume of HCl(L)×Molarity of HCl(mol/L)
Moles of HCl = 0.050 L ×0.20 mol/L = 0.010 mol
Calculate the moles of NaOH:
Moles of NaOH = Volume of NaOH(L)×Molarity of NaOH(mol/L)
Moles of NaOH = 0.075 L ×0.15 mol/L = 0.01125 mol
11
Since HCl is the limiting reactant, 0.010 mol of HCl reacts.
Step 3: Calculate the concentration of H+ions in the resulting solution.
Since 0.010 mol of HCl reacts, it produces 0.010 mol of H+ions. Calculate the
total volume of the solution:
Vtotal =VHCl +VNaOH = 50.0 mL + 75.0 mL = 125.0 mL = 0.125 L
Calculate the concentration of H+ions:
[H+] = moles of H+
volume of solution =0.010 mol
0.125 L = 0.080 M
Step 4: Calculate the pH of the resulting solution using the equation pH =
−log[H+]:
pH = −log(0.080) = −(−1.096) = 1.096
Therefore, the pH of the resulting solution is 1.096.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−9
M.
Solution
Step 1: Recall that the pH is calculated using the formula pH =−log[H+],
where [H+] is the hydrogen ion concentration.
Given [H+] = 3.5×10−9M, we can calculate the pH as follows:
Step 2: Substitute the given hydrogen ion concentration into the formula for
pH:
pH =−log3.5×10−9
Step 3: Calculate the pH using the calculator:
pH =−log3.5×10−9
pH ≈ − log(3.5) −log10−9
pH ≈ −0.5441 −(−9)
pH ≈8.456
Therefore, the pH of the solution with a hydrogen ion concentration of 3.5×
10−9M is approximately 8.456.
12
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.6×10−5
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.6×10−5
Step 3: Calculate the pH:
pH = −log3.6×10−5=−log(3.6) + log10−5=−0.5563 −(−5) = 4.4437
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.6×10−5M is approximately 4.44.
Question 21
Question
Calculate the pH of a solution that has a pOH of 2.75.
Solution
Step 1: Recall that the pH and pOH of a solution are related by the equation:
pH + pOH = 14
Step 2: Given that the pOH of the solution is 2.75, we can find the pH by
subtracting the pOH from 14:
pH = 14 −2.75
Step 3: Perform the subtraction to find the pH:
pH = 11.25
Step 4: Therefore, the pH of the solution is 11.25.
13
Question 22
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the definition of pH. The pH of a solution is defined as the
negative logarithm of the hydronium ion concentration. Mathematically, pH =
−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula.
Given [H3O+]=3.2×10−5M, we can plug this value into the formula: pH =
−log3.2×10−5.
Step 3: Calculate the pH. Using a calculator, we find: pH =−log3.2×10−5≈
−log(3.2) −log10−5≈ −0.5052 −(−5) ≈4.4948.
Step 4: Write the final answer. Therefore, the pH of the solution with a
hydronium ion concentration of 3.2×10−5M is approximately 4.49.
Question 23
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl). The
dissociation constant of HCl is 1.3×10−4. (Hint: pH =−log[H+])
Solution
Step 1: Write the dissociation of hydrochloric acid:
HCl →H++ Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely.
So the concentration of H+is equal to the initial concentration of HCl, which
is 0.025 M.
Step 3: Calculate the pH using the formula pH =−log[H+]:
pH =−log(0.025) = −log2.5×10−2
Step 4: Using the property of logarithms log(ab) = log(a) + log(b), we can
rewrite the expression as:
pH =−log(2.5) −log10−2
Step 5: Recall that −log(2.5) ≈ −0.3979 and −log10−2= 2. Therefore:
pH ≈ −0.3979 −2
14
Step 6: Add the two values to find the pH:
pH ≈ −2.3979
Step 7: Thus, the pH of a 0.025 M hydrochloric acid solution is approxi-
mately 2.40.
Question 24
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−6
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm of the hydrogen
ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.5×10−6
Step 3: Use the property of logarithms (log(xy) = log(x)+log(y)) to simplify
the expression:
pH = −[log(3.5) + log10−6]
Step 4: Recall that log10−6=−6:
pH = −[log(3.5) −6]
Step 5: Use a calculator to find the value of log(3.5), then subtract 6 and
change the sign to get the final pH value:
pH ≈ −[0.5441 −6] = −[−5.4559] = 5.4559
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.5×10−6M is approximately 5.46.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
15
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+]×[OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to calculate the hydrogen
ion concentration.
[OH−]=1.5×10−10 M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−10 = 6.67 ×10−5M
Step 3: Calculate the pH of the solution.
pH = −log[H+]=−log6.67 ×10−5=−(−4.18) = 4.18
Therefore, the pH of the solution is 4.18.
Question 26
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 3.6×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
where [H+] is the hydrogen ion concentration and [OH−] is the hydroxide ion
concentration. In a neutral solution, [H+] = [OH−]=1.0×10−7M.
Step 2: Given that the hydrogen ion concentration is 3.6×10−9M, we can
calculate pH as follows:
pH = −log3.6×10−9
Step 3: Calculate the pH:
pH = −log3.6×10−9=−log(3.6) −log10−9
Step 4: Simplify the expression:
pH ≈ − log(3.6) + 9 = −0.5563 + 9
16
Step 5: Calculate the pH:
pH ≈8.4437
Step 6: Using the relationship between pH and pOH:
pH + pOH = 14
Step 7: Calculate the pOH:
pOH = 14 −pH
Step 8: Substituting the calculated pH value:
pOH = 14 −8.4437
Step 9: Calculate the pOH:
pOH ≈5.5563
Therefore, the pH of the solution is approximately 8.4437 and the pOH is
approximately 5.5563.
Question 27
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×
10−10 M.
Solution
Step 1: Recall that the hydroxide ion concentration (OH−) is related to the pH
by the formula: pOH =−log[OH−]. We also know that pH +pOH = 14 for
any aqueous solution at 25
°
C.
Step 2: Given that [OH−]=1.5×10−10 M, we can calculate the pOH:
pOH = −log1.5×10−10=−log 1.5−log 10−10 =−(log 1.5+10 log 10) ≈ −(log 1.5+10) ≈ −(0.176+10) ≈ −10.176 ≈10.176
Step 3: Now, we can find the pH using the relationship pH +pOH = 14:
pH = 14 −pOH = 14 −10.176 = 3.824
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−10 M is approximately 3.824.
17
Question 28
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, to find the pH of the
solution, we first need to determine the hydrogen ion concentration.
Given: [H+]=3.5×10−5M
Step 2: Substitute the given hydrogen ion concentration into the pH formula
to find the pH.
pH = −log3.5×10−5
Step 3: Calculate the pH using a calculator.
pH = −log3.5×10−5
pH = −log(3.5) + log10−5
pH = −log(3.5) −5
pH ≈ −(−0.45593) −5
pH ≈0.45593 −5
pH ≈4.54407
Therefore, the pH of the solution with a hydrogen ion concentration of 3.5×
10−5M is approximately 4.54.
Question 29
Question
Calculate the pH of a solution with a hydrogen ion concentration of 1.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration in moles per liter.
Step 2: Given that the hydrogen ion concentration is 1.5×10−4M, we can
calculate the pH using the formula:
pH = −log1.5×10−4
18
Step 3: Substitute the given hydrogen ion concentration value into the for-
mula:
pH = −log1.5×10−4
Step 4: Use a calculator to find the logarithm of 1.5×10−4:
pH = −log1.5×10−4≈ − log(0.00015) ≈ −(−3.82391) ≈3.82391
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 1.5×10−4M is approximately 3.82.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Recall the relationship between pH, pOH, and the ion concentrations
in a solution:
pH +pOH = 14
Step 2: Calculate the pOH of the solution using the given hydroxide ion
concentration:
pOH = −log[OH−] = −log1.5×10−4
Step 3: Calculate the pOH value:
pOH = −log1.5×10−4=−log(1.5) + log10−4= 0.1761 + 4 = 4.1761
Step 4: Use the relationship between pH, pOH to find the pH of the solution:
pH = 14 −pOH = 14 −4.1761 = 9.8239
Therefore, the pH of the solution is approximately 9.82.
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we can calculate
the pH using the concentration given. Step 2: Substitute the given hydronium
ion concentration into the formula for pH. Step 3: Calculate the pH. Step 4:
Round the answer to the appropriate number of significant figures.
19
Step 1:
The pH of a solution can be calculated using the formula −log[H3O+].
Step 2:
Given that the hydronium ion concentration is 3.2×10−6M, we have [H3O+] =
3.2×10−6M.
Step 3:
Substitute the hydronium ion concentration into the formula:
pH = −log3.2×10−6
Step 4:
Calculating the pH:
pH = −log3.2×10−6=−log(3.2) + log10−6=−(0.5051) −6 = −6.5051
Therefore, the pH of the solution is 6.51.
Question 32
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−8
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. We are given [H+] = 3.2×10−8
M.
Step 2: Substitute [H+]=3.2×10−8into the pH formula:
pH = −log3.2×10−8
Step 3: Calculate log3.2×10−8:
log3.2×10−8≈ −7.49485
Step 4: Calculate the negative of log3.2×10−8to find the pH:
pH ≈7.49485
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−8M is approximately 7.49.
20
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−11
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Given that the hydroxide ion concentration is 3.2×10−11 M, we
can calculate the hydrogen ion concentration using the fact that in water,
[H+][OH−]=1.0×10−14:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
3.2×10−11
Step 3: Simplifying the expression gives:
[H+] = 1.0
3.2×10−14−(−11) = 3.125 ×10−4M
Step 4: Now, we can calculate the pH:
pH = −log3.125 ×10−4=−log 3.125 −log 10−4
Step 5: Further simplification gives us:
pH = −(−0.505) −(−4) = 0.505 + 4 = 4.505
Therefore, the pH of the solution is 4.505.
Question 34
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
21
where [H+] represents the concentration of hydrogen ions in the solution. Since
we are given the concentration of hydroxide ions ([OH−]), we can use the fact
that [H+][OH−]=1.0×10−14 at 25
°
C to find [H+].
Step 2: First, calculate the concentration of hydrogen ions using the concen-
tration of hydroxide ions:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
3.2×10−4
Step 3: Calculate the pH by taking the negative logarithm of the hydrogen
ion concentration:
pH = −log[H+] = −log 1.0×10−14
3.2×10−4
Question 35
Question
The pH of a 0.005 M hydrochloric acid (HCl) solution is calculated to be 2.30.
Calculate the pOH of the solution.
Solution
Step 1: Recall the relationship between pH and pOH:
pH + pOH = 14
Step 2: Given that the pH of the HCl solution is 2.30, we can find the
hydrogen ion concentration by taking the antilog of the negative of the pH
value.
[H+] = 10−pH = 10−2.30
Step 3: Calculate the hydrogen ion concentration:
[H+] = 10−2.30 = 0.00501 M
Step 4: The pOH can be calculated by taking the negative logarithm base
10 of the hydroxide ion concentration ([OH-]).
pOH = −log[OH-]
Step 5: Since the solution is a strong acid (HCl dissociates completely), the
hydroxide ion concentration is the same as the hydrogen ion concentration:
[OH-] = [H+]=0.00501 M
Step 6: Calculate the pOH of the solution:
pOH = −log(0.00501) = 2.30
Therefore, the pOH of the 0.005 M HCl solution is 2.30.
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