CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 5
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.5×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that [H3O+]=3.5×
10−6M, we can plug this value into the formula to find the pH.
pH = −log3.5×10−6
Step 2: Use the properties of logarithms to simplify the calculation. Re-
member that log(ab) = log(a) + log(b).
pH = −log(3.5) −log10−6
Step 3: Recall that log10−6=−6.
pH = −log(3.5) + 6
Step 4: Use a calculator to find the value of log(3.5). Then subtract this
value from 6 to obtain the final pH value.
pH ≈5.46
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 3.5×10−6M is approximately 5.46.
Question 2
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−6
M.
Solution
Step 1: Write the expression for the ion product of water. Since the solution
contains hydroxide ions, we can assume it is a basic solution. The ion product
of water at 25
°
C is Kw= 1.0×10−14.
Kw= [H+][OH−]
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration. Given that the hydroxide ion concentration is 2.5×10−6M, we can
find the hydrogen ion concentration using the ion product of water.
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
2.5×10−6
Step 3: Calculate the hydrogen ion concentration.
[H+]=4.0×10−9M
Step 4: Use the hydrogen ion concentration to find the pH. The pH is defined
as the negative logarithm of the hydrogen ion concentration.
pH =−log[H+]
pH =−log4.0×10−9
pH =−log(4.0) −log10−9
pH =−log(4.0) −(−9)
pH =−0.6021 + 9
pH = 8.398
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−6M is 8.398.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.0×10−3
M.
2
Solution
Step 1: Use the formula for calculating the pOH of a solution:
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH = −log5.0×10−3
Step 3: Calculate the pOH:
pOH = −log5.0×10−3
pOH = −(−2.3)
pOH = 2.3
Step 4: Use the relation between pH and pOH:
pH + pOH = 14
Step 5: Calculate the pH:
pH + 2.3 = 14
pH = 14 −2.3
pH = 11.7
Therefore, the pH of a solution with a hydroxide ion concentration of 5.0×
10−3M is 11.7.
Question 4
Question
Calculate the pH and pOH of a solution that has a hydronium ion concentration
of 1.5×10−9M.
Solution
Step 1: Recall that the pH is defined as −log[H3O+] and the pOH is defined as
−log[OH−].
Step 2: Start by finding the pH.
pH = −log[H3O+] = −log1.5×10−9
Step 3: Calculate the pH.
pH = −log1.5×10−9=−log(1.5) −log10−9
3
Step 4: Simplify the logarithms.
pH ≈ −0.176 −(−9) = 8.824
Step 5: Now, find the pOH using the relationship pH + pOH = 14.
pOH = 14 −8.824
Step 6: Calculate the pOH.
pOH = 5.176
Step 7: Therefore, the pH of the solution is 8.824 and the pOH is 5.176.
Question 5
Question
Calculate the pH of a solution that has a pOH of 2.5.
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 2.5, we can calculate the pH
as follows:
pH = 14 −pOH = 14 −2.5 = 11.5
Step 3: Therefore, the pH of the solution is 11.5 .
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
The pH of a solution is defined as −log[H3O+]. Thus, we can calculate the pH
using the given hydronium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.2×10−5
4
Step 3: Solve for pH:
pH = −log3.2×10−5=−log(3.2) + log10−5=−0.5052 + 5 = 4.4948
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.49.
Question 7
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log3.2×10−9
Step 2: Solve for pOH:
pOH =−log3.2×10−9=−(−8.495) = 8.495
Step 3: Use the relationship between pH and pOH:
pH +pOH = 14
Step 4: Solve for pH:
pH = 14 −pOH = 14 −8.495 = 5.505
Therefore, the pH of the solution is 5.505.
Question 8
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
5
Solution
Step 1: Recall the relationship between pH, hydrogen ion concentration, and
pOH:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 3.2×10−5M, we can
calculate the pH:
pH = −log3.2×10−5
Step 3: Calculate the pH:
pH = −log3.2×10−5=−(−4.49485) = 4.49485
Therefore, the pH of the solution is 4.49.
Step 4: Now, find the pOH using the fact that in a neutral solution, the
product of hydrogen ion concentration and hydroxide ion concentration is 1.0×
10−14 at 25
°
C:
[H+]×[OH−]=1.0×10−14
Step 5: Since the solution is acidic, we need to consider the hydroxide ion
concentration from the water auto-ionization, [OH−] = 1.0×10−14
3.2×10−5
pOH = −log[OH−]=−log 1.0×10−14
3.2×10−5
Step 6: Calculate the pOH:
pOH = −log 1.0×10−14
3.2×10−5=−(−8.59485) = 8.59485
Therefore, the pOH of the solution is 8.59.
Question 9
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 2.5×10−5M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 2.5×10−5M, we can
calculate the pH:
pH = −log2.5×10−5
6
Step 3: Calculating the pH:
pH = −log2.5×10−5=−log(2.5) + log10−5
Step 4: Using the properties of logarithms (log10(x) = yis equivalent to
10y=x), we get:
pH = −(log(2.5) −5)
Step 5: Calculating the pH:
pH ≈ −(0.3979 −5) ≈4.60
Step 6: Therefore the pH of the solution is 4.60.
Step 7: Since pH + pOH = 14 for a neutral solution, we can calculate the
pOH:
pOH = 14 −pH = 14 −4.60
Step 8: Calculating the pOH:
pOH = 14 −4.60 = 9.40
Step 9: Therefore the pOH of the solution is 9.40.
Question 10
Question
A solution is prepared by dissolving 0.050 mol of hydrochloric acid (HCl) in
enough water to make 0.500 L of solution. Calculate the pH of the resulting
solution.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid in water:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Calculate the concentration of HCl in the solution:
Molarity = moles of solute
volume of solution in liters =0.050 mol
0.500 L = 0.100 M
Step 3: Since HCl is a strong acid, it dissociates completely in water. There-
fore, the concentration of H+ions in solution is equal to the concentration of
HCl:
[H+]=0.100 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
7
Step 5: Substitute the concentration of H+ions into the formula to find the
pH:
pH = −log(0.100) = −(−1) = 1
Therefore, the pH of the resulting solution is 1.
Question 11
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Write the expression for the autoionization of water.
H2O⇌H++ OH−
Step 2: Write the equilibrium constant expression for the autoionization of
water.
Kw= [H+][OH−]
Step 3: Since the solution is basic with a known hydroxide ion concentration,
we can rearrange the equilibrium constant expression to solve for the hydrogen
ion concentration.
[H+] = Kw
[OH−]
Step 4: Substitute the known values into the equation. Given that Kw=
1.0×10−14 at 25
°
C,
[H+] = 1.0×10−14
3.2×10−4
[H+]=3.125 ×10−11 M
Step 5: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+] = −log3.125 ×10−11
pH = −log(3.125) + log10−11
pH = −log(3.125) −11
pH = −0.496 + 11
pH = 10.504
Therefore, the pH of the solution is 10.504.
8
Question 12
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the pH of a solution is given by pH =−log[H3O+] where
[H3O+] is the concentration of hydronium ions in the solution. Similarly,
the pOH of a solution is given by pOH =−log[OH−] where [OH−] is the
concentration of hydroxide ions in the solution. We can use the relationship
pH +pOH = 14 for neutral solutions.
Step 2: Calculate the pH of the solution using the formula pH =−log[3.2×
10−5]. pH =−log[3.2×10−5]pH =−(log 3.2+log 10−5)pH =−(0.5052+(−5))
pH = 5 −0.5052 pH = 4.4948
Step 3: Calculate the pOH of the solution using the relationship pOH =
14 −pH.pOH = 14 −4.4948 pOH = 9.5052
Therefore, the pH of the solution is 4.4948 and the pOH of the solution is
9.5052.
Question 13
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Since pOH + pH = 14 in aqueous solutions at 25
°
C, we can find the
pOH using the hydroxide ion concentration:
pOH = −log[OH−]
pOH = −log2.5×10−4
pOH = −(−3.60)
pOH = 3.60
Step 3: Now, using the relationship pOH + pH = 14, we can find the pH:
pH = 14 −3.60
9
pH = 10.40
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is 10.40.
Question 14
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH using the formula −log2.5×10−9.
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9= 9 −log(2.5)
Step 4: Using a calculator or approximations, we find:
pH ≈9−0.3979 ≈8.6021
Step 5: Now, we can calculate the pOH using the formula −log10−14/2.5×10−9.
Step 6: Calculate the pOH:
pOH = −log 10−14
2.5×10−9=−log 4×104=−log(4) −log104
Step 7: Continuing the calculation, we have:
pOH = −log(4) −4=0.6021
Step 8: Therefore, the pH of the solution is approximately 8.6021 and the
pOH is 0.6021.
Question 15
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
10
Solution
Step 1: Recall that pH is defined as −log[H+]. In this case, we are given
the hydronium ion concentration as 2.5×10−4M. Therefore, the pH can be
calculated as:
pH = −log2.5×10−4
Step 2: Substitute the given value into the equation and solve for pH:
pH = −log2.5×10−4=−log(2.5) −log10−4
Step 3: Since log(10n) = n, we can simplify the expression further:
pH = −log(2.5) −log10−4=−log(2.5) −(−4)
Step 4: Calculating the logarithm and subtracting the values gives us the
pH of the solution:
pH = −(0.3979) + 4 = 3.6021
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−4M is pH = 3.60.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the chemical equation for the dissociation of water.
H2O⇌H++ OH−
Step 2: Write the expression for the ion product of water (Kw).
Kw= [H+][OH−]
Given that Kw= 1.0×10−14 at 25
°
C.
Step 3: Calculate the concentration of hydrogen ions ([H+]) from the hy-
droxide ion concentration provided.
[OH−]=1.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−4
Step 4: Calculate the pH of the solution using the concentration of hydrogen
ions.
pH =−log[H+]
11
Question 17
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.00×10−8
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+], where [H3O+]
is the concentration of hydronium ions in the solution.
Step 2: Given that [H3O+]=3.00 ×10−8M, we can plug this value into the
pH formula:
pH = −log3.00 ×10−8
Step 3: Calculate the pH using a calculator:
pH = −log3.00 ×10−8≈ − log(3) −log10−8≈ −0.4771 ≈7.52
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.00 ×10−8M is approximately 7.52.
Question 18
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+]. In this case, the hydronium
ion concentration is 3.2×10−5M. Therefore, we have:
pH = −log3.2×10−5
Step 2: Substitute the value into the formula and calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 3: Simplify the expression by using the logarithmic properties log(ab) =
log a+ log band log(an) = nlog a:
pH = −log(3.2) −log10−5=−(log(3.2) −5)
Step 4: Use a calculator to find the value of log(3.2):
log(3.2) ≈0.505
12
Step 5: Substitute the value back into the pH equation and calculate the
pH:
pH = −(0.505 −5) = −(4.495) ≈4.5
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.5.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.6×10−5
M.
Solution
Step 1: Recall the formula relating pH and hydrogen ion concentration:
pH = −log[H+]
given that [H+]=3.6×10−5M,
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log3.6×10−5
Step 3: Use the properties of logarithms to simplify:
Step 4: Using a calculator, compute the value of −log3.6×10−5to find
the pH of the solution.
Step 5: The pH of the solution is approximately 4.44.
Therefore, the pH of a solution with a hydrogen ion concentration of 3.6×
10−5M is 4.44.
Question 20
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. To find the concentration of
hydrogen ions, we can use the relationship [H+][OH−] = 1.0×10−14 for water
at 25
°
C.
13
Step 2: Calculate the concentration of hydrogen ions using the given hy-
droxide ion concentration:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
2.5×10−5= 4.0×10−10 M
Step 3: Calculate the pH using the concentration of hydrogen ions:
pH = −log4.0×10−10=−(log(4) + log10−10) = −(log(4) −10) ≈9.3979
Therefore, the pH of the solution is approximately 9.3979.
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 4.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+] where [H+] is the concentration
of hydronium ions in the solution.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log4.5×10−9
Step 3: Calculate the pH using a calculator:
pH ≈ − log4.5×10−9≈ −(−8.35) ≈8.35
Therefore, the pH of the solution is approximately 8.35.
Question 22
Question
Calculate the pH of a solution with a pOH of 2.60.
Solution
Step 1: Recall the relationship between pH, pOH, and the ion product of water.
pH +pOH = 14
Given that the pOH is 2.60, we can find the pH using the equation:
pH = 14 −pOH
14
Step 2: Calculate the pH using the formula
pH = 14 −2.60
pH = 11.40
Therefore, the pH of the solution is 11.40.
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 2.5×10−4M, we can substitute this value into the formula
to calculate the pH.
pH = −log2.5×10−4
Step 2: Use the properties of logarithms to simplify the expression.
pH = −log(2.5) + log10−4
Step 3: Recognize that log10−4=−4, and evaluate log(2.5) using a cal-
culator.
pH = −log(2.5) −4
Step 4: Calculate log(2.5) using a calculator.
pH ≈ −0.3979 −4
Step 5: Perform the subtraction to find the pH.
pH ≈ −4.3979
Step 6: Final answer - The pH of the solution with a hydronium ion concen-
tration of 2.5×10−4M is approximately 4.40.
Question 24
Question
Calculate the pH of a solution with a hydrogen ion concentration of 1.5×10−8
M.
15
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log1.5×10−8
Step 3: Calculate the pH by taking the negative logarithm of the hydrogen
ion concentration:
pH = −log1.5×10−8=−log(1.5) −log10−8
Step 4: Simplify the expression using logarithmic properties:
pH = −log(1.5) −(−8) ×log(10) = −log(1.5) + 8
Step 5: Use a calculator to find the numerical value of the pH:
pH ≈ −0.1761 + 8 ≈7.8239
Step 6: Therefore, the pH of the solution is approximately 7.82.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Use the relationship between Kw, [H+], and [OH−] to calculate the
concentration of hydronium ions [H+].
Kw= [H+][OH−]=1.0×10−14
⇒[H+] = Kw
[OH−]=1×10−14
2.5×10−4= 4.0×10−11 M
Step 2: Calculate the pH using the formula pH =−log[H+].
pH =−log4.0×10−11=−log(4.0)−log10−11=−(log(4.0)+(−11 log(10)))
=−(log(4.0)−11) ≈ −(log(3.981)−11) = −(0.599−11) = −(−10.401) = 10.401
Therefore, the pH of the solution is 10.401.
16
Question 26
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Determine the pOH of the solution using the hydroxide ion concentra-
tion.
Given: [OH−] = 1.5×10−9M
We use the relationship between pOH and [OH−]:
pOH =−log[OH−]
pOH =−log1.5×10−9
pOH ≈8.82
Step 2: Calculate the pH of the solution using the pOH value.
pH +pOH = 14
Therefore, pH = 14 −pOH
pH = 14 −8.82
pH ≈5.18
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−9M is approximately 5.18.
Question 27
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+]. To find the pH of the solution,
we first need to calculate the hydronium ion concentration given in the question.
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
directly use the formula for pH to find the value. Thus, the pH is determined
as follows:
pH = −log3.2×10−5
17
Step 3: Calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 4: Simplify the expression:
pH = −log(3.2) −(−5)
Step 5: Further simplify the expression:
pH = −0.5052 −(−5) = −0.5052 + 5
Step 6: Calculate the final answer:
pH = 4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
Question 28
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−11 M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 1.5×10−11 M, we can
directly calculate the pH using the formula pH =−log1.5×10−11.
pH = −log1.5×10−11
Step 3: Using a calculator, we find that pH is approximately 10.82.
Step 4: Since pH + pOH = 14, we can find pOH by subtracting the pH from
14.
pOH = 14 −10.82
Step 5: Calculating pOH, we get:
pOH ≈3.18
Step 6: Therefore, the pH of the solution is 10.82 and the pOH is 3.18.
Question 29
Question
Calculate the pH of a solution with a pOH of 3.2.
18
Solution
Step 1: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 3.2 = 14
Step 3: Solve for pH:
pH = 14 −3.2
Step 4: Calculate the pH:
pH = 10.8
Step 5: Therefore, the pH of the solution with a pOH of 3.2 is 10.8 .
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
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 find the hydrogen ion
concentration:
[OH−] = 2.5×10−5M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−5
Step 3: Calculate the hydrogen ion concentration:
[H+] = 4.0×10−10 M
Step 4: Calculate the pH using the formula: pH =−log [H+].
pH =−log 4.0×10−10
Step 5: Calculate the pH:
pH = 9.4
Therefore, the pH of the solution is 9.4.
19
Question 31
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log3.0×10−5
pOH ≈4.52
Step 2: Use the relationship between pH and pOH to find the pH:
pH +pOH = 14
pH + 4.52 = 14
pH = 14 −4.52
pH ≈9.48
Therefore, the pH of the solution is approximately 9.48.
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
Solution
Step 1: Calculate the pOH of the solution using the given hydroxide ion con-
centration.
pOH = −log[OH−]
pOH = −log1.5×10−10
pOH ≈9.82
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
pH + 9.82 = 14
pH = 14 −9.82
pH ≈4.18
Therefore, the pH of the solution is approximately 4.18.
20
Question 33
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall the formula to calculate pH:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula
and solve for pH:
pH = −log2.5×10−6
pH = −log(2.5) −log10−6
pH = −(log(2.5) + log10−6)
Step 3: Use the property of logarithms that log(a) + log(b) = log(ab) to
simplify the expression:
pH = −log2.5×10−6
pH = −log2.5×10−6
pH = −log2.5×10−6
Step 4: Calculate the pH using a calculator:
pH ≈ −(log2.5×10−6)
pH ≈ −(−5.60)
pH ≈5.60
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−6M is approximately 5.60.
Question 34
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
21
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
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
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9=−0.3979 −(−9) = 8.6
Therefore, the pH of the solution is 8.6.
Step 4: Since pH + pOH = 14, we can calculate the pOH:
pOH = 14 −pH = 14 −8.6=5.4
Therefore, the pOH of the solution is 5.4.
Question 35
Question
A solution is prepared by dissolving 0.00500 moles of hydrochloric acid (HCl) in
enough water to make 250.0 mL of solution. Calculate the pH of the resulting
solution.
Solution
Step 1: Calculate the concentration of HCl in the solution. Given: Number of
moles of HCl = 0.00500 mol Volume of solution = 250.0 mL = 0.2500 L
Concentration of HCl = 0.00500mol
0.2500L= 0.0200 M
Step 2: Determine the pH of the solution using the formula pH =−log[H+].
Since HCl is a strong acid, it dissociates completely in water to form H ions.
Thus, [H+] = concentration of HCl = 0.0200 M
pH =−log(0.0200) = −(−1.69897) = 1.69897
Therefore, the pH of the resulting solution is 1.70.
22
Question 2
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−6
M.
Solution
Step 1: Write the expression for the ion product of water. Since the solution
contains hydroxide ions, we can assume it is a basic solution. The ion product
of water at 25
°
C is Kw= 1.0×10−14.
Kw= [H+][OH−]
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration. Given that the hydroxide ion concentration is 2.5×10−6M, we can
find the hydrogen ion concentration using the ion product of water.
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
2.5×10−6
Step 3: Calculate the hydrogen ion concentration.
[H+]=4.0×10−9M
Step 4: Use the hydrogen ion concentration to find the pH. The pH is defined
as the negative logarithm of the hydrogen ion concentration.
pH =−log[H+]
pH =−log4.0×10−9
pH =−log(4.0) −log10−9
pH =−log(4.0) −(−9)
pH =−0.6021 + 9
pH = 8.398
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−6M is 8.398.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.0×10−3
M.
2
Solution
Step 1: Use the formula for calculating the pOH of a solution:
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH = −log5.0×10−3
Step 3: Calculate the pOH:
pOH = −log5.0×10−3
pOH = −(−2.3)
pOH = 2.3
Step 4: Use the relation between pH and pOH:
pH + pOH = 14
Step 5: Calculate the pH:
pH + 2.3 = 14
pH = 14 −2.3
pH = 11.7
Therefore, the pH of a solution with a hydroxide ion concentration of 5.0×
10−3M is 11.7.
Question 4
Question
Calculate the pH and pOH of a solution that has a hydronium ion concentration
of 1.5×10−9M.
Solution
Step 1: Recall that the pH is defined as −log[H3O+] and the pOH is defined as
−log[OH−].
Step 2: Start by finding the pH.
pH = −log[H3O+] = −log1.5×10−9
Step 3: Calculate the pH.
pH = −log1.5×10−9=−log(1.5) −log10−9
3
Step 4: Simplify the logarithms.
pH ≈ −0.176 −(−9) = 8.824
Step 5: Now, find the pOH using the relationship pH + pOH = 14.
pOH = 14 −8.824
Step 6: Calculate the pOH.
pOH = 5.176
Step 7: Therefore, the pH of the solution is 8.824 and the pOH is 5.176.
Question 5
Question
Calculate the pH of a solution that has a pOH of 2.5.
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 2.5, we can calculate the pH
as follows:
pH = 14 −pOH = 14 −2.5 = 11.5
Step 3: Therefore, the pH of the solution is 11.5 .
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
The pH of a solution is defined as −log[H3O+]. Thus, we can calculate the pH
using the given hydronium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.2×10−5
4
Step 3: Solve for pH:
pH = −log3.2×10−5=−log(3.2) + log10−5=−0.5052 + 5 = 4.4948
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.49.
Question 7
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log3.2×10−9
Step 2: Solve for pOH:
pOH =−log3.2×10−9=−(−8.495) = 8.495
Step 3: Use the relationship between pH and pOH:
pH +pOH = 14
Step 4: Solve for pH:
pH = 14 −pOH = 14 −8.495 = 5.505
Therefore, the pH of the solution is 5.505.
Question 8
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
5
Solution
Step 1: Recall the relationship between pH, hydrogen ion concentration, and
pOH:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 3.2×10−5M, we can
calculate the pH:
pH = −log3.2×10−5
Step 3: Calculate the pH:
pH = −log3.2×10−5=−(−4.49485) = 4.49485
Therefore, the pH of the solution is 4.49.
Step 4: Now, find the pOH using the fact that in a neutral solution, the
product of hydrogen ion concentration and hydroxide ion concentration is 1.0×
10−14 at 25
°
C:
[H+]×[OH−]=1.0×10−14
Step 5: Since the solution is acidic, we need to consider the hydroxide ion
concentration from the water auto-ionization, [OH−] = 1.0×10−14
3.2×10−5
pOH = −log[OH−]=−log 1.0×10−14
3.2×10−5
Step 6: Calculate the pOH:
pOH = −log 1.0×10−14
3.2×10−5=−(−8.59485) = 8.59485
Therefore, the pOH of the solution is 8.59.
Question 9
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 2.5×10−5M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 2.5×10−5M, we can
calculate the pH:
pH = −log2.5×10−5
6
Step 3: Calculating the pH:
pH = −log2.5×10−5=−log(2.5) + log10−5
Step 4: Using the properties of logarithms (log10(x) = yis equivalent to
10y=x), we get:
pH = −(log(2.5) −5)
Step 5: Calculating the pH:
pH ≈ −(0.3979 −5) ≈4.60
Step 6: Therefore the pH of the solution is 4.60.
Step 7: Since pH + pOH = 14 for a neutral solution, we can calculate the
pOH:
pOH = 14 −pH = 14 −4.60
Step 8: Calculating the pOH:
pOH = 14 −4.60 = 9.40
Step 9: Therefore the pOH of the solution is 9.40.
Question 10
Question
A solution is prepared by dissolving 0.050 mol of hydrochloric acid (HCl) in
enough water to make 0.500 L of solution. Calculate the pH of the resulting
solution.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid in water:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Calculate the concentration of HCl in the solution:
Molarity = moles of solute
volume of solution in liters =0.050 mol
0.500 L = 0.100 M
Step 3: Since HCl is a strong acid, it dissociates completely in water. There-
fore, the concentration of H+ions in solution is equal to the concentration of
HCl:
[H+]=0.100 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
7
Step 5: Substitute the concentration of H+ions into the formula to find the
pH:
pH = −log(0.100) = −(−1) = 1
Therefore, the pH of the resulting solution is 1.
Question 11
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Write the expression for the autoionization of water.
H2O⇌H++ OH−
Step 2: Write the equilibrium constant expression for the autoionization of
water.
Kw= [H+][OH−]
Step 3: Since the solution is basic with a known hydroxide ion concentration,
we can rearrange the equilibrium constant expression to solve for the hydrogen
ion concentration.
[H+] = Kw
[OH−]
Step 4: Substitute the known values into the equation. Given that Kw=
1.0×10−14 at 25
°
C,
[H+] = 1.0×10−14
3.2×10−4
[H+]=3.125 ×10−11 M
Step 5: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+] = −log3.125 ×10−11
pH = −log(3.125) + log10−11
pH = −log(3.125) −11
pH = −0.496 + 11
pH = 10.504
Therefore, the pH of the solution is 10.504.
8
Question 12
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the pH of a solution is given by pH =−log[H3O+] where
[H3O+] is the concentration of hydronium ions in the solution. Similarly,
the pOH of a solution is given by pOH =−log[OH−] where [OH−] is the
concentration of hydroxide ions in the solution. We can use the relationship
pH +pOH = 14 for neutral solutions.
Step 2: Calculate the pH of the solution using the formula pH =−log[3.2×
10−5]. pH =−log[3.2×10−5]pH =−(log 3.2+log 10−5)pH =−(0.5052+(−5))
pH = 5 −0.5052 pH = 4.4948
Step 3: Calculate the pOH of the solution using the relationship pOH =
14 −pH.pOH = 14 −4.4948 pOH = 9.5052
Therefore, the pH of the solution is 4.4948 and the pOH of the solution is
9.5052.
Question 13
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Since pOH + pH = 14 in aqueous solutions at 25
°
C, we can find the
pOH using the hydroxide ion concentration:
pOH = −log[OH−]
pOH = −log2.5×10−4
pOH = −(−3.60)
pOH = 3.60
Step 3: Now, using the relationship pOH + pH = 14, we can find the pH:
pH = 14 −3.60
9
pH = 10.40
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is 10.40.
Question 14
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH using the formula −log2.5×10−9.
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9= 9 −log(2.5)
Step 4: Using a calculator or approximations, we find:
pH ≈9−0.3979 ≈8.6021
Step 5: Now, we can calculate the pOH using the formula −log10−14/2.5×10−9.
Step 6: Calculate the pOH:
pOH = −log 10−14
2.5×10−9=−log 4×104=−log(4) −log104
Step 7: Continuing the calculation, we have:
pOH = −log(4) −4=0.6021
Step 8: Therefore, the pH of the solution is approximately 8.6021 and the
pOH is 0.6021.
Question 15
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
10
Solution
Step 1: Recall that pH is defined as −log[H+]. In this case, we are given
the hydronium ion concentration as 2.5×10−4M. Therefore, the pH can be
calculated as:
pH = −log2.5×10−4
Step 2: Substitute the given value into the equation and solve for pH:
pH = −log2.5×10−4=−log(2.5) −log10−4
Step 3: Since log(10n) = n, we can simplify the expression further:
pH = −log(2.5) −log10−4=−log(2.5) −(−4)
Step 4: Calculating the logarithm and subtracting the values gives us the
pH of the solution:
pH = −(0.3979) + 4 = 3.6021
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−4M is pH = 3.60.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the chemical equation for the dissociation of water.
H2O⇌H++ OH−
Step 2: Write the expression for the ion product of water (Kw).
Kw= [H+][OH−]
Given that Kw= 1.0×10−14 at 25
°
C.
Step 3: Calculate the concentration of hydrogen ions ([H+]) from the hy-
droxide ion concentration provided.
[OH−]=1.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−4
Step 4: Calculate the pH of the solution using the concentration of hydrogen
ions.
pH =−log[H+]
11
Question 17
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.00×10−8
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+], where [H3O+]
is the concentration of hydronium ions in the solution.
Step 2: Given that [H3O+]=3.00 ×10−8M, we can plug this value into the
pH formula:
pH = −log3.00 ×10−8
Step 3: Calculate the pH using a calculator:
pH = −log3.00 ×10−8≈ − log(3) −log10−8≈ −0.4771 ≈7.52
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.00 ×10−8M is approximately 7.52.
Question 18
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+]. In this case, the hydronium
ion concentration is 3.2×10−5M. Therefore, we have:
pH = −log3.2×10−5
Step 2: Substitute the value into the formula and calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 3: Simplify the expression by using the logarithmic properties log(ab) =
log a+ log band log(an) = nlog a:
pH = −log(3.2) −log10−5=−(log(3.2) −5)
Step 4: Use a calculator to find the value of log(3.2):
log(3.2) ≈0.505
12
Step 5: Substitute the value back into the pH equation and calculate the
pH:
pH = −(0.505 −5) = −(4.495) ≈4.5
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.5.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.6×10−5
M.
Solution
Step 1: Recall the formula relating pH and hydrogen ion concentration:
pH = −log[H+]
given that [H+]=3.6×10−5M,
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log3.6×10−5
Step 3: Use the properties of logarithms to simplify:
Step 4: Using a calculator, compute the value of −log3.6×10−5to find
the pH of the solution.
Step 5: The pH of the solution is approximately 4.44.
Therefore, the pH of a solution with a hydrogen ion concentration of 3.6×
10−5M is 4.44.
Question 20
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. To find the concentration of
hydrogen ions, we can use the relationship [H+][OH−] = 1.0×10−14 for water
at 25
°
C.
13
Step 2: Calculate the concentration of hydrogen ions using the given hy-
droxide ion concentration:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
2.5×10−5= 4.0×10−10 M
Step 3: Calculate the pH using the concentration of hydrogen ions:
pH = −log4.0×10−10=−(log(4) + log10−10) = −(log(4) −10) ≈9.3979
Therefore, the pH of the solution is approximately 9.3979.
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 4.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+] where [H+] is the concentration
of hydronium ions in the solution.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log4.5×10−9
Step 3: Calculate the pH using a calculator:
pH ≈ − log4.5×10−9≈ −(−8.35) ≈8.35
Therefore, the pH of the solution is approximately 8.35.
Question 22
Question
Calculate the pH of a solution with a pOH of 2.60.
Solution
Step 1: Recall the relationship between pH, pOH, and the ion product of water.
pH +pOH = 14
Given that the pOH is 2.60, we can find the pH using the equation:
pH = 14 −pOH
14
Step 2: Calculate the pH using the formula
pH = 14 −2.60
pH = 11.40
Therefore, the pH of the solution is 11.40.
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 2.5×10−4M, we can substitute this value into the formula
to calculate the pH.
pH = −log2.5×10−4
Step 2: Use the properties of logarithms to simplify the expression.
pH = −log(2.5) + log10−4
Step 3: Recognize that log10−4=−4, and evaluate log(2.5) using a cal-
culator.
pH = −log(2.5) −4
Step 4: Calculate log(2.5) using a calculator.
pH ≈ −0.3979 −4
Step 5: Perform the subtraction to find the pH.
pH ≈ −4.3979
Step 6: Final answer - The pH of the solution with a hydronium ion concen-
tration of 2.5×10−4M is approximately 4.40.
Question 24
Question
Calculate the pH of a solution with a hydrogen ion concentration of 1.5×10−8
M.
15
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log1.5×10−8
Step 3: Calculate the pH by taking the negative logarithm of the hydrogen
ion concentration:
pH = −log1.5×10−8=−log(1.5) −log10−8
Step 4: Simplify the expression using logarithmic properties:
pH = −log(1.5) −(−8) ×log(10) = −log(1.5) + 8
Step 5: Use a calculator to find the numerical value of the pH:
pH ≈ −0.1761 + 8 ≈7.8239
Step 6: Therefore, the pH of the solution is approximately 7.82.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Use the relationship between Kw, [H+], and [OH−] to calculate the
concentration of hydronium ions [H+].
Kw= [H+][OH−]=1.0×10−14
⇒[H+] = Kw
[OH−]=1×10−14
2.5×10−4= 4.0×10−11 M
Step 2: Calculate the pH using the formula pH =−log[H+].
pH =−log4.0×10−11=−log(4.0)−log10−11=−(log(4.0)+(−11 log(10)))
=−(log(4.0)−11) ≈ −(log(3.981)−11) = −(0.599−11) = −(−10.401) = 10.401
Therefore, the pH of the solution is 10.401.
16
Question 26
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Determine the pOH of the solution using the hydroxide ion concentra-
tion.
Given: [OH−] = 1.5×10−9M
We use the relationship between pOH and [OH−]:
pOH =−log[OH−]
pOH =−log1.5×10−9
pOH ≈8.82
Step 2: Calculate the pH of the solution using the pOH value.
pH +pOH = 14
Therefore, pH = 14 −pOH
pH = 14 −8.82
pH ≈5.18
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−9M is approximately 5.18.
Question 27
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+]. To find the pH of the solution,
we first need to calculate the hydronium ion concentration given in the question.
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
directly use the formula for pH to find the value. Thus, the pH is determined
as follows:
pH = −log3.2×10−5
17
Step 3: Calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 4: Simplify the expression:
pH = −log(3.2) −(−5)
Step 5: Further simplify the expression:
pH = −0.5052 −(−5) = −0.5052 + 5
Step 6: Calculate the final answer:
pH = 4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
Question 28
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−11 M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 1.5×10−11 M, we can
directly calculate the pH using the formula pH =−log1.5×10−11.
pH = −log1.5×10−11
Step 3: Using a calculator, we find that pH is approximately 10.82.
Step 4: Since pH + pOH = 14, we can find pOH by subtracting the pH from
14.
pOH = 14 −10.82
Step 5: Calculating pOH, we get:
pOH ≈3.18
Step 6: Therefore, the pH of the solution is 10.82 and the pOH is 3.18.
Question 29
Question
Calculate the pH of a solution with a pOH of 3.2.
18
Solution
Step 1: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 3.2 = 14
Step 3: Solve for pH:
pH = 14 −3.2
Step 4: Calculate the pH:
pH = 10.8
Step 5: Therefore, the pH of the solution with a pOH of 3.2 is 10.8 .
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
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 find the hydrogen ion
concentration:
[OH−] = 2.5×10−5M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−5
Step 3: Calculate the hydrogen ion concentration:
[H+] = 4.0×10−10 M
Step 4: Calculate the pH using the formula: pH =−log [H+].
pH =−log 4.0×10−10
Step 5: Calculate the pH:
pH = 9.4
Therefore, the pH of the solution is 9.4.
19
Question 31
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log3.0×10−5
pOH ≈4.52
Step 2: Use the relationship between pH and pOH to find the pH:
pH +pOH = 14
pH + 4.52 = 14
pH = 14 −4.52
pH ≈9.48
Therefore, the pH of the solution is approximately 9.48.
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
Solution
Step 1: Calculate the pOH of the solution using the given hydroxide ion con-
centration.
pOH = −log[OH−]
pOH = −log1.5×10−10
pOH ≈9.82
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
pH + 9.82 = 14
pH = 14 −9.82
pH ≈4.18
Therefore, the pH of the solution is approximately 4.18.
20
Question 33
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall the formula to calculate pH:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula
and solve for pH:
pH = −log2.5×10−6
pH = −log(2.5) −log10−6
pH = −(log(2.5) + log10−6)
Step 3: Use the property of logarithms that log(a) + log(b) = log(ab) to
simplify the expression:
pH = −log2.5×10−6
pH = −log2.5×10−6
pH = −log2.5×10−6
Step 4: Calculate the pH using a calculator:
pH ≈ −(log2.5×10−6)
pH ≈ −(−5.60)
pH ≈5.60
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−6M is approximately 5.60.
Question 34
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
21
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
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
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9=−0.3979 −(−9) = 8.6
Therefore, the pH of the solution is 8.6.
Step 4: Since pH + pOH = 14, we can calculate the pOH:
pOH = 14 −pH = 14 −8.6=5.4
Therefore, the pOH of the solution is 5.4.
Question 35
Question
A solution is prepared by dissolving 0.00500 moles of hydrochloric acid (HCl) in
enough water to make 250.0 mL of solution. Calculate the pH of the resulting
solution.
Solution
Step 1: Calculate the concentration of HCl in the solution. Given: Number of
moles of HCl = 0.00500 mol Volume of solution = 250.0 mL = 0.2500 L
Concentration of HCl = 0.00500mol
0.2500L= 0.0200 M
Step 2: Determine the pH of the solution using the formula pH =−log[H+].
Since HCl is a strong acid, it dissociates completely in water to form H ions.
Thus, [H+] = concentration of HCl = 0.0200 M
pH =−log(0.0200) = −(−1.69897) = 1.69897
Therefore, the pH of the resulting solution is 1.70.
22
Question 2
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−6
M.
Solution
Step 1: Write the expression for the ion product of water. Since the solution
contains hydroxide ions, we can assume it is a basic solution. The ion product
of water at 25
°
C is Kw= 1.0×10−14.
Kw= [H+][OH−]
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration. Given that the hydroxide ion concentration is 2.5×10−6M, we can
find the hydrogen ion concentration using the ion product of water.
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
2.5×10−6
Step 3: Calculate the hydrogen ion concentration.
[H+]=4.0×10−9M
Step 4: Use the hydrogen ion concentration to find the pH. The pH is defined
as the negative logarithm of the hydrogen ion concentration.
pH =−log[H+]
pH =−log4.0×10−9
pH =−log(4.0) −log10−9
pH =−log(4.0) −(−9)
pH =−0.6021 + 9
pH = 8.398
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−6M is 8.398.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.0×10−3
M.
2
Solution
Step 1: Use the formula for calculating the pOH of a solution:
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH = −log5.0×10−3
Step 3: Calculate the pOH:
pOH = −log5.0×10−3
pOH = −(−2.3)
pOH = 2.3
Step 4: Use the relation between pH and pOH:
pH + pOH = 14
Step 5: Calculate the pH:
pH + 2.3 = 14
pH = 14 −2.3
pH = 11.7
Therefore, the pH of a solution with a hydroxide ion concentration of 5.0×
10−3M is 11.7.
Question 4
Question
Calculate the pH and pOH of a solution that has a hydronium ion concentration
of 1.5×10−9M.
Solution
Step 1: Recall that the pH is defined as −log[H3O+] and the pOH is defined as
−log[OH−].
Step 2: Start by finding the pH.
pH = −log[H3O+] = −log1.5×10−9
Step 3: Calculate the pH.
pH = −log1.5×10−9=−log(1.5) −log10−9
3
Step 4: Simplify the logarithms.
pH ≈ −0.176 −(−9) = 8.824
Step 5: Now, find the pOH using the relationship pH + pOH = 14.
pOH = 14 −8.824
Step 6: Calculate the pOH.
pOH = 5.176
Step 7: Therefore, the pH of the solution is 8.824 and the pOH is 5.176.
Question 5
Question
Calculate the pH of a solution that has a pOH of 2.5.
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 2.5, we can calculate the pH
as follows:
pH = 14 −pOH = 14 −2.5 = 11.5
Step 3: Therefore, the pH of the solution is 11.5 .
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
The pH of a solution is defined as −log[H3O+]. Thus, we can calculate the pH
using the given hydronium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.2×10−5
4
Step 3: Solve for pH:
pH = −log3.2×10−5=−log(3.2) + log10−5=−0.5052 + 5 = 4.4948
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.49.
Question 7
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log3.2×10−9
Step 2: Solve for pOH:
pOH =−log3.2×10−9=−(−8.495) = 8.495
Step 3: Use the relationship between pH and pOH:
pH +pOH = 14
Step 4: Solve for pH:
pH = 14 −pOH = 14 −8.495 = 5.505
Therefore, the pH of the solution is 5.505.
Question 8
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
5
Solution
Step 1: Recall the relationship between pH, hydrogen ion concentration, and
pOH:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 3.2×10−5M, we can
calculate the pH:
pH = −log3.2×10−5
Step 3: Calculate the pH:
pH = −log3.2×10−5=−(−4.49485) = 4.49485
Therefore, the pH of the solution is 4.49.
Step 4: Now, find the pOH using the fact that in a neutral solution, the
product of hydrogen ion concentration and hydroxide ion concentration is 1.0×
10−14 at 25
°
C:
[H+]×[OH−]=1.0×10−14
Step 5: Since the solution is acidic, we need to consider the hydroxide ion
concentration from the water auto-ionization, [OH−] = 1.0×10−14
3.2×10−5
pOH = −log[OH−]=−log 1.0×10−14
3.2×10−5
Step 6: Calculate the pOH:
pOH = −log 1.0×10−14
3.2×10−5=−(−8.59485) = 8.59485
Therefore, the pOH of the solution is 8.59.
Question 9
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 2.5×10−5M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 2.5×10−5M, we can
calculate the pH:
pH = −log2.5×10−5
6
Step 3: Calculating the pH:
pH = −log2.5×10−5=−log(2.5) + log10−5
Step 4: Using the properties of logarithms (log10(x) = yis equivalent to
10y=x), we get:
pH = −(log(2.5) −5)
Step 5: Calculating the pH:
pH ≈ −(0.3979 −5) ≈4.60
Step 6: Therefore the pH of the solution is 4.60.
Step 7: Since pH + pOH = 14 for a neutral solution, we can calculate the
pOH:
pOH = 14 −pH = 14 −4.60
Step 8: Calculating the pOH:
pOH = 14 −4.60 = 9.40
Step 9: Therefore the pOH of the solution is 9.40.
Question 10
Question
A solution is prepared by dissolving 0.050 mol of hydrochloric acid (HCl) in
enough water to make 0.500 L of solution. Calculate the pH of the resulting
solution.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid in water:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Calculate the concentration of HCl in the solution:
Molarity = moles of solute
volume of solution in liters =0.050 mol
0.500 L = 0.100 M
Step 3: Since HCl is a strong acid, it dissociates completely in water. There-
fore, the concentration of H+ions in solution is equal to the concentration of
HCl:
[H+]=0.100 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
7
Step 5: Substitute the concentration of H+ions into the formula to find the
pH:
pH = −log(0.100) = −(−1) = 1
Therefore, the pH of the resulting solution is 1.
Question 11
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Write the expression for the autoionization of water.
H2O⇌H++ OH−
Step 2: Write the equilibrium constant expression for the autoionization of
water.
Kw= [H+][OH−]
Step 3: Since the solution is basic with a known hydroxide ion concentration,
we can rearrange the equilibrium constant expression to solve for the hydrogen
ion concentration.
[H+] = Kw
[OH−]
Step 4: Substitute the known values into the equation. Given that Kw=
1.0×10−14 at 25
°
C,
[H+] = 1.0×10−14
3.2×10−4
[H+]=3.125 ×10−11 M
Step 5: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+] = −log3.125 ×10−11
pH = −log(3.125) + log10−11
pH = −log(3.125) −11
pH = −0.496 + 11
pH = 10.504
Therefore, the pH of the solution is 10.504.
8
Question 12
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the pH of a solution is given by pH =−log[H3O+] where
[H3O+] is the concentration of hydronium ions in the solution. Similarly,
the pOH of a solution is given by pOH =−log[OH−] where [OH−] is the
concentration of hydroxide ions in the solution. We can use the relationship
pH +pOH = 14 for neutral solutions.
Step 2: Calculate the pH of the solution using the formula pH =−log[3.2×
10−5]. pH =−log[3.2×10−5]pH =−(log 3.2+log 10−5)pH =−(0.5052+(−5))
pH = 5 −0.5052 pH = 4.4948
Step 3: Calculate the pOH of the solution using the relationship pOH =
14 −pH.pOH = 14 −4.4948 pOH = 9.5052
Therefore, the pH of the solution is 4.4948 and the pOH of the solution is
9.5052.
Question 13
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Since pOH + pH = 14 in aqueous solutions at 25
°
C, we can find the
pOH using the hydroxide ion concentration:
pOH = −log[OH−]
pOH = −log2.5×10−4
pOH = −(−3.60)
pOH = 3.60
Step 3: Now, using the relationship pOH + pH = 14, we can find the pH:
pH = 14 −3.60
9
pH = 10.40
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is 10.40.
Question 14
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH using the formula −log2.5×10−9.
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9= 9 −log(2.5)
Step 4: Using a calculator or approximations, we find:
pH ≈9−0.3979 ≈8.6021
Step 5: Now, we can calculate the pOH using the formula −log10−14/2.5×10−9.
Step 6: Calculate the pOH:
pOH = −log 10−14
2.5×10−9=−log 4×104=−log(4) −log104
Step 7: Continuing the calculation, we have:
pOH = −log(4) −4=0.6021
Step 8: Therefore, the pH of the solution is approximately 8.6021 and the
pOH is 0.6021.
Question 15
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
10
Solution
Step 1: Recall that pH is defined as −log[H+]. In this case, we are given
the hydronium ion concentration as 2.5×10−4M. Therefore, the pH can be
calculated as:
pH = −log2.5×10−4
Step 2: Substitute the given value into the equation and solve for pH:
pH = −log2.5×10−4=−log(2.5) −log10−4
Step 3: Since log(10n) = n, we can simplify the expression further:
pH = −log(2.5) −log10−4=−log(2.5) −(−4)
Step 4: Calculating the logarithm and subtracting the values gives us the
pH of the solution:
pH = −(0.3979) + 4 = 3.6021
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−4M is pH = 3.60.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the chemical equation for the dissociation of water.
H2O⇌H++ OH−
Step 2: Write the expression for the ion product of water (Kw).
Kw= [H+][OH−]
Given that Kw= 1.0×10−14 at 25
°
C.
Step 3: Calculate the concentration of hydrogen ions ([H+]) from the hy-
droxide ion concentration provided.
[OH−]=1.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−4
Step 4: Calculate the pH of the solution using the concentration of hydrogen
ions.
pH =−log[H+]
11
Question 17
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.00×10−8
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+], where [H3O+]
is the concentration of hydronium ions in the solution.
Step 2: Given that [H3O+]=3.00 ×10−8M, we can plug this value into the
pH formula:
pH = −log3.00 ×10−8
Step 3: Calculate the pH using a calculator:
pH = −log3.00 ×10−8≈ − log(3) −log10−8≈ −0.4771 ≈7.52
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.00 ×10−8M is approximately 7.52.
Question 18
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+]. In this case, the hydronium
ion concentration is 3.2×10−5M. Therefore, we have:
pH = −log3.2×10−5
Step 2: Substitute the value into the formula and calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 3: Simplify the expression by using the logarithmic properties log(ab) =
log a+ log band log(an) = nlog a:
pH = −log(3.2) −log10−5=−(log(3.2) −5)
Step 4: Use a calculator to find the value of log(3.2):
log(3.2) ≈0.505
12
Step 5: Substitute the value back into the pH equation and calculate the
pH:
pH = −(0.505 −5) = −(4.495) ≈4.5
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.5.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.6×10−5
M.
Solution
Step 1: Recall the formula relating pH and hydrogen ion concentration:
pH = −log[H+]
given that [H+]=3.6×10−5M,
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log3.6×10−5
Step 3: Use the properties of logarithms to simplify:
Step 4: Using a calculator, compute the value of −log3.6×10−5to find
the pH of the solution.
Step 5: The pH of the solution is approximately 4.44.
Therefore, the pH of a solution with a hydrogen ion concentration of 3.6×
10−5M is 4.44.
Question 20
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. To find the concentration of
hydrogen ions, we can use the relationship [H+][OH−] = 1.0×10−14 for water
at 25
°
C.
13
Step 2: Calculate the concentration of hydrogen ions using the given hy-
droxide ion concentration:
[H+] = 1.0×10−14
[OH−]=1.0×10−14
2.5×10−5= 4.0×10−10 M
Step 3: Calculate the pH using the concentration of hydrogen ions:
pH = −log4.0×10−10=−(log(4) + log10−10) = −(log(4) −10) ≈9.3979
Therefore, the pH of the solution is approximately 9.3979.
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 4.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+] where [H+] is the concentration
of hydronium ions in the solution.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log4.5×10−9
Step 3: Calculate the pH using a calculator:
pH ≈ − log4.5×10−9≈ −(−8.35) ≈8.35
Therefore, the pH of the solution is approximately 8.35.
Question 22
Question
Calculate the pH of a solution with a pOH of 2.60.
Solution
Step 1: Recall the relationship between pH, pOH, and the ion product of water.
pH +pOH = 14
Given that the pOH is 2.60, we can find the pH using the equation:
pH = 14 −pOH
14
Step 2: Calculate the pH using the formula
pH = 14 −2.60
pH = 11.40
Therefore, the pH of the solution is 11.40.
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 2.5×10−4M, we can substitute this value into the formula
to calculate the pH.
pH = −log2.5×10−4
Step 2: Use the properties of logarithms to simplify the expression.
pH = −log(2.5) + log10−4
Step 3: Recognize that log10−4=−4, and evaluate log(2.5) using a cal-
culator.
pH = −log(2.5) −4
Step 4: Calculate log(2.5) using a calculator.
pH ≈ −0.3979 −4
Step 5: Perform the subtraction to find the pH.
pH ≈ −4.3979
Step 6: Final answer - The pH of the solution with a hydronium ion concen-
tration of 2.5×10−4M is approximately 4.40.
Question 24
Question
Calculate the pH of a solution with a hydrogen ion concentration of 1.5×10−8
M.
15
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log1.5×10−8
Step 3: Calculate the pH by taking the negative logarithm of the hydrogen
ion concentration:
pH = −log1.5×10−8=−log(1.5) −log10−8
Step 4: Simplify the expression using logarithmic properties:
pH = −log(1.5) −(−8) ×log(10) = −log(1.5) + 8
Step 5: Use a calculator to find the numerical value of the pH:
pH ≈ −0.1761 + 8 ≈7.8239
Step 6: Therefore, the pH of the solution is approximately 7.82.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Use the relationship between Kw, [H+], and [OH−] to calculate the
concentration of hydronium ions [H+].
Kw= [H+][OH−]=1.0×10−14
⇒[H+] = Kw
[OH−]=1×10−14
2.5×10−4= 4.0×10−11 M
Step 2: Calculate the pH using the formula pH =−log[H+].
pH =−log4.0×10−11=−log(4.0)−log10−11=−(log(4.0)+(−11 log(10)))
=−(log(4.0)−11) ≈ −(log(3.981)−11) = −(0.599−11) = −(−10.401) = 10.401
Therefore, the pH of the solution is 10.401.
16
Question 26
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Determine the pOH of the solution using the hydroxide ion concentra-
tion.
Given: [OH−] = 1.5×10−9M
We use the relationship between pOH and [OH−]:
pOH =−log[OH−]
pOH =−log1.5×10−9
pOH ≈8.82
Step 2: Calculate the pH of the solution using the pOH value.
pH +pOH = 14
Therefore, pH = 14 −pOH
pH = 14 −8.82
pH ≈5.18
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−9M is approximately 5.18.
Question 27
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+]. To find the pH of the solution,
we first need to calculate the hydronium ion concentration given in the question.
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
directly use the formula for pH to find the value. Thus, the pH is determined
as follows:
pH = −log3.2×10−5
17
Step 3: Calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 4: Simplify the expression:
pH = −log(3.2) −(−5)
Step 5: Further simplify the expression:
pH = −0.5052 −(−5) = −0.5052 + 5
Step 6: Calculate the final answer:
pH = 4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
Question 28
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−11 M.
Solution
Step 1: Recall that pH is defined as −log[H+] and pOH is defined as −log[OH−].
Step 2: Given that the hydrogen ion concentration is 1.5×10−11 M, we can
directly calculate the pH using the formula pH =−log1.5×10−11.
pH = −log1.5×10−11
Step 3: Using a calculator, we find that pH is approximately 10.82.
Step 4: Since pH + pOH = 14, we can find pOH by subtracting the pH from
14.
pOH = 14 −10.82
Step 5: Calculating pOH, we get:
pOH ≈3.18
Step 6: Therefore, the pH of the solution is 10.82 and the pOH is 3.18.
Question 29
Question
Calculate the pH of a solution with a pOH of 3.2.
18
Solution
Step 1: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 3.2 = 14
Step 3: Solve for pH:
pH = 14 −3.2
Step 4: Calculate the pH:
pH = 10.8
Step 5: Therefore, the pH of the solution with a pOH of 3.2 is 10.8 .
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
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 find the hydrogen ion
concentration:
[OH−] = 2.5×10−5M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−5
Step 3: Calculate the hydrogen ion concentration:
[H+] = 4.0×10−10 M
Step 4: Calculate the pH using the formula: pH =−log [H+].
pH =−log 4.0×10−10
Step 5: Calculate the pH:
pH = 9.4
Therefore, the pH of the solution is 9.4.
19
Question 31
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log3.0×10−5
pOH ≈4.52
Step 2: Use the relationship between pH and pOH to find the pH:
pH +pOH = 14
pH + 4.52 = 14
pH = 14 −4.52
pH ≈9.48
Therefore, the pH of the solution is approximately 9.48.
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
Solution
Step 1: Calculate the pOH of the solution using the given hydroxide ion con-
centration.
pOH = −log[OH−]
pOH = −log1.5×10−10
pOH ≈9.82
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
pH + 9.82 = 14
pH = 14 −9.82
pH ≈4.18
Therefore, the pH of the solution is approximately 4.18.
20
Question 33
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall the formula to calculate pH:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula
and solve for pH:
pH = −log2.5×10−6
pH = −log(2.5) −log10−6
pH = −(log(2.5) + log10−6)
Step 3: Use the property of logarithms that log(a) + log(b) = log(ab) to
simplify the expression:
pH = −log2.5×10−6
pH = −log2.5×10−6
pH = −log2.5×10−6
Step 4: Calculate the pH using a calculator:
pH ≈ −(log2.5×10−6)
pH ≈ −(−5.60)
pH ≈5.60
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−6M is approximately 5.60.
Question 34
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
21
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
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
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9=−0.3979 −(−9) = 8.6
Therefore, the pH of the solution is 8.6.
Step 4: Since pH + pOH = 14, we can calculate the pOH:
pOH = 14 −pH = 14 −8.6=5.4
Therefore, the pOH of the solution is 5.4.
Question 35
Question
A solution is prepared by dissolving 0.00500 moles of hydrochloric acid (HCl) in
enough water to make 250.0 mL of solution. Calculate the pH of the resulting
solution.
Solution
Step 1: Calculate the concentration of HCl in the solution. Given: Number of
moles of HCl = 0.00500 mol Volume of solution = 250.0 mL = 0.2500 L
Concentration of HCl = 0.00500mol
0.2500L= 0.0200 M
Step 2: Determine the pH of the solution using the formula pH =−log[H+].
Since HCl is a strong acid, it dissociates completely in water to form H ions.
Thus, [H+] = concentration of HCl = 0.0200 M
pH =−log(0.0200) = −(−1.69897) = 1.69897
Therefore, the pH of the resulting solution is 1.70.
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