CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 6
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H3O+]
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
substitute this value into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−5=−(−4.49485) = 4.49
Therefore, the pH of the solution is 4.49.
Question 2
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula pH =
−log[H+]. Given that the hydrogen ion concentration is 2.5×10−5M, we can
substitute this value into the formula to find the pH.
pH = −log2.5×10−5
Step 2: To calculate the pH, we first take the negative logarithm of the
hydrogen ion concentration.
pH = −log2.5×10−5=−log(2.5) −log10−5
Step 3: Since log10−5=−5, we have:
pH = −log(2.5) −(−5) = −log(2.5) + 5
Step 4: Using a calculator, we find log(2.5) ≈0.3979. Therefore,
pH ≈ −0.3979 + 5
Step 5: Finally, we calculate the pH value:
pH ≈4.6021
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−5M is approximately 4.6021.
Question 3
Question
A solution has a pH of 3.75. Calculate the pOH of the solution and determine
if the solution is acidic, basic, or neutral.
Solution
Step 1: Recall the relationship between pH and pOH: The sum of pH and pOH
in any solution is always 14. Mathematically,
pH + pOH = 14
Step 2: Substitute the given pH value into the equation to find pOH:
3.75 + pOH = 14
pOH = 14 −3.75
pOH = 10.25
Step 3: Interpret the pOH value to determine the nature of the solution:
Since the pOH is greater than 7, the solution is basic.
Therefore, the pOH of the solution is 10.25, and the solution is basic.
2
Question 4
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+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log2.5×10−9
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9
Step 4: Simplify the expression using the properties of logarithms:
pH = −(log(2.5) + log10−9)
Step 5: Recall that log10−9=−9:
pH = −(log(2.5) −9) = −log(2.5) + 9
Step 6: Use a calculator to find the final pH value:
pH = −log(2.5) + 9 ≈8.60
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−9M is approximately 8.60.
Question 5
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−6M.
Solution
Step 1: Calculate the pH using the formula pH =−log[H+].
pH = −log1.5×10−6
pH = −log(1.5) + log10−6
pH ≈ −0.176 + 6
pH ≈5.824
3
Step 2: Calculate the pOH using the formula pOH =−log[OH−]. Since
pH +pOH = 14 for water at 25
°
C,
pOH = 14 −pH
pOH = 14 −5.824
pOH ≈8.176
Therefore, the pH of the solution is approximately 5.824 and the pOH is
approximately 8.176.
Question 6
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 the negative base-10 logarithm of the
hydrogen ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log2.5×10−9
Step 3: Use a calculator to evaluate the logarithm:
pH ≈ − log2.5×10−9≈ −(log 2.5 + log 10−9)
Step 4: Simplify the expression:
pH ≈ −(log 2.5−9) ≈ −(0.3979 −9)
Step 5: Calculate the pH:
pH ≈ −(−8.6021) ≈8.6021
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−9M is approximately 8.60.
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.6×10−9
M.
4
Solution
Step 1: Recall that pH is defined as −log[H+] where [H+] represents the hydro-
gen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
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) + log10−9) = −(log(3.6) −9)
Step 5: Use the property of logarithms log(ab) = log(a) + log(b) to simplify
further:
pH = −(0.5563 −9) = −(−8.4437)
Step 6: Calculate the final pH value:
pH ≈8.44
Therefore, the pH of the solution with a hydrogen ion concentration of 3.6×
10−9M is approximately 8.44.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 3.2×10−9M, we can plug this value into the pH formula.
Step 2: Calculate the pH using the formula −log3.2×10−9.
pH = −log3.2×10−9
Step 3: Simplify the expression.
pH = −log(3.2) −log10−9
Step 4: Recall that log10−9=−9. Thus, we have:
pH = −log(3.2) −(−9)
5
Step 5: Use the property of logarithms log(a)−log(b) = log(a/b) to simplify.
pH = log 1
3.2+ 9
Step 6: Use a calculator to find the value of log 1
3.2.
log 1
3.2≈ −0.505
Step 7: Substitute the value back into the pH equation.
pH ≈ −0.505 + 9
Step 8: Add the values together to find the final pH.
pH ≈8.495
Step 9: Therefore, the pH of a solution with a hydronium ion concentration
of 3.2×10−9M is approximately 8.495.
Question 9
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Remember that pH is defined as −log[H3O+]. Therefore, to find the pH
of the solution, we will first need to calculate the concentration of hydronium
ions.
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
write this as: [H3O+]=3.2×10−5M.
Step 3: Substitute the given concentration into the pH formula. We have:
pH = −log3.2×10−5.
Step 4: Calculate the pH using a calculator. The pH of the solution is
approximately
−log3.2×10−5≈4.495.
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is 4.495.
6
Question 10
Question
Calculate the pH of a solution with a hydroxide ion concentration of 6.3×10−4
M.
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Write the expression for the ion product of water:
Kw= [H+][OH−]
Step 3: Given that Kw= 1.0×10−14 at 25◦C, and the hydroxide ion con-
centration is 6.3×10−4M, we can find the concentration of hydronium ion by
rearranging the equation:
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
6.3×10−4
[H+] = 1.59 ×10−11 M
Step 4: Calculate the pH using the equation:
pH = −log[H+]
pH = −log1.59 ×10−11
pH = −(log 1.59 + log 10−11)
pH = −(0.201 + 11)
pH = −11.201
pH ≈11.2
Therefore, the pH of the solution with a hydroxide ion concentration of
6.3×10−4M is approximately 11.2.
Question 11
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.78×10−4
M.
7
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. We are given
[H3O+]=3.78 ×10−4M.
Step 2: Substitute the given concentration into the pH formula:
pH = −log3.78 ×10−4
Step 3: Use a calculator to find the logarithm:
pH = −log3.78 ×10−4=−log(3.78) + log10−4
Step 4: Simplify the expression further:
pH = −log(3.78) −4
Step 5: Calculate the logarithm:
pH ≈ −(−0.577) −4
Step 6: Calculate the pH:
pH ≈0.577 −4
Step 7: Final calculation:
pH ≈ −3.423
Therefore, the pH of the solution is approximately -3.423.
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the expression for the ion product of water. The ion product of
water (Kw) at 25
°
C is 1.0×10−14.
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the hydroxide ion concentration to find the concentration of
hydronium ions. Since [H+] = Kw
[OH−], we can substitute in the given hydroxide
ion concentration to find the concentration of hydronium ions.
[H+] = 1.0×10−14
1.5×10−4= 6.67 ×10−11 M
8
Step 3: Calculate the pH of the solution. The pH of a solution is defined as
−log[H+]. Therefore, we can find the pH by taking the negative logarithm of
the hydronium ion concentration calculated in the previous step.
pH =−log6.67 ×10−11=−(log(6.67)+log10−11) = −(−0.825+11) = 0.825+11 = 11.825
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−4M is 11.825.
Question 13
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−3M.
Solution
Step 1: Use the formula pH =−log[H+] to calculate the pH of the solution.
pH = −log2.5×10−3=−log(2.5) + log10−3=−(0.3979) + 3 = 2.60
Step 2: Use the fact that pH +pOH = 14 to determine the pOH of the
solution.
pOH = 14 −pH = 14 −2.60 = 11.40
Therefore, the pH of the solution is 2.60 and the pOH is 11.40.
Question 14
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 hydroxide ion concentration ([OH−]) and
pH:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH =−log2.5×10−4
Step 3: Calculate the pOH:
pOH =−log2.5×10−4=−log(2.5)−log10−4=−(log(2.5)−4) ≈ −(−0.3979−4)
9
pOH ≈4.3979
Step 4: Use the relationship between pH and pOH:
pH +pOH = 14
Step 5: Substitute the calculated pOH value into the formula to find the pH:
pH + 4.3979 = 14
pH = 14 −4.3979 = 9.6021
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is approximately 9.60.
Question 15
Question
Calculate the pH of a solution that has a hydronium ion concentration of 4.5×
10−3M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that [H3O+]=4.5×
10−3M, we can calculate the pH as follows:
pH = −log4.5×10−3
Step 2: Using the properties of logarithms, we can simplify the expression:
pH = −log(4.5) −log10−3
pH = −log(4.5) + 3
Step 3: Calculate log(4.5):
log(4.5) ≈0.6532
Step 4: Substitute the value back into the pH equation:
pH ≈ −0.6532 + 3
pH ≈2.35
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 4.5×10−3M is approximately 2.35.
10
Question 16
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+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula for
pH:
pH = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9=−log(2.5) −log10−9
Step 4: Since log10−9=−9, we have:
pH = −log(2.5) −(−9) = −log(2.5) + 9
Step 5: Using a calculator, find log(2.5) ≈0.3979 and substitute back into
the equation:
pH ≈ −0.3979 + 9
Step 6: Final step, calculate the pH:
pH ≈8.6021
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−9M is approximately 8.6021.
Question 17
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Given that the hydrogen ion concentration is 3.2×10−6M, we can
calculate the pH as:
pH = −log3.2×10−6
11
Step 3: Calculate the logarithm of the hydrogen ion concentration:
pH = −log3.2×10−6=−log(3.2) + log10−6
Step 4: Since log10−6=−6, we have:
pH = −log(3.2) −6
Step 5: Use a calculator to evaluate log(3.2) ≈0.505, then substitute it into
the equation:
pH ≈ −(0.505) −6
Step 6: Finally, calculate the pH of the solution:
pH ≈ −0.505 −6 = −6.505
Step 7: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−6M is approximately 6.505.
Question 18
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−9M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 3: Simplify the expression to find the pH:
pH ≈ −0.176 −(−9) ≈8.824
Step 4: Recall that the pOH of a solution is calculated using the formula:
pOH = −log[OH−]
Step 5: Since the solution is neutral, we can use the relationship:
pH + pOH = 14
12
Step 6: Substitute the calculated pH into the equation to find the pOH:
8.824 + pOH = 14
Step 7: Solve for pOH:
pOH = 14 −8.824 = 5.176
Therefore, the pH of the solution is approximately 8.824 and the pOH is
approximately 5.176.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydrogen ion concentration.
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the pH formula.
pH = −log2.5×10−10
Step 3: Calculate the pH using a calculator.
pH = −log2.5×10−10=−(−9.60) = 9.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−10 M is 9.60.
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
13
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Convert the hydronium ion
concentration to pH using the formula:
pH = −log1.5×10−3
Step 2: Calculate the pH:
pH = −log1.5×10−3=−log(1.5) + log10−3
Step 3: Use the property of logarithms that log(ab) = log(a) + log(b):
pH = −(log(1.5) + 3)
Step 4: Calculate the pH:
pH = −(0.1761 + 3) = −3.1761
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 3.18 .
Question 21
Question
Calculate the pH of a 0.010 M hydrochloric acid solution.
Solution
Step 1: Write the chemical equation for the dissociation of hydrochloric acid:
HCl →H++ Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely.
Thus, the concentration of H+ions in the solution is equal to the initial con-
centration of the acid, which is 0.010 M.
Step 3: Use the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.010)
Step 5: Calculate the pH:
pH = 2
Therefore, the pH of a 0.010 M hydrochloric acid solution is 2.
14
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Write the expression for the ion product of water:
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the concentration
of hydrogen ions:
[OH−] = 2.5×10−3M
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions:
pH = −log[H+] = −log4.0×10−12=−log(4.0) −log10−12
pH = 0.602 −(−12) = 12 −0.602 = 11.398
Therefore, the pH of the solution is 11.398.
Question 23
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.17 ×10−6
M.
Solution
Step 1: Write the formula relating pH and hydrogen ion concentration: pH =
−log[H+].
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log3.17 ×10−6
Step 3: Calculate the pH:
pH =−log3.17 ×10−6=−log(3.17) + log10−6= 5.498 −6 = −0.502
Therefore, the pH of the solution is 0.502 .
15
Question 24
Question
What is the pH of a solution that is 0.020 M in hydrochloric acid (HCl) and
0.040 M in hydroxide ions (OH−)?
Solution
Step 1: Write the chemical equation for the dissociation of hydrochloric acid.
Step 2: Determine the concentration of hydrogen ions (H+). Step 3: Calculate
the pH of the solution.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.8×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH = −log[OH−]
pOH = −log5.8×10−9
pOH ≈ − log(5.8) = −0.763
Step 2: Calculate the pH of the solution using the formula:
pH + pOH = 14
pH = 14 −pOH
pH = 14 −(−0.763)
pH = 14 + 0.763 = 14.763
Therefore, the pH of the solution with a hydroxide ion concentration of
5.8×10−9M is approximately 14.763.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
16
Solution
Step 1: Recall that pH is calculated using the formula pH =−log[H+], where
[H+] represents the concentration of hydrogen ions in moles per liter. Step 2:
Substitute [H+]=2.5×10−9M into the pH formula to find the pH. Step 3:
pH =−log2.5×10−9
Step 4: Use the properties of logarithms to simplify the expression. Step 5:
pH =−log(2.5) −log10−9
Step 6: Recall that log10−9=−9. Step 7:
pH =−log(2.5) −(−9)
Step 8:
pH =−log(2.5) + 9
Step 9: Use a calculator to find the value of log(2.5). Step 10:
pH ≈ −0.3979 + 9
Step 11:
pH ≈8.6021
Step 12: Therefore, the pH of the solution is approximately 8.6021.
Question 27
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.2×
10−9M.
Solution
Step 1: Write the expression for Kw.
Kw= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the expression
for Kw.
1.0×10−14 = (3.2×10−9)[H+]
Step 3: Solve for the concentration of hydronium ions.
[H+] = 1.0×10−14
3.2×10−9= 3.125 ×10−6M
Step 4: Calculate the pH using the formula pH =−log[H+].
pH =−log3.125 ×10−6=−(−5.505) = 5.505
Therefore, the pH of the solution is 5.505.
17
Question 28
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[H3O+], where [H3O+] is the hydro-
nium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.5×10−4
Step 3: Use a calculator to find the pH value:
pH = −log3.5×10−4=−(−3.4559) = 3.4559
Step 4: Therefore, the pH of the solution is approximately 3.46.
Question 29
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. Step 2:
Substitute the given hydronium ion concentration into the pH formula:
pH = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) + log10−3
Step 4: Since log10−3=−3, the pH becomes:
pH = −log(2.5) −3
Step 5: Use a calculator to find the value of −log(2.5). Step 6: Calculate the
final pH value.
18
Question 30
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, we can calculate the
pH using the given hydrogen ion concentration:
pH = −log2.5×10−10
Step 2: Substitute the value of the hydrogen ion concentration into the
formula and calculate the pH:
pH = −log2.5×10−10=−log(2.5) −log10−10
Step 3: Simplify the expression by using the properties of logarithms:
pH = −log(2.5) −log10−10=−log(2.5) −(−10) = −log(2.5) + 10
Step 4: Use a calculator to find the numerical value of log(2.5), then calculate
the pH:
pH ≈ −0.39794 + 10 = 9.60206
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−10 M is approximately 9.60.
Question 31
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions and hydroxide ions:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the concentration of hydrogen ions, [H+]=3.2×10−9
M, we can calculate the pH using the formula: pH = −log3.2×10−9.
19
Step 3: Calculate the pH:
pH = −log3.2×10−9=−(log 3.2+log 10−9) = −(log 3.2−9) ≈ −(−0.4948−9) ≈9.5
Step 4: Now, we can calculate the pOH using the relationship: pH + pOH =
14. Therefore, pOH = 14 −9.5.
Step 5: Calculate the pOH:
pOH = 14 −9.5=4.5
Therefore, the pH of the solution is 9.5 and the pOH is 4.5.
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5 ×10−3
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
pOH = −log[OH−] = −log2.5×10−3
pOH = −log(2.5) −log10−3=−log(2.5) + 3
pOH ≈ −0.3979 + 3 ≈2.6021
Step 2: Calculate the pH using the pOH. The pH and pOH of a solution add
up to 14.
pH = 14 −pOH = 14 −2.6021
pH ≈11.3979
Therefore, the pH of the solution is approximately 11.40.
Question 33
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−3M. Given that Kw= 1.0×10−14 at 25
°
C.
20
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the ion product
constant expression.
1.0×10−14 = [H+](2.5×10−3)
Step 3: Solve for the concentration of hydrogen ions, [H+].
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 4: Calculate the pH using the concentration of hydrogen ions.
pH = −log[H+]=−log4.0×10−12≈11.40
Therefore, the pH of the solution is approximately 11.40.
Question 34
Question
A 0.010 M solution of hydrochloric acid (HCl) has a pH of 2. What is the pOH
of this solution?
Solution
Step 1: Recall the relationship between pH and pOH in aqueous solutions:
pH + pOH = 14
Step 2: Given that the pH of the solution is 2, we can calculate the hydrogen
ion concentration ([H+])usingtheformula : pH = −log[H+]
2 = −log[H+]
[H+] = 10−2M = 0.01 M
Step 3: Next, calculate the hydroxide ion concentration ([OH−])usingthef ormula :
[H+]×[OH−] = 1.0×10−14 M2
(0.01)([OH−]) = 1.0×10−14
[OH−] = 1.0×10−14
0.01 = 1.0×10−12 M
Step 4: Finally, determine the pOH of the solution using the formula:
pOH = −log[OH−]
pOH = −log1.0×10−12
pOH = 12
Therefore, the pOH of the 0.010 M solution of hydrochloric acid is 12.
21
Question 4
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+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log2.5×10−9
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9
Step 4: Simplify the expression using the properties of logarithms:
pH = −(log(2.5) + log10−9)
Step 5: Recall that log10−9=−9:
pH = −(log(2.5) −9) = −log(2.5) + 9
Step 6: Use a calculator to find the final pH value:
pH = −log(2.5) + 9 ≈8.60
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−9M is approximately 8.60.
Question 5
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−6M.
Solution
Step 1: Calculate the pH using the formula pH =−log[H+].
pH = −log1.5×10−6
pH = −log(1.5) + log10−6
pH ≈ −0.176 + 6
pH ≈5.824
3
Step 2: Calculate the pOH using the formula pOH =−log[OH−]. Since
pH +pOH = 14 for water at 25
°
C,
pOH = 14 −pH
pOH = 14 −5.824
pOH ≈8.176
Therefore, the pH of the solution is approximately 5.824 and the pOH is
approximately 8.176.
Question 6
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 the negative base-10 logarithm of the
hydrogen ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log2.5×10−9
Step 3: Use a calculator to evaluate the logarithm:
pH ≈ − log2.5×10−9≈ −(log 2.5 + log 10−9)
Step 4: Simplify the expression:
pH ≈ −(log 2.5−9) ≈ −(0.3979 −9)
Step 5: Calculate the pH:
pH ≈ −(−8.6021) ≈8.6021
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−9M is approximately 8.60.
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.6×10−9
M.
4
Solution
Step 1: Recall that pH is defined as −log[H+] where [H+] represents the hydro-
gen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
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) + log10−9) = −(log(3.6) −9)
Step 5: Use the property of logarithms log(ab) = log(a) + log(b) to simplify
further:
pH = −(0.5563 −9) = −(−8.4437)
Step 6: Calculate the final pH value:
pH ≈8.44
Therefore, the pH of the solution with a hydrogen ion concentration of 3.6×
10−9M is approximately 8.44.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 3.2×10−9M, we can plug this value into the pH formula.
Step 2: Calculate the pH using the formula −log3.2×10−9.
pH = −log3.2×10−9
Step 3: Simplify the expression.
pH = −log(3.2) −log10−9
Step 4: Recall that log10−9=−9. Thus, we have:
pH = −log(3.2) −(−9)
5
Step 5: Use the property of logarithms log(a)−log(b) = log(a/b) to simplify.
pH = log 1
3.2+ 9
Step 6: Use a calculator to find the value of log 1
3.2.
log 1
3.2≈ −0.505
Step 7: Substitute the value back into the pH equation.
pH ≈ −0.505 + 9
Step 8: Add the values together to find the final pH.
pH ≈8.495
Step 9: Therefore, the pH of a solution with a hydronium ion concentration
of 3.2×10−9M is approximately 8.495.
Question 9
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Remember that pH is defined as −log[H3O+]. Therefore, to find the pH
of the solution, we will first need to calculate the concentration of hydronium
ions.
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
write this as: [H3O+]=3.2×10−5M.
Step 3: Substitute the given concentration into the pH formula. We have:
pH = −log3.2×10−5.
Step 4: Calculate the pH using a calculator. The pH of the solution is
approximately
−log3.2×10−5≈4.495.
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is 4.495.
6
Question 10
Question
Calculate the pH of a solution with a hydroxide ion concentration of 6.3×10−4
M.
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Write the expression for the ion product of water:
Kw= [H+][OH−]
Step 3: Given that Kw= 1.0×10−14 at 25◦C, and the hydroxide ion con-
centration is 6.3×10−4M, we can find the concentration of hydronium ion by
rearranging the equation:
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
6.3×10−4
[H+] = 1.59 ×10−11 M
Step 4: Calculate the pH using the equation:
pH = −log[H+]
pH = −log1.59 ×10−11
pH = −(log 1.59 + log 10−11)
pH = −(0.201 + 11)
pH = −11.201
pH ≈11.2
Therefore, the pH of the solution with a hydroxide ion concentration of
6.3×10−4M is approximately 11.2.
Question 11
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.78×10−4
M.
7
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. We are given
[H3O+]=3.78 ×10−4M.
Step 2: Substitute the given concentration into the pH formula:
pH = −log3.78 ×10−4
Step 3: Use a calculator to find the logarithm:
pH = −log3.78 ×10−4=−log(3.78) + log10−4
Step 4: Simplify the expression further:
pH = −log(3.78) −4
Step 5: Calculate the logarithm:
pH ≈ −(−0.577) −4
Step 6: Calculate the pH:
pH ≈0.577 −4
Step 7: Final calculation:
pH ≈ −3.423
Therefore, the pH of the solution is approximately -3.423.
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the expression for the ion product of water. The ion product of
water (Kw) at 25
°
C is 1.0×10−14.
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the hydroxide ion concentration to find the concentration of
hydronium ions. Since [H+] = Kw
[OH−], we can substitute in the given hydroxide
ion concentration to find the concentration of hydronium ions.
[H+] = 1.0×10−14
1.5×10−4= 6.67 ×10−11 M
8
Step 3: Calculate the pH of the solution. The pH of a solution is defined as
−log[H+]. Therefore, we can find the pH by taking the negative logarithm of
the hydronium ion concentration calculated in the previous step.
pH =−log6.67 ×10−11=−(log(6.67)+log10−11) = −(−0.825+11) = 0.825+11 = 11.825
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−4M is 11.825.
Question 13
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−3M.
Solution
Step 1: Use the formula pH =−log[H+] to calculate the pH of the solution.
pH = −log2.5×10−3=−log(2.5) + log10−3=−(0.3979) + 3 = 2.60
Step 2: Use the fact that pH +pOH = 14 to determine the pOH of the
solution.
pOH = 14 −pH = 14 −2.60 = 11.40
Therefore, the pH of the solution is 2.60 and the pOH is 11.40.
Question 14
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 hydroxide ion concentration ([OH−]) and
pH:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH =−log2.5×10−4
Step 3: Calculate the pOH:
pOH =−log2.5×10−4=−log(2.5)−log10−4=−(log(2.5)−4) ≈ −(−0.3979−4)
9
pOH ≈4.3979
Step 4: Use the relationship between pH and pOH:
pH +pOH = 14
Step 5: Substitute the calculated pOH value into the formula to find the pH:
pH + 4.3979 = 14
pH = 14 −4.3979 = 9.6021
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is approximately 9.60.
Question 15
Question
Calculate the pH of a solution that has a hydronium ion concentration of 4.5×
10−3M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that [H3O+]=4.5×
10−3M, we can calculate the pH as follows:
pH = −log4.5×10−3
Step 2: Using the properties of logarithms, we can simplify the expression:
pH = −log(4.5) −log10−3
pH = −log(4.5) + 3
Step 3: Calculate log(4.5):
log(4.5) ≈0.6532
Step 4: Substitute the value back into the pH equation:
pH ≈ −0.6532 + 3
pH ≈2.35
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 4.5×10−3M is approximately 2.35.
10
Question 16
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+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula for
pH:
pH = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9=−log(2.5) −log10−9
Step 4: Since log10−9=−9, we have:
pH = −log(2.5) −(−9) = −log(2.5) + 9
Step 5: Using a calculator, find log(2.5) ≈0.3979 and substitute back into
the equation:
pH ≈ −0.3979 + 9
Step 6: Final step, calculate the pH:
pH ≈8.6021
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−9M is approximately 8.6021.
Question 17
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Given that the hydrogen ion concentration is 3.2×10−6M, we can
calculate the pH as:
pH = −log3.2×10−6
11
Step 3: Calculate the logarithm of the hydrogen ion concentration:
pH = −log3.2×10−6=−log(3.2) + log10−6
Step 4: Since log10−6=−6, we have:
pH = −log(3.2) −6
Step 5: Use a calculator to evaluate log(3.2) ≈0.505, then substitute it into
the equation:
pH ≈ −(0.505) −6
Step 6: Finally, calculate the pH of the solution:
pH ≈ −0.505 −6 = −6.505
Step 7: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−6M is approximately 6.505.
Question 18
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−9M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 3: Simplify the expression to find the pH:
pH ≈ −0.176 −(−9) ≈8.824
Step 4: Recall that the pOH of a solution is calculated using the formula:
pOH = −log[OH−]
Step 5: Since the solution is neutral, we can use the relationship:
pH + pOH = 14
12
Step 6: Substitute the calculated pH into the equation to find the pOH:
8.824 + pOH = 14
Step 7: Solve for pOH:
pOH = 14 −8.824 = 5.176
Therefore, the pH of the solution is approximately 8.824 and the pOH is
approximately 5.176.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydrogen ion concentration.
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the pH formula.
pH = −log2.5×10−10
Step 3: Calculate the pH using a calculator.
pH = −log2.5×10−10=−(−9.60) = 9.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−10 M is 9.60.
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
13
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Convert the hydronium ion
concentration to pH using the formula:
pH = −log1.5×10−3
Step 2: Calculate the pH:
pH = −log1.5×10−3=−log(1.5) + log10−3
Step 3: Use the property of logarithms that log(ab) = log(a) + log(b):
pH = −(log(1.5) + 3)
Step 4: Calculate the pH:
pH = −(0.1761 + 3) = −3.1761
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 3.18 .
Question 21
Question
Calculate the pH of a 0.010 M hydrochloric acid solution.
Solution
Step 1: Write the chemical equation for the dissociation of hydrochloric acid:
HCl →H++ Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely.
Thus, the concentration of H+ions in the solution is equal to the initial con-
centration of the acid, which is 0.010 M.
Step 3: Use the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.010)
Step 5: Calculate the pH:
pH = 2
Therefore, the pH of a 0.010 M hydrochloric acid solution is 2.
14
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Write the expression for the ion product of water:
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the concentration
of hydrogen ions:
[OH−] = 2.5×10−3M
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions:
pH = −log[H+] = −log4.0×10−12=−log(4.0) −log10−12
pH = 0.602 −(−12) = 12 −0.602 = 11.398
Therefore, the pH of the solution is 11.398.
Question 23
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.17 ×10−6
M.
Solution
Step 1: Write the formula relating pH and hydrogen ion concentration: pH =
−log[H+].
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log3.17 ×10−6
Step 3: Calculate the pH:
pH =−log3.17 ×10−6=−log(3.17) + log10−6= 5.498 −6 = −0.502
Therefore, the pH of the solution is 0.502 .
15
Question 24
Question
What is the pH of a solution that is 0.020 M in hydrochloric acid (HCl) and
0.040 M in hydroxide ions (OH−)?
Solution
Step 1: Write the chemical equation for the dissociation of hydrochloric acid.
Step 2: Determine the concentration of hydrogen ions (H+). Step 3: Calculate
the pH of the solution.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.8×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH = −log[OH−]
pOH = −log5.8×10−9
pOH ≈ − log(5.8) = −0.763
Step 2: Calculate the pH of the solution using the formula:
pH + pOH = 14
pH = 14 −pOH
pH = 14 −(−0.763)
pH = 14 + 0.763 = 14.763
Therefore, the pH of the solution with a hydroxide ion concentration of
5.8×10−9M is approximately 14.763.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
16
Solution
Step 1: Recall that pH is calculated using the formula pH =−log[H+], where
[H+] represents the concentration of hydrogen ions in moles per liter. Step 2:
Substitute [H+]=2.5×10−9M into the pH formula to find the pH. Step 3:
pH =−log2.5×10−9
Step 4: Use the properties of logarithms to simplify the expression. Step 5:
pH =−log(2.5) −log10−9
Step 6: Recall that log10−9=−9. Step 7:
pH =−log(2.5) −(−9)
Step 8:
pH =−log(2.5) + 9
Step 9: Use a calculator to find the value of log(2.5). Step 10:
pH ≈ −0.3979 + 9
Step 11:
pH ≈8.6021
Step 12: Therefore, the pH of the solution is approximately 8.6021.
Question 27
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.2×
10−9M.
Solution
Step 1: Write the expression for Kw.
Kw= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the expression
for Kw.
1.0×10−14 = (3.2×10−9)[H+]
Step 3: Solve for the concentration of hydronium ions.
[H+] = 1.0×10−14
3.2×10−9= 3.125 ×10−6M
Step 4: Calculate the pH using the formula pH =−log[H+].
pH =−log3.125 ×10−6=−(−5.505) = 5.505
Therefore, the pH of the solution is 5.505.
17
Question 28
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[H3O+], where [H3O+] is the hydro-
nium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.5×10−4
Step 3: Use a calculator to find the pH value:
pH = −log3.5×10−4=−(−3.4559) = 3.4559
Step 4: Therefore, the pH of the solution is approximately 3.46.
Question 29
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. Step 2:
Substitute the given hydronium ion concentration into the pH formula:
pH = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) + log10−3
Step 4: Since log10−3=−3, the pH becomes:
pH = −log(2.5) −3
Step 5: Use a calculator to find the value of −log(2.5). Step 6: Calculate the
final pH value.
18
Question 30
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, we can calculate the
pH using the given hydrogen ion concentration:
pH = −log2.5×10−10
Step 2: Substitute the value of the hydrogen ion concentration into the
formula and calculate the pH:
pH = −log2.5×10−10=−log(2.5) −log10−10
Step 3: Simplify the expression by using the properties of logarithms:
pH = −log(2.5) −log10−10=−log(2.5) −(−10) = −log(2.5) + 10
Step 4: Use a calculator to find the numerical value of log(2.5), then calculate
the pH:
pH ≈ −0.39794 + 10 = 9.60206
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−10 M is approximately 9.60.
Question 31
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions and hydroxide ions:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the concentration of hydrogen ions, [H+]=3.2×10−9
M, we can calculate the pH using the formula: pH = −log3.2×10−9.
19
Step 3: Calculate the pH:
pH = −log3.2×10−9=−(log 3.2+log 10−9) = −(log 3.2−9) ≈ −(−0.4948−9) ≈9.5
Step 4: Now, we can calculate the pOH using the relationship: pH + pOH =
14. Therefore, pOH = 14 −9.5.
Step 5: Calculate the pOH:
pOH = 14 −9.5=4.5
Therefore, the pH of the solution is 9.5 and the pOH is 4.5.
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5 ×10−3
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
pOH = −log[OH−] = −log2.5×10−3
pOH = −log(2.5) −log10−3=−log(2.5) + 3
pOH ≈ −0.3979 + 3 ≈2.6021
Step 2: Calculate the pH using the pOH. The pH and pOH of a solution add
up to 14.
pH = 14 −pOH = 14 −2.6021
pH ≈11.3979
Therefore, the pH of the solution is approximately 11.40.
Question 33
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−3M. Given that Kw= 1.0×10−14 at 25
°
C.
20
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the ion product
constant expression.
1.0×10−14 = [H+](2.5×10−3)
Step 3: Solve for the concentration of hydrogen ions, [H+].
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 4: Calculate the pH using the concentration of hydrogen ions.
pH = −log[H+]=−log4.0×10−12≈11.40
Therefore, the pH of the solution is approximately 11.40.
Question 34
Question
A 0.010 M solution of hydrochloric acid (HCl) has a pH of 2. What is the pOH
of this solution?
Solution
Step 1: Recall the relationship between pH and pOH in aqueous solutions:
pH + pOH = 14
Step 2: Given that the pH of the solution is 2, we can calculate the hydrogen
ion concentration ([H+])usingtheformula : pH = −log[H+]
2 = −log[H+]
[H+] = 10−2M = 0.01 M
Step 3: Next, calculate the hydroxide ion concentration ([OH−])usingthef ormula :
[H+]×[OH−] = 1.0×10−14 M2
(0.01)([OH−]) = 1.0×10−14
[OH−] = 1.0×10−14
0.01 = 1.0×10−12 M
Step 4: Finally, determine the pOH of the solution using the formula:
pOH = −log[OH−]
pOH = −log1.0×10−12
pOH = 12
Therefore, the pOH of the 0.010 M solution of hydrochloric acid is 12.
21
Question 4
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+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log2.5×10−9
Step 3: Calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9
Step 4: Simplify the expression using the properties of logarithms:
pH = −(log(2.5) + log10−9)
Step 5: Recall that log10−9=−9:
pH = −(log(2.5) −9) = −log(2.5) + 9
Step 6: Use a calculator to find the final pH value:
pH = −log(2.5) + 9 ≈8.60
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−9M is approximately 8.60.
Question 5
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−6M.
Solution
Step 1: Calculate the pH using the formula pH =−log[H+].
pH = −log1.5×10−6
pH = −log(1.5) + log10−6
pH ≈ −0.176 + 6
pH ≈5.824
3
Step 2: Calculate the pOH using the formula pOH =−log[OH−]. Since
pH +pOH = 14 for water at 25
°
C,
pOH = 14 −pH
pOH = 14 −5.824
pOH ≈8.176
Therefore, the pH of the solution is approximately 5.824 and the pOH is
approximately 8.176.
Question 6
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 the negative base-10 logarithm of the
hydrogen ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log2.5×10−9
Step 3: Use a calculator to evaluate the logarithm:
pH ≈ − log2.5×10−9≈ −(log 2.5 + log 10−9)
Step 4: Simplify the expression:
pH ≈ −(log 2.5−9) ≈ −(0.3979 −9)
Step 5: Calculate the pH:
pH ≈ −(−8.6021) ≈8.6021
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−9M is approximately 8.60.
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.6×10−9
M.
4
Solution
Step 1: Recall that pH is defined as −log[H+] where [H+] represents the hydro-
gen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
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) + log10−9) = −(log(3.6) −9)
Step 5: Use the property of logarithms log(ab) = log(a) + log(b) to simplify
further:
pH = −(0.5563 −9) = −(−8.4437)
Step 6: Calculate the final pH value:
pH ≈8.44
Therefore, the pH of the solution with a hydrogen ion concentration of 3.6×
10−9M is approximately 8.44.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 3.2×10−9M, we can plug this value into the pH formula.
Step 2: Calculate the pH using the formula −log3.2×10−9.
pH = −log3.2×10−9
Step 3: Simplify the expression.
pH = −log(3.2) −log10−9
Step 4: Recall that log10−9=−9. Thus, we have:
pH = −log(3.2) −(−9)
5
Step 5: Use the property of logarithms log(a)−log(b) = log(a/b) to simplify.
pH = log 1
3.2+ 9
Step 6: Use a calculator to find the value of log 1
3.2.
log 1
3.2≈ −0.505
Step 7: Substitute the value back into the pH equation.
pH ≈ −0.505 + 9
Step 8: Add the values together to find the final pH.
pH ≈8.495
Step 9: Therefore, the pH of a solution with a hydronium ion concentration
of 3.2×10−9M is approximately 8.495.
Question 9
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Remember that pH is defined as −log[H3O+]. Therefore, to find the pH
of the solution, we will first need to calculate the concentration of hydronium
ions.
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
write this as: [H3O+]=3.2×10−5M.
Step 3: Substitute the given concentration into the pH formula. We have:
pH = −log3.2×10−5.
Step 4: Calculate the pH using a calculator. The pH of the solution is
approximately
−log3.2×10−5≈4.495.
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is 4.495.
6
Question 10
Question
Calculate the pH of a solution with a hydroxide ion concentration of 6.3×10−4
M.
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Write the expression for the ion product of water:
Kw= [H+][OH−]
Step 3: Given that Kw= 1.0×10−14 at 25◦C, and the hydroxide ion con-
centration is 6.3×10−4M, we can find the concentration of hydronium ion by
rearranging the equation:
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
6.3×10−4
[H+] = 1.59 ×10−11 M
Step 4: Calculate the pH using the equation:
pH = −log[H+]
pH = −log1.59 ×10−11
pH = −(log 1.59 + log 10−11)
pH = −(0.201 + 11)
pH = −11.201
pH ≈11.2
Therefore, the pH of the solution with a hydroxide ion concentration of
6.3×10−4M is approximately 11.2.
Question 11
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.78×10−4
M.
7
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. We are given
[H3O+]=3.78 ×10−4M.
Step 2: Substitute the given concentration into the pH formula:
pH = −log3.78 ×10−4
Step 3: Use a calculator to find the logarithm:
pH = −log3.78 ×10−4=−log(3.78) + log10−4
Step 4: Simplify the expression further:
pH = −log(3.78) −4
Step 5: Calculate the logarithm:
pH ≈ −(−0.577) −4
Step 6: Calculate the pH:
pH ≈0.577 −4
Step 7: Final calculation:
pH ≈ −3.423
Therefore, the pH of the solution is approximately -3.423.
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the expression for the ion product of water. The ion product of
water (Kw) at 25
°
C is 1.0×10−14.
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the hydroxide ion concentration to find the concentration of
hydronium ions. Since [H+] = Kw
[OH−], we can substitute in the given hydroxide
ion concentration to find the concentration of hydronium ions.
[H+] = 1.0×10−14
1.5×10−4= 6.67 ×10−11 M
8
Step 3: Calculate the pH of the solution. The pH of a solution is defined as
−log[H+]. Therefore, we can find the pH by taking the negative logarithm of
the hydronium ion concentration calculated in the previous step.
pH =−log6.67 ×10−11=−(log(6.67)+log10−11) = −(−0.825+11) = 0.825+11 = 11.825
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−4M is 11.825.
Question 13
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−3M.
Solution
Step 1: Use the formula pH =−log[H+] to calculate the pH of the solution.
pH = −log2.5×10−3=−log(2.5) + log10−3=−(0.3979) + 3 = 2.60
Step 2: Use the fact that pH +pOH = 14 to determine the pOH of the
solution.
pOH = 14 −pH = 14 −2.60 = 11.40
Therefore, the pH of the solution is 2.60 and the pOH is 11.40.
Question 14
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 hydroxide ion concentration ([OH−]) and
pH:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH =−log2.5×10−4
Step 3: Calculate the pOH:
pOH =−log2.5×10−4=−log(2.5)−log10−4=−(log(2.5)−4) ≈ −(−0.3979−4)
9
pOH ≈4.3979
Step 4: Use the relationship between pH and pOH:
pH +pOH = 14
Step 5: Substitute the calculated pOH value into the formula to find the pH:
pH + 4.3979 = 14
pH = 14 −4.3979 = 9.6021
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is approximately 9.60.
Question 15
Question
Calculate the pH of a solution that has a hydronium ion concentration of 4.5×
10−3M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that [H3O+]=4.5×
10−3M, we can calculate the pH as follows:
pH = −log4.5×10−3
Step 2: Using the properties of logarithms, we can simplify the expression:
pH = −log(4.5) −log10−3
pH = −log(4.5) + 3
Step 3: Calculate log(4.5):
log(4.5) ≈0.6532
Step 4: Substitute the value back into the pH equation:
pH ≈ −0.6532 + 3
pH ≈2.35
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 4.5×10−3M is approximately 2.35.
10
Question 16
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+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the formula for
pH:
pH = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9=−log(2.5) −log10−9
Step 4: Since log10−9=−9, we have:
pH = −log(2.5) −(−9) = −log(2.5) + 9
Step 5: Using a calculator, find log(2.5) ≈0.3979 and substitute back into
the equation:
pH ≈ −0.3979 + 9
Step 6: Final step, calculate the pH:
pH ≈8.6021
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−9M is approximately 8.6021.
Question 17
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Given that the hydrogen ion concentration is 3.2×10−6M, we can
calculate the pH as:
pH = −log3.2×10−6
11
Step 3: Calculate the logarithm of the hydrogen ion concentration:
pH = −log3.2×10−6=−log(3.2) + log10−6
Step 4: Since log10−6=−6, we have:
pH = −log(3.2) −6
Step 5: Use a calculator to evaluate log(3.2) ≈0.505, then substitute it into
the equation:
pH ≈ −(0.505) −6
Step 6: Finally, calculate the pH of the solution:
pH ≈ −0.505 −6 = −6.505
Step 7: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−6M is approximately 6.505.
Question 18
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
1.5×10−9M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 3: Simplify the expression to find the pH:
pH ≈ −0.176 −(−9) ≈8.824
Step 4: Recall that the pOH of a solution is calculated using the formula:
pOH = −log[OH−]
Step 5: Since the solution is neutral, we can use the relationship:
pH + pOH = 14
12
Step 6: Substitute the calculated pH into the equation to find the pOH:
8.824 + pOH = 14
Step 7: Solve for pOH:
pOH = 14 −8.824 = 5.176
Therefore, the pH of the solution is approximately 8.824 and the pOH is
approximately 5.176.
Question 19
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydrogen ion concentration.
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the pH formula.
pH = −log2.5×10−10
Step 3: Calculate the pH using a calculator.
pH = −log2.5×10−10=−(−9.60) = 9.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−10 M is 9.60.
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
13
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Convert the hydronium ion
concentration to pH using the formula:
pH = −log1.5×10−3
Step 2: Calculate the pH:
pH = −log1.5×10−3=−log(1.5) + log10−3
Step 3: Use the property of logarithms that log(ab) = log(a) + log(b):
pH = −(log(1.5) + 3)
Step 4: Calculate the pH:
pH = −(0.1761 + 3) = −3.1761
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 3.18 .
Question 21
Question
Calculate the pH of a 0.010 M hydrochloric acid solution.
Solution
Step 1: Write the chemical equation for the dissociation of hydrochloric acid:
HCl →H++ Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely.
Thus, the concentration of H+ions in the solution is equal to the initial con-
centration of the acid, which is 0.010 M.
Step 3: Use the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.010)
Step 5: Calculate the pH:
pH = 2
Therefore, the pH of a 0.010 M hydrochloric acid solution is 2.
14
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Write the expression for the ion product of water:
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the concentration
of hydrogen ions:
[OH−] = 2.5×10−3M
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions:
pH = −log[H+] = −log4.0×10−12=−log(4.0) −log10−12
pH = 0.602 −(−12) = 12 −0.602 = 11.398
Therefore, the pH of the solution is 11.398.
Question 23
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.17 ×10−6
M.
Solution
Step 1: Write the formula relating pH and hydrogen ion concentration: pH =
−log[H+].
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log3.17 ×10−6
Step 3: Calculate the pH:
pH =−log3.17 ×10−6=−log(3.17) + log10−6= 5.498 −6 = −0.502
Therefore, the pH of the solution is 0.502 .
15
Question 24
Question
What is the pH of a solution that is 0.020 M in hydrochloric acid (HCl) and
0.040 M in hydroxide ions (OH−)?
Solution
Step 1: Write the chemical equation for the dissociation of hydrochloric acid.
Step 2: Determine the concentration of hydrogen ions (H+). Step 3: Calculate
the pH of the solution.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.8×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH = −log[OH−]
pOH = −log5.8×10−9
pOH ≈ − log(5.8) = −0.763
Step 2: Calculate the pH of the solution using the formula:
pH + pOH = 14
pH = 14 −pOH
pH = 14 −(−0.763)
pH = 14 + 0.763 = 14.763
Therefore, the pH of the solution with a hydroxide ion concentration of
5.8×10−9M is approximately 14.763.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
16
Solution
Step 1: Recall that pH is calculated using the formula pH =−log[H+], where
[H+] represents the concentration of hydrogen ions in moles per liter. Step 2:
Substitute [H+]=2.5×10−9M into the pH formula to find the pH. Step 3:
pH =−log2.5×10−9
Step 4: Use the properties of logarithms to simplify the expression. Step 5:
pH =−log(2.5) −log10−9
Step 6: Recall that log10−9=−9. Step 7:
pH =−log(2.5) −(−9)
Step 8:
pH =−log(2.5) + 9
Step 9: Use a calculator to find the value of log(2.5). Step 10:
pH ≈ −0.3979 + 9
Step 11:
pH ≈8.6021
Step 12: Therefore, the pH of the solution is approximately 8.6021.
Question 27
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.2×
10−9M.
Solution
Step 1: Write the expression for Kw.
Kw= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the expression
for Kw.
1.0×10−14 = (3.2×10−9)[H+]
Step 3: Solve for the concentration of hydronium ions.
[H+] = 1.0×10−14
3.2×10−9= 3.125 ×10−6M
Step 4: Calculate the pH using the formula pH =−log[H+].
pH =−log3.125 ×10−6=−(−5.505) = 5.505
Therefore, the pH of the solution is 5.505.
17
Question 28
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[H3O+], where [H3O+] is the hydro-
nium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log3.5×10−4
Step 3: Use a calculator to find the pH value:
pH = −log3.5×10−4=−(−3.4559) = 3.4559
Step 4: Therefore, the pH of the solution is approximately 3.46.
Question 29
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. Step 2:
Substitute the given hydronium ion concentration into the pH formula:
pH = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) + log10−3
Step 4: Since log10−3=−3, the pH becomes:
pH = −log(2.5) −3
Step 5: Use a calculator to find the value of −log(2.5). Step 6: Calculate the
final pH value.
18
Question 30
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Therefore, we can calculate the
pH using the given hydrogen ion concentration:
pH = −log2.5×10−10
Step 2: Substitute the value of the hydrogen ion concentration into the
formula and calculate the pH:
pH = −log2.5×10−10=−log(2.5) −log10−10
Step 3: Simplify the expression by using the properties of logarithms:
pH = −log(2.5) −log10−10=−log(2.5) −(−10) = −log(2.5) + 10
Step 4: Use a calculator to find the numerical value of log(2.5), then calculate
the pH:
pH ≈ −0.39794 + 10 = 9.60206
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−10 M is approximately 9.60.
Question 31
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions and hydroxide ions:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the concentration of hydrogen ions, [H+]=3.2×10−9
M, we can calculate the pH using the formula: pH = −log3.2×10−9.
19
Step 3: Calculate the pH:
pH = −log3.2×10−9=−(log 3.2+log 10−9) = −(log 3.2−9) ≈ −(−0.4948−9) ≈9.5
Step 4: Now, we can calculate the pOH using the relationship: pH + pOH =
14. Therefore, pOH = 14 −9.5.
Step 5: Calculate the pOH:
pOH = 14 −9.5=4.5
Therefore, the pH of the solution is 9.5 and the pOH is 4.5.
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5 ×10−3
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
pOH = −log[OH−] = −log2.5×10−3
pOH = −log(2.5) −log10−3=−log(2.5) + 3
pOH ≈ −0.3979 + 3 ≈2.6021
Step 2: Calculate the pH using the pOH. The pH and pOH of a solution add
up to 14.
pH = 14 −pOH = 14 −2.6021
pH ≈11.3979
Therefore, the pH of the solution is approximately 11.40.
Question 33
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−3M. Given that Kw= 1.0×10−14 at 25
°
C.
20
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the ion product
constant expression.
1.0×10−14 = [H+](2.5×10−3)
Step 3: Solve for the concentration of hydrogen ions, [H+].
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 4: Calculate the pH using the concentration of hydrogen ions.
pH = −log[H+]=−log4.0×10−12≈11.40
Therefore, the pH of the solution is approximately 11.40.
Question 34
Question
A 0.010 M solution of hydrochloric acid (HCl) has a pH of 2. What is the pOH
of this solution?
Solution
Step 1: Recall the relationship between pH and pOH in aqueous solutions:
pH + pOH = 14
Step 2: Given that the pH of the solution is 2, we can calculate the hydrogen
ion concentration ([H+])usingtheformula : pH = −log[H+]
2 = −log[H+]
[H+] = 10−2M = 0.01 M
Step 3: Next, calculate the hydroxide ion concentration ([OH−])usingthef ormula :
[H+]×[OH−] = 1.0×10−14 M2
(0.01)([OH−]) = 1.0×10−14
[OH−] = 1.0×10−14
0.01 = 1.0×10−12 M
Step 4: Finally, determine the pOH of the solution using the formula:
pOH = −log[OH−]
pOH = −log1.0×10−12
pOH = 12
Therefore, the pOH of the 0.010 M solution of hydrochloric acid is 12.
21
Question 35
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−7
M.
Solution
Step 1: Use the relationship between pOH and [OH−] to find the pOH of the
solution.
pOH =−log[OH−]
pOH =−log2.5×10−7
pOH ≈6.60
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH +pOH = 14
pH = 14 −pOH
pH = 14 −6.60
pH ≈7.40
Step 3: Therefore, the pH of the solution with a hydroxide ion concentration
of 2.5×10−7M is approximately 7.40.
22
