CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 2
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration. The formula for pH is:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3=−(−2.6) = 2.6
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−3M is 2.6.
Question 2
Question
Calculate the pH of a solution with a hydrogen ion concentration of 1.5×10−9
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 pH formula:
pH = −log1.5×10−9
Step 3: Calculate the pH using a calculator:
pH ≈ − log1.5×10−9≈ −(−8.82) ≈8.82
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 1.5×10−9M is approximately 8.82.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.0 ×10−3
M.
Solution
Step 1: Write the expression for calculating pOH.
pOH = −log[OH−]
Step 2: Substitute the hydroxide ion concentration into the pOH expression.
pOH = −log5.0×10−3
Step 3: Calculate the pOH.
pOH = −log5.0×10−3≈2.3
Step 4: Calculate the pH using the relationship between pH and pOH.
pH +pOH = 14
Step 5: Substitute the calculated pOH into the pH expression.
pH + 2.3 = 14
Step 6: Solve for pH.
pH = 14 −2.3 = 11.7
Therefore, the pH of the solution is 11.7.
2
Question 4
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. We are given the concentration
of H3O+as 2.5×10−3M, so we can directly calculate the pH using this formula.
Step 2: Substitute the given concentration into the formula for pH:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3=−(−2.60) = 2.60
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−3M is pH = 2.60.
Question 5
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−9
M.
Solution
Step 1: Use the relationship between hydroxide ion concentration and pOH to
find the pOH of the solution.
pOH = −log[OH−]
pOH = −log3.0×10−9
pOH ≈ − log(3.0) −(−9 log(10))
pOH ≈0.5229 + 9
pOH ≈9.5229
Step 2: Use the relationship between pOH and pH to find the pH of the
solution.
pH + pOH = 14
pH + 9.5229 = 14
pH = 14 −9.5229
pH ≈4.4771
Therefore, the pH of the solution with a hydroxide ion concentration of
3.0×10−9M is approximately 4.48.
3
Question 6
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall the relationship between hydroxide ion concentration ([OH−])
and the pOH of a solution:
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH = −log2.5×10−4
Step 3: Calculate the pOH by taking the negative logarithm:
pOH = −log2.5×10−4=−(−3.60) = 3.60
Step 4: Remember that the pH of a solution is related to the pOH by the
following equation:
pH + pOH = 14
Step 5: Substitute the calculated pOH into the equation to find the pH:
pH + 3.60 = 14
pH = 14 −3.60 = 10.40
Therefore, the pH of a solution with a hydroxide ion concentration of 2.5×
10−4M is 10.40.
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2 ×10−3
M.
Solution
Step 1: The pH of a solution is defined as the negative logarithm of the hydrogen
ion concentration. The formula is given by:
pH = −log[H+]
4
Given that [H+]=2×10−3M, we can substitute this value into the formula to
find the pH.
pH = −log2×10−3
Step 2: To calculate the pH, we first need to find the value inside the loga-
rithm:
pH = −log(0.002)
Step 3: Next, we simplify the logarithm calculation:
pH = −log2×10−3=−(−3) = 3
Therefore, the pH of the solution with a hydrogen ion concentration of 2 ×
10−3M is 3.
Question 8
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 −log10([H3O+]).
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log10(3.2×10−5)
Step 3: Calculate the pH using a calculator:
pH ≈ − log10(3.2×10−5)≈ −(−4.49485) ≈4.49
Step 4: Therefore, the pH of the solution is approximately 4.49.
Question 9
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
5
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 expression.
Kw= (x)(2.5×10−4)
Step 3: Since the solution is neutral, we can assume that [H+] = [OH−], and
thus x= 2.5×10−4.
Step 4: Calculate the pH using the formula pH = −log[H+].
pH = −log2.5×10−4
Step 5: Perform the calculation to find the pH.
pH = −log2.5×10−4=−(−3.60) = 3.60
Answer: The pH of the solution is 3.60.
Question 10
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 6.3×
10−5M.
Solution
Step 1: Write the expression for the ion product constant of water:
Kw= [H+][OH−]=1.0×10−14
Step 2: Given that [OH−] = 6.3×10−5M, we can solve for [H+]:
[H+] = Kw
[OH−]=1.0×10−14
6.3×10−5
Step 3: Calculate [H+]:
[H+]=1.59 ×10−10 M
Step 4: Calculate the pH using the formula pH =−log[H+]:
pH =−log1.59 ×10−10
Step 5: Calculate the pH:
pH ≈9.80
Therefore, the pH of the solution is approximately 9.80.
6
Question 11
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−8M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−8M, we can
calculate the pH and pOH values.
pH = −log2.5×10−8
pOH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) −log10−8=−log(2.5) −(−8)
Step 4: Use a calculator to find −log(2.5).
−log(2.5) ≈ −0.3979
Step 5: Substitute the value back into the pH equation:
pH ≈ −0.3979 + 8
Step 6: Calculate the pH value:
pH ≈7.6021
Step 7: Calculate the pOH in a similar manner:
pOH = −log2.5×10−8
Step 8: Substitute the value and calculate:
pOH = −log2.5×10−8=−log(2.5) −log10−8=−log(2.5) −(−8)
Step 9: Use a calculator to find −log(2.5).
−log(2.5) ≈ −0.3979
Step 10: Substitute the value back into the pOH equation:
pOH ≈ −0.3979 + 8
Step 11: Calculate the pOH value:
pOH ≈7.6021
Step 12: Therefore, the pH of the solution is approximately 7.60 and the
pOH is approximately 7.60.
7
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the equation: pOH =−log[OH−]
Given: [OH−]=2.5×10−4M
pOH =−log2.5×10−4
pOH ≈ − log(2.5) + log10−4
pOH ≈ − log(2.5) −4
pOH ≈ −0.3979 −4
pOH ≈ −4.3979
Step 2: Calculate the pH of the solution using the equation: pH +pOH = 14
pH + (−4.3979) = 14
pH = 14 + 4.3979
pH ≈18.3979
Therefore, the pH of the solution is approximately 18.40-12.3979, which
equals 3.6021.
Question 13
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 concentration of hydroxide ions to find the concentration of
hydronium ions.
[OH−] = 2.5×10−5M
8
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−5
Step 3: Calculate the pH of the solution.
pH = −log [H+] = −log 1.0×10−14
2.5×10−5
pH = −log 4.0×10−10 = 9.4
Therefore, the pH of the solution is 9.4.
Question 14
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.0×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
Given: [OH−] = 2.0×10−4M
pOH =−log[OH−] = −log2.0×10−4
pOH =−log(2.0) + log10−4=−log(2) −4
pOH ≈2.7
Step 2: Calculate the pOH + pH = 14 for a neutral solution.
pOH + pH = 14
pH = 14 −pOH = 14 −2.7
pH ≈11.3
Therefore, the pH of the solution with a hydroxide ion concentration of
2.0×10−4M is approximately 11.3.
Question 15
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
9
Solution
Step 1: Write the expression for the ion product constant of water:
Kw= [H+][OH−] = 1.0×10−14
Step 2: Given that [OH−] = 1.5×10−3M, we can solve for [H+].
Kw= [H+][OH−] = 1.0×10−14
1.0×10−14 = [H+](1.5×10−3)
[H+] = 1.0×10−14
1.5×10−3
[H+] = 6.67 ×10−12 M
Step 3: Calculate the pH using the formula pH =−log[H+].
pH =−log6.67 ×10−12
pH =−log(6.67) + log10−12
pH =−0.823 + 12
pH = 11.177
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is 11.177.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Write the expression for Kw.
Since: Kw= [H+][OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydronium ion
concentration.
Given: [OH−]=2.5×10−4M
Thus: [H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
Step 3: Calculate the hydronium ion concentration.
Therefore: [H+] = 4.0×10−11 M
10
Step 4: Use the hydronium ion concentration to calculate the pH.
pH = −log[H+]=−log4.0×10−11
Step 5: Calculate the pH.
Therefore: pH = 10.4
Question 17
Question
Calculate the pH of a solution that has a hydronium ion concentration of 1.5×
10−3M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration in a solution:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log1.5×10−3
Step 3: Calculate the pH:
pH = −log1.5×10−3=−log 1.5−log 10−3
Step 4: Simplify the expression:
pH = −log 1.5−(−3)
Step 5: Calculate the pH using a calculator:
pH ≈ −0.176 −(−3) ≈2.824
Step 6: Therefore, the pH of the solution is approximately 2.824.
Question 18
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
11
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration:
pH = −log[H+]
Step 2: Given that the hydrogen ion concentration is 3.2×10−9M, we can
substitute this value into the pH formula:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9
pH = −(−8.49485)
pH ≈8.49
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−9M is approximately 8.49.
Question 19
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.0×
10−4M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Step 1: pOH =−log3.0×10−4=−log 3.0−log 10−4=−0.4771 = 0.48
Step 2: Calculate the pH of the solution using the formula:
pH = 14 −pOH
Step 2: pH = 14 −0.48 = 13.52
Therefore, the pH of the solution is 13.52.
Question 20
Question
Calculate the pH of a 0.025 M hydrochloric acid solution.
12
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Since hydrochloric acid is a strong acid, it completely dissociates
into its ions. Therefore, the concentration of the hydrogen ions (H+) is equal
to the initial concentration of the hydrochloric acid: 0.025 M.
Step 3: Calculate the pH using the formula: pH = −log [H+].
pH = −log (0.025)
Step 4: Calculate the pH.
pH = −log (0.025) = −(−1.60) = 1.60
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.60.
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 4.5×10−5
M.
Solution
Step 1: Recall that the pH is defined as −log[H3O+]. Given the hydronium ion
concentration, we have [H3O+]=4.5×10−5M.
Step 2: Substitute the given value into the formula for pH:
pH = −log4.5×10−5
Step 3: Calculate the negative logarithm:
pH = −log4.5×10−5=−(log 4.5 + log 10−5)
Step 4: Simplify the expression:
pH = −(log 4.5−5) = −(0.6532 −5)
Step 5: Further simplify the expression:
pH = −(−4.3468) = 4.35
Step 6: Therefore, the pH of the solution is 4.35.
13
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Write the expression for the ion product constant of water, Kw.
Step 1: Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration.
Step 2: [H+] = Kw
[OH−]=1.0×10−14
1.5×10−9
Step 3: Calculate the hydrogen ion concentration.
Step 3: [H+] = 6.7×10−6M
Step 4: Calculate the pH of the solution.
Step 4: pH = −log [H+] = −log 6.7×10−6
Step 4: pH ≈5.17
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×
10−4M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH ≈ −(−3.60) = 3.60
Step 4: Therefore, the pH of the solution is 3.60 .
14
Question 24
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 2.5×10−3M, we can calculate the pH using the formula:
pH = −log2.5×10−3
Step 2: Substitute the given value into the formula:
pH = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) −log10−3
Step 4: Simplify the expression:
pH = −log(2.5) −(−3)
Step 5: Using the property of logarithms log(a)−log(b) = log a
b: pH =
−log(2.5) + 3
Step 6: Using a calculator, find the pH:
pH ≈ −0.3979 + 3 ≈2.6021
Step 7: Therefore, the pH of a solution with a hydronium ion concentration
of 2.5×10−3M is approximately 2.60.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M. (Hint: Remember that pH + pOH = 14.)
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH =−log1.5×10−3=−log(1.5)+log10−3=−(log(1.5)−3) = −(log(1.5)−3) ≈2.52
15
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH + 2.52 = 14
pH = 14 −2.52 = 11.48
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 11.48.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: The pH of a solution can be calculated using the formula:
pH = −log[H+]
where [H+] is the hydrogen ion concentration in moles per liter.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 4: Simplify the logarithms using the properties of logarithms:
pH = −(0.5052) −(−5) = 5 −0.5052
Step 5: Finally, calculate the pH of the solution:
pH ≈4.4948
Therefore, the pH of the solution with a hydrogen ion concentration of 3.2×
10−5M is approximately 4.4948.
Question 27
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
16
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration: pH =−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
to find the pH:
pH = −log3.2×10−6
pH = −log(3.2) + log10−6
pH = −(log(3.2) −6)
pH = −(0.5052 −6)
Step 3: Perform the subtraction inside the parentheses:
pH = −(5.4948)
Step 4: Calculate the final pH value:
pH ≈ −5.49
Therefore, the pH of the solution is approximately 5.49.
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 the pH of a solution is defined as the negative base-10
logarithm of the hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the equation:
pH = −log3.5×10−4
Step 3: Calculate the pH of the solution
pH = −log3.5×10−4
pH = −(−3.45593)
pH = 3.46
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.5×10−4M is 3.46.
17
Question 29
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.6×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula pOH =−log[OH−].
pOH =−log3.6×10−4
pOH =−log(3.6) −log10−4
pOH =−(−0.443) −(−4)
pOH = 0.443 + 4
pOH = 4.443
Step 2: Calculate the pH of the solution using the formula pH +pOH = 14.
pH + 4.443 = 14
pH = 14 −4.443
pH = 9.557
Therefore, the pH of a solution with a hydroxide ion concentration of 3.6×
10−4M is 9.557.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log2.5×10−4
pOH =−log(2.5) −log10−4
pOH =−log(2.5) + 4
18
pOH ≈0.60 + 4
pOH ≈4.60
Step 2: Calculate the pH of the solution using the relation:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.60
pH ≈9.40
Therefore, the pH of the solution is approximately 9.40.
Question 31
Question
Calculate the pH of a 0.005 M aqueous solution of hydrochloric acid (HCl).
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl (aq) →H3O+(aq) + Cl−(aq)
Step 2: Calculate the concentration of H3O+ions in the solution. Since
hydrochloric acid is a strong acid, it completely dissociates to give one mole of
H3O+ions for every mole of HCl dissolved. Hence, the concentration of H3O+
ions is 0.005 M.
Step 3: Calculate the pH using the formula:
pH = −log[H3O+]
Substitute the concentration of H3O+ions into the formula:
pH = −log(0.005)
Step 4: Calculate the pH:
pH = −log(0.005) = −(−2.30) = 2.30
Therefore, the pH of a 0.005 M aqueous solution of hydrochloric acid is 2.30.
Question 32
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−5
M.
19
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH =−log[H+] where [H+] is the hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log2.5×10−5
Step 3: Calculate the pH using a calculator:
pH =−log2.5×10−5≈ −(−4.6) ≈4.6
Step 4: Therefore, the pH of the solution is approximately 4.6.
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log1.5×10−5
pOH ≈4.82
Step 2: Calculate the pH of the solution using the relationship between pH
and pOH:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.82
pH ≈9.18
The pH of the solution is approximately 9.18.
Question 34
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
20
Solution
Step 1: Write the expression for the ion product constant of water. The ion
product constant of water (Kw) is equal to 1.0×10−14 at 25
°
C. The expression
for Kwis given by:
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration. Given that [OH−]=1.5×10−3M, we can rearrange the Kw
expression to solve for [H+]:
1.0×10−14 =x(1.5×10−3)
x=1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 3: Calculate the pH of the solution. The pH is calculated using the
equation:
pH = −log[H+]
pH = −log6.67 ×10−12
pH = −log(6.67) −log10−12
pH = −log(6.67) −(−12)
pH ≈ −0.8230 −(−12) = 11.177
The pH of the solution with a hydroxide ion concentration of 1.5×10−3M
is approximately 11.177.
Question 35
Question
Calculate the pH and pOH of a solution with a hydroxide 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: Use the relation [H+][OH−]=1.0×10−14 at 25
°
C to find the
concentration of hydrogen ions in the solution.
[H+] = 1.0×10−14
[OH−]=1.0×10−14
2.5×10−9= 4.0×10−6M
Step 3: Calculate the pH using the formula pH =−log[H+].
pH =−log4.0×10−6=−(−5.4) = 5.4
21
Question 4
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. We are given the concentration
of H3O+as 2.5×10−3M, so we can directly calculate the pH using this formula.
Step 2: Substitute the given concentration into the formula for pH:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3=−(−2.60) = 2.60
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−3M is pH = 2.60.
Question 5
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−9
M.
Solution
Step 1: Use the relationship between hydroxide ion concentration and pOH to
find the pOH of the solution.
pOH = −log[OH−]
pOH = −log3.0×10−9
pOH ≈ − log(3.0) −(−9 log(10))
pOH ≈0.5229 + 9
pOH ≈9.5229
Step 2: Use the relationship between pOH and pH to find the pH of the
solution.
pH + pOH = 14
pH + 9.5229 = 14
pH = 14 −9.5229
pH ≈4.4771
Therefore, the pH of the solution with a hydroxide ion concentration of
3.0×10−9M is approximately 4.48.
3
Question 6
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall the relationship between hydroxide ion concentration ([OH−])
and the pOH of a solution:
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH = −log2.5×10−4
Step 3: Calculate the pOH by taking the negative logarithm:
pOH = −log2.5×10−4=−(−3.60) = 3.60
Step 4: Remember that the pH of a solution is related to the pOH by the
following equation:
pH + pOH = 14
Step 5: Substitute the calculated pOH into the equation to find the pH:
pH + 3.60 = 14
pH = 14 −3.60 = 10.40
Therefore, the pH of a solution with a hydroxide ion concentration of 2.5×
10−4M is 10.40.
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2 ×10−3
M.
Solution
Step 1: The pH of a solution is defined as the negative logarithm of the hydrogen
ion concentration. The formula is given by:
pH = −log[H+]
4
Given that [H+]=2×10−3M, we can substitute this value into the formula to
find the pH.
pH = −log2×10−3
Step 2: To calculate the pH, we first need to find the value inside the loga-
rithm:
pH = −log(0.002)
Step 3: Next, we simplify the logarithm calculation:
pH = −log2×10−3=−(−3) = 3
Therefore, the pH of the solution with a hydrogen ion concentration of 2 ×
10−3M is 3.
Question 8
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 −log10([H3O+]).
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log10(3.2×10−5)
Step 3: Calculate the pH using a calculator:
pH ≈ − log10(3.2×10−5)≈ −(−4.49485) ≈4.49
Step 4: Therefore, the pH of the solution is approximately 4.49.
Question 9
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
5
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 expression.
Kw= (x)(2.5×10−4)
Step 3: Since the solution is neutral, we can assume that [H+] = [OH−], and
thus x= 2.5×10−4.
Step 4: Calculate the pH using the formula pH = −log[H+].
pH = −log2.5×10−4
Step 5: Perform the calculation to find the pH.
pH = −log2.5×10−4=−(−3.60) = 3.60
Answer: The pH of the solution is 3.60.
Question 10
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 6.3×
10−5M.
Solution
Step 1: Write the expression for the ion product constant of water:
Kw= [H+][OH−]=1.0×10−14
Step 2: Given that [OH−] = 6.3×10−5M, we can solve for [H+]:
[H+] = Kw
[OH−]=1.0×10−14
6.3×10−5
Step 3: Calculate [H+]:
[H+]=1.59 ×10−10 M
Step 4: Calculate the pH using the formula pH =−log[H+]:
pH =−log1.59 ×10−10
Step 5: Calculate the pH:
pH ≈9.80
Therefore, the pH of the solution is approximately 9.80.
6
Question 11
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−8M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−8M, we can
calculate the pH and pOH values.
pH = −log2.5×10−8
pOH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) −log10−8=−log(2.5) −(−8)
Step 4: Use a calculator to find −log(2.5).
−log(2.5) ≈ −0.3979
Step 5: Substitute the value back into the pH equation:
pH ≈ −0.3979 + 8
Step 6: Calculate the pH value:
pH ≈7.6021
Step 7: Calculate the pOH in a similar manner:
pOH = −log2.5×10−8
Step 8: Substitute the value and calculate:
pOH = −log2.5×10−8=−log(2.5) −log10−8=−log(2.5) −(−8)
Step 9: Use a calculator to find −log(2.5).
−log(2.5) ≈ −0.3979
Step 10: Substitute the value back into the pOH equation:
pOH ≈ −0.3979 + 8
Step 11: Calculate the pOH value:
pOH ≈7.6021
Step 12: Therefore, the pH of the solution is approximately 7.60 and the
pOH is approximately 7.60.
7
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the equation: pOH =−log[OH−]
Given: [OH−]=2.5×10−4M
pOH =−log2.5×10−4
pOH ≈ − log(2.5) + log10−4
pOH ≈ − log(2.5) −4
pOH ≈ −0.3979 −4
pOH ≈ −4.3979
Step 2: Calculate the pH of the solution using the equation: pH +pOH = 14
pH + (−4.3979) = 14
pH = 14 + 4.3979
pH ≈18.3979
Therefore, the pH of the solution is approximately 18.40-12.3979, which
equals 3.6021.
Question 13
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 concentration of hydroxide ions to find the concentration of
hydronium ions.
[OH−] = 2.5×10−5M
8
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−5
Step 3: Calculate the pH of the solution.
pH = −log [H+] = −log 1.0×10−14
2.5×10−5
pH = −log 4.0×10−10 = 9.4
Therefore, the pH of the solution is 9.4.
Question 14
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.0×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
Given: [OH−] = 2.0×10−4M
pOH =−log[OH−] = −log2.0×10−4
pOH =−log(2.0) + log10−4=−log(2) −4
pOH ≈2.7
Step 2: Calculate the pOH + pH = 14 for a neutral solution.
pOH + pH = 14
pH = 14 −pOH = 14 −2.7
pH ≈11.3
Therefore, the pH of the solution with a hydroxide ion concentration of
2.0×10−4M is approximately 11.3.
Question 15
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
9
Solution
Step 1: Write the expression for the ion product constant of water:
Kw= [H+][OH−] = 1.0×10−14
Step 2: Given that [OH−] = 1.5×10−3M, we can solve for [H+].
Kw= [H+][OH−] = 1.0×10−14
1.0×10−14 = [H+](1.5×10−3)
[H+] = 1.0×10−14
1.5×10−3
[H+] = 6.67 ×10−12 M
Step 3: Calculate the pH using the formula pH =−log[H+].
pH =−log6.67 ×10−12
pH =−log(6.67) + log10−12
pH =−0.823 + 12
pH = 11.177
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is 11.177.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Write the expression for Kw.
Since: Kw= [H+][OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydronium ion
concentration.
Given: [OH−]=2.5×10−4M
Thus: [H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
Step 3: Calculate the hydronium ion concentration.
Therefore: [H+] = 4.0×10−11 M
10
Step 4: Use the hydronium ion concentration to calculate the pH.
pH = −log[H+]=−log4.0×10−11
Step 5: Calculate the pH.
Therefore: pH = 10.4
Question 17
Question
Calculate the pH of a solution that has a hydronium ion concentration of 1.5×
10−3M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration in a solution:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log1.5×10−3
Step 3: Calculate the pH:
pH = −log1.5×10−3=−log 1.5−log 10−3
Step 4: Simplify the expression:
pH = −log 1.5−(−3)
Step 5: Calculate the pH using a calculator:
pH ≈ −0.176 −(−3) ≈2.824
Step 6: Therefore, the pH of the solution is approximately 2.824.
Question 18
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
11
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration:
pH = −log[H+]
Step 2: Given that the hydrogen ion concentration is 3.2×10−9M, we can
substitute this value into the pH formula:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9
pH = −(−8.49485)
pH ≈8.49
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−9M is approximately 8.49.
Question 19
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.0×
10−4M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Step 1: pOH =−log3.0×10−4=−log 3.0−log 10−4=−0.4771 = 0.48
Step 2: Calculate the pH of the solution using the formula:
pH = 14 −pOH
Step 2: pH = 14 −0.48 = 13.52
Therefore, the pH of the solution is 13.52.
Question 20
Question
Calculate the pH of a 0.025 M hydrochloric acid solution.
12
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Since hydrochloric acid is a strong acid, it completely dissociates
into its ions. Therefore, the concentration of the hydrogen ions (H+) is equal
to the initial concentration of the hydrochloric acid: 0.025 M.
Step 3: Calculate the pH using the formula: pH = −log [H+].
pH = −log (0.025)
Step 4: Calculate the pH.
pH = −log (0.025) = −(−1.60) = 1.60
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.60.
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 4.5×10−5
M.
Solution
Step 1: Recall that the pH is defined as −log[H3O+]. Given the hydronium ion
concentration, we have [H3O+]=4.5×10−5M.
Step 2: Substitute the given value into the formula for pH:
pH = −log4.5×10−5
Step 3: Calculate the negative logarithm:
pH = −log4.5×10−5=−(log 4.5 + log 10−5)
Step 4: Simplify the expression:
pH = −(log 4.5−5) = −(0.6532 −5)
Step 5: Further simplify the expression:
pH = −(−4.3468) = 4.35
Step 6: Therefore, the pH of the solution is 4.35.
13
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Write the expression for the ion product constant of water, Kw.
Step 1: Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration.
Step 2: [H+] = Kw
[OH−]=1.0×10−14
1.5×10−9
Step 3: Calculate the hydrogen ion concentration.
Step 3: [H+] = 6.7×10−6M
Step 4: Calculate the pH of the solution.
Step 4: pH = −log [H+] = −log 6.7×10−6
Step 4: pH ≈5.17
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×
10−4M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH ≈ −(−3.60) = 3.60
Step 4: Therefore, the pH of the solution is 3.60 .
14
Question 24
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 2.5×10−3M, we can calculate the pH using the formula:
pH = −log2.5×10−3
Step 2: Substitute the given value into the formula:
pH = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) −log10−3
Step 4: Simplify the expression:
pH = −log(2.5) −(−3)
Step 5: Using the property of logarithms log(a)−log(b) = log a
b: pH =
−log(2.5) + 3
Step 6: Using a calculator, find the pH:
pH ≈ −0.3979 + 3 ≈2.6021
Step 7: Therefore, the pH of a solution with a hydronium ion concentration
of 2.5×10−3M is approximately 2.60.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M. (Hint: Remember that pH + pOH = 14.)
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH =−log1.5×10−3=−log(1.5)+log10−3=−(log(1.5)−3) = −(log(1.5)−3) ≈2.52
15
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH + 2.52 = 14
pH = 14 −2.52 = 11.48
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 11.48.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: The pH of a solution can be calculated using the formula:
pH = −log[H+]
where [H+] is the hydrogen ion concentration in moles per liter.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 4: Simplify the logarithms using the properties of logarithms:
pH = −(0.5052) −(−5) = 5 −0.5052
Step 5: Finally, calculate the pH of the solution:
pH ≈4.4948
Therefore, the pH of the solution with a hydrogen ion concentration of 3.2×
10−5M is approximately 4.4948.
Question 27
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
16
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration: pH =−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
to find the pH:
pH = −log3.2×10−6
pH = −log(3.2) + log10−6
pH = −(log(3.2) −6)
pH = −(0.5052 −6)
Step 3: Perform the subtraction inside the parentheses:
pH = −(5.4948)
Step 4: Calculate the final pH value:
pH ≈ −5.49
Therefore, the pH of the solution is approximately 5.49.
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 the pH of a solution is defined as the negative base-10
logarithm of the hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the equation:
pH = −log3.5×10−4
Step 3: Calculate the pH of the solution
pH = −log3.5×10−4
pH = −(−3.45593)
pH = 3.46
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.5×10−4M is 3.46.
17
Question 29
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.6×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula pOH =−log[OH−].
pOH =−log3.6×10−4
pOH =−log(3.6) −log10−4
pOH =−(−0.443) −(−4)
pOH = 0.443 + 4
pOH = 4.443
Step 2: Calculate the pH of the solution using the formula pH +pOH = 14.
pH + 4.443 = 14
pH = 14 −4.443
pH = 9.557
Therefore, the pH of a solution with a hydroxide ion concentration of 3.6×
10−4M is 9.557.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log2.5×10−4
pOH =−log(2.5) −log10−4
pOH =−log(2.5) + 4
18
pOH ≈0.60 + 4
pOH ≈4.60
Step 2: Calculate the pH of the solution using the relation:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.60
pH ≈9.40
Therefore, the pH of the solution is approximately 9.40.
Question 31
Question
Calculate the pH of a 0.005 M aqueous solution of hydrochloric acid (HCl).
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl (aq) →H3O+(aq) + Cl−(aq)
Step 2: Calculate the concentration of H3O+ions in the solution. Since
hydrochloric acid is a strong acid, it completely dissociates to give one mole of
H3O+ions for every mole of HCl dissolved. Hence, the concentration of H3O+
ions is 0.005 M.
Step 3: Calculate the pH using the formula:
pH = −log[H3O+]
Substitute the concentration of H3O+ions into the formula:
pH = −log(0.005)
Step 4: Calculate the pH:
pH = −log(0.005) = −(−2.30) = 2.30
Therefore, the pH of a 0.005 M aqueous solution of hydrochloric acid is 2.30.
Question 32
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−5
M.
19
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH =−log[H+] where [H+] is the hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log2.5×10−5
Step 3: Calculate the pH using a calculator:
pH =−log2.5×10−5≈ −(−4.6) ≈4.6
Step 4: Therefore, the pH of the solution is approximately 4.6.
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log1.5×10−5
pOH ≈4.82
Step 2: Calculate the pH of the solution using the relationship between pH
and pOH:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.82
pH ≈9.18
The pH of the solution is approximately 9.18.
Question 34
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
20
Solution
Step 1: Write the expression for the ion product constant of water. The ion
product constant of water (Kw) is equal to 1.0×10−14 at 25
°
C. The expression
for Kwis given by:
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration. Given that [OH−]=1.5×10−3M, we can rearrange the Kw
expression to solve for [H+]:
1.0×10−14 =x(1.5×10−3)
x=1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 3: Calculate the pH of the solution. The pH is calculated using the
equation:
pH = −log[H+]
pH = −log6.67 ×10−12
pH = −log(6.67) −log10−12
pH = −log(6.67) −(−12)
pH ≈ −0.8230 −(−12) = 11.177
The pH of the solution with a hydroxide ion concentration of 1.5×10−3M
is approximately 11.177.
Question 35
Question
Calculate the pH and pOH of a solution with a hydroxide 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: Use the relation [H+][OH−]=1.0×10−14 at 25
°
C to find the
concentration of hydrogen ions in the solution.
[H+] = 1.0×10−14
[OH−]=1.0×10−14
2.5×10−9= 4.0×10−6M
Step 3: Calculate the pH using the formula pH =−log[H+].
pH =−log4.0×10−6=−(−5.4) = 5.4
21
Question 4
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. We are given the concentration
of H3O+as 2.5×10−3M, so we can directly calculate the pH using this formula.
Step 2: Substitute the given concentration into the formula for pH:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3=−(−2.60) = 2.60
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−3M is pH = 2.60.
Question 5
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−9
M.
Solution
Step 1: Use the relationship between hydroxide ion concentration and pOH to
find the pOH of the solution.
pOH = −log[OH−]
pOH = −log3.0×10−9
pOH ≈ − log(3.0) −(−9 log(10))
pOH ≈0.5229 + 9
pOH ≈9.5229
Step 2: Use the relationship between pOH and pH to find the pH of the
solution.
pH + pOH = 14
pH + 9.5229 = 14
pH = 14 −9.5229
pH ≈4.4771
Therefore, the pH of the solution with a hydroxide ion concentration of
3.0×10−9M is approximately 4.48.
3
Question 6
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall the relationship between hydroxide ion concentration ([OH−])
and the pOH of a solution:
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula:
pOH = −log2.5×10−4
Step 3: Calculate the pOH by taking the negative logarithm:
pOH = −log2.5×10−4=−(−3.60) = 3.60
Step 4: Remember that the pH of a solution is related to the pOH by the
following equation:
pH + pOH = 14
Step 5: Substitute the calculated pOH into the equation to find the pH:
pH + 3.60 = 14
pH = 14 −3.60 = 10.40
Therefore, the pH of a solution with a hydroxide ion concentration of 2.5×
10−4M is 10.40.
Question 7
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2 ×10−3
M.
Solution
Step 1: The pH of a solution is defined as the negative logarithm of the hydrogen
ion concentration. The formula is given by:
pH = −log[H+]
4
Given that [H+]=2×10−3M, we can substitute this value into the formula to
find the pH.
pH = −log2×10−3
Step 2: To calculate the pH, we first need to find the value inside the loga-
rithm:
pH = −log(0.002)
Step 3: Next, we simplify the logarithm calculation:
pH = −log2×10−3=−(−3) = 3
Therefore, the pH of the solution with a hydrogen ion concentration of 2 ×
10−3M is 3.
Question 8
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 −log10([H3O+]).
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log10(3.2×10−5)
Step 3: Calculate the pH using a calculator:
pH ≈ − log10(3.2×10−5)≈ −(−4.49485) ≈4.49
Step 4: Therefore, the pH of the solution is approximately 4.49.
Question 9
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
5
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 expression.
Kw= (x)(2.5×10−4)
Step 3: Since the solution is neutral, we can assume that [H+] = [OH−], and
thus x= 2.5×10−4.
Step 4: Calculate the pH using the formula pH = −log[H+].
pH = −log2.5×10−4
Step 5: Perform the calculation to find the pH.
pH = −log2.5×10−4=−(−3.60) = 3.60
Answer: The pH of the solution is 3.60.
Question 10
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 6.3×
10−5M.
Solution
Step 1: Write the expression for the ion product constant of water:
Kw= [H+][OH−]=1.0×10−14
Step 2: Given that [OH−] = 6.3×10−5M, we can solve for [H+]:
[H+] = Kw
[OH−]=1.0×10−14
6.3×10−5
Step 3: Calculate [H+]:
[H+]=1.59 ×10−10 M
Step 4: Calculate the pH using the formula pH =−log[H+]:
pH =−log1.59 ×10−10
Step 5: Calculate the pH:
pH ≈9.80
Therefore, the pH of the solution is approximately 9.80.
6
Question 11
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−8M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−8M, we can
calculate the pH and pOH values.
pH = −log2.5×10−8
pOH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) −log10−8=−log(2.5) −(−8)
Step 4: Use a calculator to find −log(2.5).
−log(2.5) ≈ −0.3979
Step 5: Substitute the value back into the pH equation:
pH ≈ −0.3979 + 8
Step 6: Calculate the pH value:
pH ≈7.6021
Step 7: Calculate the pOH in a similar manner:
pOH = −log2.5×10−8
Step 8: Substitute the value and calculate:
pOH = −log2.5×10−8=−log(2.5) −log10−8=−log(2.5) −(−8)
Step 9: Use a calculator to find −log(2.5).
−log(2.5) ≈ −0.3979
Step 10: Substitute the value back into the pOH equation:
pOH ≈ −0.3979 + 8
Step 11: Calculate the pOH value:
pOH ≈7.6021
Step 12: Therefore, the pH of the solution is approximately 7.60 and the
pOH is approximately 7.60.
7
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the equation: pOH =−log[OH−]
Given: [OH−]=2.5×10−4M
pOH =−log2.5×10−4
pOH ≈ − log(2.5) + log10−4
pOH ≈ − log(2.5) −4
pOH ≈ −0.3979 −4
pOH ≈ −4.3979
Step 2: Calculate the pH of the solution using the equation: pH +pOH = 14
pH + (−4.3979) = 14
pH = 14 + 4.3979
pH ≈18.3979
Therefore, the pH of the solution is approximately 18.40-12.3979, which
equals 3.6021.
Question 13
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 concentration of hydroxide ions to find the concentration of
hydronium ions.
[OH−] = 2.5×10−5M
8
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−5
Step 3: Calculate the pH of the solution.
pH = −log [H+] = −log 1.0×10−14
2.5×10−5
pH = −log 4.0×10−10 = 9.4
Therefore, the pH of the solution is 9.4.
Question 14
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.0×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
Given: [OH−] = 2.0×10−4M
pOH =−log[OH−] = −log2.0×10−4
pOH =−log(2.0) + log10−4=−log(2) −4
pOH ≈2.7
Step 2: Calculate the pOH + pH = 14 for a neutral solution.
pOH + pH = 14
pH = 14 −pOH = 14 −2.7
pH ≈11.3
Therefore, the pH of the solution with a hydroxide ion concentration of
2.0×10−4M is approximately 11.3.
Question 15
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
9
Solution
Step 1: Write the expression for the ion product constant of water:
Kw= [H+][OH−] = 1.0×10−14
Step 2: Given that [OH−] = 1.5×10−3M, we can solve for [H+].
Kw= [H+][OH−] = 1.0×10−14
1.0×10−14 = [H+](1.5×10−3)
[H+] = 1.0×10−14
1.5×10−3
[H+] = 6.67 ×10−12 M
Step 3: Calculate the pH using the formula pH =−log[H+].
pH =−log6.67 ×10−12
pH =−log(6.67) + log10−12
pH =−0.823 + 12
pH = 11.177
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is 11.177.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Write the expression for Kw.
Since: Kw= [H+][OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydronium ion
concentration.
Given: [OH−]=2.5×10−4M
Thus: [H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
Step 3: Calculate the hydronium ion concentration.
Therefore: [H+] = 4.0×10−11 M
10
Step 4: Use the hydronium ion concentration to calculate the pH.
pH = −log[H+]=−log4.0×10−11
Step 5: Calculate the pH.
Therefore: pH = 10.4
Question 17
Question
Calculate the pH of a solution that has a hydronium ion concentration of 1.5×
10−3M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration in a solution:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log1.5×10−3
Step 3: Calculate the pH:
pH = −log1.5×10−3=−log 1.5−log 10−3
Step 4: Simplify the expression:
pH = −log 1.5−(−3)
Step 5: Calculate the pH using a calculator:
pH ≈ −0.176 −(−3) ≈2.824
Step 6: Therefore, the pH of the solution is approximately 2.824.
Question 18
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
11
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration:
pH = −log[H+]
Step 2: Given that the hydrogen ion concentration is 3.2×10−9M, we can
substitute this value into the pH formula:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9
pH = −(−8.49485)
pH ≈8.49
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−9M is approximately 8.49.
Question 19
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.0×
10−4M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Step 1: pOH =−log3.0×10−4=−log 3.0−log 10−4=−0.4771 = 0.48
Step 2: Calculate the pH of the solution using the formula:
pH = 14 −pOH
Step 2: pH = 14 −0.48 = 13.52
Therefore, the pH of the solution is 13.52.
Question 20
Question
Calculate the pH of a 0.025 M hydrochloric acid solution.
12
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Since hydrochloric acid is a strong acid, it completely dissociates
into its ions. Therefore, the concentration of the hydrogen ions (H+) is equal
to the initial concentration of the hydrochloric acid: 0.025 M.
Step 3: Calculate the pH using the formula: pH = −log [H+].
pH = −log (0.025)
Step 4: Calculate the pH.
pH = −log (0.025) = −(−1.60) = 1.60
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.60.
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 4.5×10−5
M.
Solution
Step 1: Recall that the pH is defined as −log[H3O+]. Given the hydronium ion
concentration, we have [H3O+]=4.5×10−5M.
Step 2: Substitute the given value into the formula for pH:
pH = −log4.5×10−5
Step 3: Calculate the negative logarithm:
pH = −log4.5×10−5=−(log 4.5 + log 10−5)
Step 4: Simplify the expression:
pH = −(log 4.5−5) = −(0.6532 −5)
Step 5: Further simplify the expression:
pH = −(−4.3468) = 4.35
Step 6: Therefore, the pH of the solution is 4.35.
13
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Write the expression for the ion product constant of water, Kw.
Step 1: Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration.
Step 2: [H+] = Kw
[OH−]=1.0×10−14
1.5×10−9
Step 3: Calculate the hydrogen ion concentration.
Step 3: [H+] = 6.7×10−6M
Step 4: Calculate the pH of the solution.
Step 4: pH = −log [H+] = −log 6.7×10−6
Step 4: pH ≈5.17
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×
10−4M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH ≈ −(−3.60) = 3.60
Step 4: Therefore, the pH of the solution is 3.60 .
14
Question 24
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Given that the hydronium
ion concentration is 2.5×10−3M, we can calculate the pH using the formula:
pH = −log2.5×10−3
Step 2: Substitute the given value into the formula:
pH = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) −log10−3
Step 4: Simplify the expression:
pH = −log(2.5) −(−3)
Step 5: Using the property of logarithms log(a)−log(b) = log a
b: pH =
−log(2.5) + 3
Step 6: Using a calculator, find the pH:
pH ≈ −0.3979 + 3 ≈2.6021
Step 7: Therefore, the pH of a solution with a hydronium ion concentration
of 2.5×10−3M is approximately 2.60.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M. (Hint: Remember that pH + pOH = 14.)
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH =−log1.5×10−3=−log(1.5)+log10−3=−(log(1.5)−3) = −(log(1.5)−3) ≈2.52
15
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH + 2.52 = 14
pH = 14 −2.52 = 11.48
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 11.48.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: The pH of a solution can be calculated using the formula:
pH = −log[H+]
where [H+] is the hydrogen ion concentration in moles per liter.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 4: Simplify the logarithms using the properties of logarithms:
pH = −(0.5052) −(−5) = 5 −0.5052
Step 5: Finally, calculate the pH of the solution:
pH ≈4.4948
Therefore, the pH of the solution with a hydrogen ion concentration of 3.2×
10−5M is approximately 4.4948.
Question 27
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
16
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration: pH =−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
to find the pH:
pH = −log3.2×10−6
pH = −log(3.2) + log10−6
pH = −(log(3.2) −6)
pH = −(0.5052 −6)
Step 3: Perform the subtraction inside the parentheses:
pH = −(5.4948)
Step 4: Calculate the final pH value:
pH ≈ −5.49
Therefore, the pH of the solution is approximately 5.49.
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 the pH of a solution is defined as the negative base-10
logarithm of the hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the equation:
pH = −log3.5×10−4
Step 3: Calculate the pH of the solution
pH = −log3.5×10−4
pH = −(−3.45593)
pH = 3.46
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.5×10−4M is 3.46.
17
Question 29
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.6×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula pOH =−log[OH−].
pOH =−log3.6×10−4
pOH =−log(3.6) −log10−4
pOH =−(−0.443) −(−4)
pOH = 0.443 + 4
pOH = 4.443
Step 2: Calculate the pH of the solution using the formula pH +pOH = 14.
pH + 4.443 = 14
pH = 14 −4.443
pH = 9.557
Therefore, the pH of a solution with a hydroxide ion concentration of 3.6×
10−4M is 9.557.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log2.5×10−4
pOH =−log(2.5) −log10−4
pOH =−log(2.5) + 4
18
pOH ≈0.60 + 4
pOH ≈4.60
Step 2: Calculate the pH of the solution using the relation:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.60
pH ≈9.40
Therefore, the pH of the solution is approximately 9.40.
Question 31
Question
Calculate the pH of a 0.005 M aqueous solution of hydrochloric acid (HCl).
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl (aq) →H3O+(aq) + Cl−(aq)
Step 2: Calculate the concentration of H3O+ions in the solution. Since
hydrochloric acid is a strong acid, it completely dissociates to give one mole of
H3O+ions for every mole of HCl dissolved. Hence, the concentration of H3O+
ions is 0.005 M.
Step 3: Calculate the pH using the formula:
pH = −log[H3O+]
Substitute the concentration of H3O+ions into the formula:
pH = −log(0.005)
Step 4: Calculate the pH:
pH = −log(0.005) = −(−2.30) = 2.30
Therefore, the pH of a 0.005 M aqueous solution of hydrochloric acid is 2.30.
Question 32
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−5
M.
19
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH =−log[H+] where [H+] is the hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log2.5×10−5
Step 3: Calculate the pH using a calculator:
pH =−log2.5×10−5≈ −(−4.6) ≈4.6
Step 4: Therefore, the pH of the solution is approximately 4.6.
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
pOH =−log1.5×10−5
pOH ≈4.82
Step 2: Calculate the pH of the solution using the relationship between pH
and pOH:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.82
pH ≈9.18
The pH of the solution is approximately 9.18.
Question 34
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
20
Solution
Step 1: Write the expression for the ion product constant of water. The ion
product constant of water (Kw) is equal to 1.0×10−14 at 25
°
C. The expression
for Kwis given by:
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration. Given that [OH−]=1.5×10−3M, we can rearrange the Kw
expression to solve for [H+]:
1.0×10−14 =x(1.5×10−3)
x=1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 3: Calculate the pH of the solution. The pH is calculated using the
equation:
pH = −log[H+]
pH = −log6.67 ×10−12
pH = −log(6.67) −log10−12
pH = −log(6.67) −(−12)
pH ≈ −0.8230 −(−12) = 11.177
The pH of the solution with a hydroxide ion concentration of 1.5×10−3M
is approximately 11.177.
Question 35
Question
Calculate the pH and pOH of a solution with a hydroxide 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: Use the relation [H+][OH−]=1.0×10−14 at 25
°
C to find the
concentration of hydrogen ions in the solution.
[H+] = 1.0×10−14
[OH−]=1.0×10−14
2.5×10−9= 4.0×10−6M
Step 3: Calculate the pH using the formula pH =−log[H+].
pH =−log4.0×10−6=−(−5.4) = 5.4
21
Step 4: Calculate the pOH using the formula pOH =−log[OH−].
pOH =−log2.5×10−9=−(−8.6) = 8.6
Step 5: Therefore, the pH of the solution is 5.4 and the pOH of the solution
is 8.6.
22
