CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 10
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−4
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.2×10−4
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−4
pH = −log(3.2) + log10−4
pH = −0.5051 + 4
pH = 3.4949
Step 4: Therefore, the pH of the solution is 3.49.
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 pH is defined as −log[H+]. Given that the hydrogen ion
concentration is 2.5×10−5M, we can plug this into the formula to find the pH.
pH = −log2.5×10−5
Step 2: Calculate the pH using the formula.
pH = −log2.5×10−5=−log(2.5) + log10−5
Step 3: Recall that −log(2.5) ≈ −0.3979, so the previous expression simpli-
fies to:
pH ≈ −(−0.3979) −5=0.3979 −5
Step 4: Finally, calculate the pH of the solution.
pH ≈0.3979 −5 = −4.6021
Therefore, the pH of the solution is approximately 4.60.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5 ×10−4
M.
Solution
Step 1: Write the expression for pOH and convert the given hydroxide ion
concentration to pOH. We know that pOH =−log[OH−].
pOH =−log5×10−4
pOH ≈3.3
Step 2: Use the relationship between pH and pOH to find pH. Since pH +
pOH = 14, we have pH = 14 −pOH.
pH = 14 −3.3
pH ≈10.7
Thus, the pH of the solution is approximately 10.7.
2
Question 4
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the pH is calculated using the formula
pH = −log[H+].
Given that the hydrogen ion concentration is 3.2×10−5M, we can substitute
this value into the formula to find the pH.
Step 2: Calculate the pH using the formula:
pH = −log3.2×10−5=−log(3.2) −log10−5.
Step 3: Since log10−5=−5, the expression simplifies to
pH = −log(3.2) −(−5) = −log(3.2) + 5.
Step 4: Using a calculator, we find that log(3.2) ≈0.505. Therefore,
pH ≈ −0.505 + 5 = 4.495.
Step 5: To find the pOH, we can use the relationship between pH and pOH
in a neutral solution:
pH + pOH = 14.
Step 6: Since the solution is acidic, the pOH can be calculated by rearranging
the equation:
pOH = 14 −pH.
Step 7: Plug in the calculated pH value to find the pOH:
pOH = 14 −4.495 = 9.505.
Step 8: Therefore, the pH of the solution is approximately 4.495 and the
pOH is approximately 9.505.
Question 5
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.6×10−3
M.
3
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Given that [OH−]=5.6×10−3M, we have:
pOH =−log5.6×10−3
pOH =−log(5.6) + log10−3
pOH =−(−0.7482) + (−3)
pOH = 0.7482 −3
pOH =−2.2518
Step 2: Calculate the pH of the solution using the relationship between pH
and pOH:
pH +pOH = 14
Substitute the known value of pOH into the equation to solve for pH:
pH −2.2518 = 14
pH = 14 + 2.2518
pH = 16.2518
Therefore, the pH of the solution with a hydroxide ion concentration of
5.6×10−3M is approximately 16.25.
Question 6
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 base-10 logarithm of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given value of the hydronium ion concentration into
the formula:
pH = −log2.5×10−3
4
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) + log10−3=−log(2.5) −3
Step 4: Use a calculator to find the value of log(2.5) ≈0.3979:
pH ≈ −(0.3979) −3≈ −0.3979 −3≈ −3.3979
Step 5: Therefore, the pH of the solution is approximately 3.40.
Question 7
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration given to find the concentration
of hydrogen ions.
Kw= [H+][3.2×10−5] = 1.0×10−14
[H+] = 1.0×10−14
3.2×10−5
[H+] = 3.125 ×10−10
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions.
pH = −log[H+]=−log3.125 ×10−10
pH = −(log(3.125) + log10−10)
pH = −(−0.505 + (−10))
pH = 0.505 + 10 = 10.505
Therefore, the pH of the solution is 10.505.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
5
Solution
Step 1: Recall that pH is defined as −log[H3O+] where [H3O+] is the concen-
tration of hydronium ions in the solution.
Step 2: Given that the concentration of hydronium ions is 3.2×10−5M, we
can calculate the pH as follows:
pH = −log3.2×10−5
Step 3: Performing the calculation:
pH = −log3.2×10−5=−log 3.2−log 10−5=−log 3.2+5
Step 4: Using the property of logarithms that log AB = log A+ log B, we
simplify the expression further:
pH = −log 3.2 + 5 = −(log 3 + log 10) + 5 = −(log 3 + 1) + 5
Step 5: Finally, evaluating the expression:
pH = −(log 3 + 1) + 5 ≈ −(≈0.48 + 1) + 5 ≈ −(1.48) + 5 ≈ −1.48 + 5 ≈3.52
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 3.52.
Question 9
Question
Calculate the pH of a 0.025 M hydrochloric acid solution. (Kw= 1.0×10−14 )
Solution
Step 1: Write the balanced chemical equation for the ionization of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Identify the initial concentration of the acid, which is 0.025 M. Since
hydrochloric acid is a strong acid, it completely ionizes to form H+ions and
Cl−ions.
Step 3: Calculate the concentration of H+ions in the solution:
[H+]=0.025 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
Step 5: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
6
Step 6: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−(−1.6) = 1.6
Therefore, the pH of the 0.025 M hydrochloric acid solution is 1.6.
Question 10
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
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 = −log2.5×10−8
Step 3: Calculate the pH using a calculator:
pH ≈ − log2.5×10−8≈ −(−7.60) ≈7.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.60.
Question 11
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+]. Given that the concentration
of H3O+is 3.5×10−4M, we can plug this value into the formula to find the
pH.
pH = −log3.5×10−4
Step 2: Calculate the pH using the given concentration.
pH = −log3.5×10−4=−log(3.5)+log10−4=−(−0.5441)+(−4) = 0.5441−4 = −3.4559
Step 3: Therefore, the pH of the solution is −3.46.
7
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−5
M.
Solution
Step 1: Write the chemical equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Calculate the concentration of hydrogen ions using the ion product
constant for water:
Kw= [H+][OH−]=1.0×10−14
[H+] = Kw
[OH−]=1.0×10−14
3.5×10−5= 2.857 ×10−10 M
Step 3: Calculate the pH using the formula:
pH = −log[H+] = −log2.857 ×10−10=−(log 2.857+log 10−10 ) = −(log 2.857−10) = −(−9.545) = 9.545
Therefore, the pH of the solution is 9.545.
Question 13
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH is defined as the negative base-10 logarithm of the
hydrogen ion concentration. The formula for pH is given by:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−5≈ −(log 3.2 + log 10−5)
pH ≈ −(log 3.2−5) ≈ −(0.5051 −5) ≈ −(−4.4949)
pH ≈4.4949
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately 4.49.
8
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
where [H+] represents the concentration of hydronium ions in the solution.
Step 2: Substituting the given hydronium ion concentration into the formula,
we get:
pH = −log1.5×10−3
Step 3: Use a calculator to evaluate the logarithm:
pH = −log1.5×10−3=−log(1.5) + log10−3
Step 4: Given that log(1.5) ≈0.1761 and log10−3=−3, we have:
pH = −0.1761 −3
Step 5: Simplifying, we get:
pH = −3.1761
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 3.1761.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9≈ − log(3.2) + 9 ≈ −0.5052 + 9 ≈8.4948
Step 4: Therefore, the pH of the solution is approximately 8.49.
9
Question 16
Question
Calculate the pH of a solution that has a concentration of hydroxide ions, OH−,
of 1.5×10−4M.
Solution
Given that the concentration of hydroxide ions is 1.5×10−4M, we can use the
relationship between pOH and pH to find the pH of the solution.
Step 1: Calculate the pOH of the solution using the formula:
pOH = −logOH−=−log1.5×10−4
pOH ≈3.82
Step 2: Use the following relationship between pH and pOH to find the pH
of the solution:
pH + pOH = 14
pH = 14 −3.82
pH ≈10.18
Therefore, the pH of the solution with a concentration of hydroxide ions of
1.5×10−4M is approximately 10.18.
Question 17
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in moles per liter.
Step 2: Given that the hydrogen ion concentration is 3.5×10−5M, we can
plug this value into the pH formula:
pH = −log3.5×10−5
Step 3: Calculate the pH:
pH = −log3.5×10−5=−log(3.5) + log10−5
Step 4: Recall that log10−5=−5, so we have:
pH = −log(3.5) −5
10
Step 5: Using a calculator, find log(3.5) ≈0.5441. Therefore:
pH = −0.5441 −5
Step 6: Finally, calculate the pH:
pH ≈ −5.5441
Step 7: Therefore, the pH of the solution is approximately 5.54.
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration, [H3O+]. The formula for calculating pH is:
pH = −log [H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log 3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−5
Step 4: Recall that log(10n) = n, we simplify the expression further:
pH = −log(3.2) −(−5)
Step 5: Calculate log(3.2) ≈0.5052 using a calculator:
pH = −0.5052 + 5
Step 6: Finally, calculate the pH of the solution:
pH ≈4.4948
Thus, the pH of the solution with a hydronium ion concentration of 3.2×10−5
M is approximately 4.49.
11
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.75×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. First, determine the concen-
tration of hydronium ions given in the problem.
[H3O+]=3.75 ×10−5M
Step 2: Substitute the given concentration into the formula for pH.
pH = −log3.75 ×10−5
Step 3: Calculate the pH using a calculator.
pH = −log3.75 ×10−5≈ − log(3.75) = −(−0.425) ≈0.425
Answer: The pH of the solution is approximately 0.425.
Question 20
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+]. Given that the hydrogen ion
concentration is 1.5×10−9M, we can calculate the pH as follows:
pH = −log1.5×10−9
Step 2: Substitute the given value into the formula and calculate the pH:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 3: Now, calculate the pH:
pH = −log(1.5) −log10−9=−0.1761 −(−9) = 8.8239
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 1.5×10−9M is 8.82.
12
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. In this case, the concentration of
H3O+is 3.2×10−5M. We can calculate the pH by taking the negative logarithm
of this concentration.
pH = −log3.2×10−5
pH = −log(3.2) −log10−5
pH = −log(3.2) −(−5)
pH = −0.5052 −(−5)
pH ≈4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
Question 22
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.0×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Given that [H+] = 3.0×10−4
M, we can calculate the pH using the formula −log3.0×10−4.
Step 2: Substitute the concentration of hydronium ions into the formula:
pH = −log3.0×10−4
Step 3: Calculate the pH:
pH = −log3.0×10−4=−log(3.0) + log10−4=−0.4771 + 4 = 3.5229
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 3.0×10−4M is approximately 3.52.
13
Question 23
Question
A 0.025 M solution of hydrochloric acid (HCl) has a pH of 2.85. Calculate the
pOH of the solution.
Solution
Step 1: Recall the definition of pH and pOH.
The pH of a solution is given by the formula pH = −log[H+].
The pOH of a solution is related to pH by the formula pOH = 14 −pH.
Step 2: Calculate the concentration of H+ions in the solution using the pH
value.
pH = −log[H+]
2.85 = −log[H+]
[H+] = 10−2.85
[H+] = 1.41 ×10−3M
Step 3: Calculate the pOH of the solution using the concentration of H+
ions.
pOH = 14 −pH
pOH = 14 −2.85
pOH = 11.15
Step 4: Therefore, the pOH of the 0.025 M hydrochloric acid solution with
a pH of 2.85 is 11.15.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
14
Solution
Step 1: Write the expression for the ion product constant of water.
Kw = [H+][OH−]
Step 2: Since Kw is a constant at a given temperature (25
°
C), we can use it
to find the hydrogen ion concentration.
Kw = (1.0×10−14) = [H+](2.5×10−5)
Step 3: Solve for the hydrogen ion concentration.
∴[H+] = 1.0×10−14
2.5×10−5
Step 4: Calculate the hydrogen ion concentration.
∴[H+] = 4.0×10−10 M
Step 5: Calculate the pH using the formula pH =−log[H+].
∴pH =−log4.0×10−10
Step 6: Calculate the pH of the solution.
∴pH =−(log 4.0 + log 10−10) = −(−9.39794000867)
Step 7: Round the pH to two decimal places.
∴pH ≈9.40
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−5M is approximately 9.40.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Write the expression for the ion product constant of water (Kw).
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the hydroxide ion concentration given to calculate the concen-
tration of hydronium ions.
[OH−]=1.5×10−3M
15
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−3≈6.67 ×10−12 M
Step 3: Calculate the pH of the solution.
pH = −log [H+] = −log (6.67 ×10−12)≈11.18
Therefore, the pH of the solution is approximately 11.18.
Question 26
Question
Calculate the pOH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pOH of a solution is defined as the negative base-10
logarithm of the hydroxide ion concentration (OH −) in moles per liter.
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the equation.
pOH = −log2.5×10−3
Step 3: Calculate the pOH.
pOH = −log2.5×10−3=−log(2.5) −log10−3=−0.3979 −(−3) = 2.6021
Step 4: Therefore, the pOH of the solution is 2.6021.
Question 27
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH = −log[OH−]
Given that [OH−]=3.5×10−4M, we have:
pOH = −log3.5×10−4
16
pOH ≈ − log(3.5) + 4
pOH ≈3.46
Step 2: Calculate the pH of the solution using the formula:
pH + pOH = 14
Since we know the pOH from Step 1, we can find the pH:
pH + 3.46 = 14
pH = 14 −3.46
pH ≈10.54
Therefore, the pH of the solution is approximately 10.54.
Question 28
Question
A solution has a hydroxide ion concentration of 7.5×10−6M. Calculate the pH
of the solution.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −log7.5×10−6
pOH ≈5.12
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH = 14 −5.12
pH ≈8.88
Therefore, the pH of the solution is approximately 8.88.
Question 29
Question
Calculate the pH of a solution with a concentration of hydroxide ions [OH−] =
2.0×10−5M.
17
Solution
Step 1: Use the relationship between [OH−] and [H+] to find the concentration
of hydronium ions.
Kw= [H+][OH−]=1.0×10−14
[H+] = 1.0×10−14
2.0×10−5= 5.0×10−10 M
Step 2: Calculate the pH using the formula pH =−log[H+].
pH =−log5.0×10−10=−(log(5.0)+log10−10) = −(0.69897−10) = 9.30103
Therefore, the pH of the solution is 9.30103.
Question 30
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration, so we can use the formula:
pH = −log[H+]
Step 2: Plug in the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using the given concentration:
pH = −log3.2×10−5=−log(3.2)+log10−5=−(−0.505)−5=0.505−5 = −4.495
Step 4: Therefore, the pH of a solution with a hydrogen ion concentration
of 3.2×10−5M is −4.495 .
Question 31
Question
Find the pH and pOH of a solution with a hydroxide ion concentration of 3.98×
10−6M.
18
Solution
Step 1: Start by using the equation Kw= [H+][OH−] to find the concentration
of H+ions in the solution:
Kw= (1.0×10−14) = [H+][OH−]
1.0×10−14 = [H+](3.98 ×10−6)
[H+] = 1.0×10−14
3.98 ×10−6
[H+]=2.51 ×10−9M
Step 2: Calculate the pH using the formula pH =−log [H+].
pH =−log2.51 ×10−9
pH ≈8.60
Step 3: Calculate the pOH using the formula pOH =−log [OH−].
pOH =−log3.98 ×10−6
pOH ≈5.40
Therefore, the pH of the solution is approximately 8.60 and the pOH of the
solution is approximately 5.40.
Question 32
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl).
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 dissociates completely
into ions. Therefore, the concentration of H+ions in the solution is equal to the
initial concentration of HCl, which is 0.025 M.
Step 3: Calculate the pH of the solution using the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
Step 5: Calculate the pH:
pH = −log(0.025) = 1.6
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.6.
19
Question 33
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. So, we can calculate the pH
using the given hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) −log10−8
Step 4: Since log10−8=−8, we have:
pH = −log(2.5) −(−8) = −log(2.5) + 8
Step 5: Now, using a calculator, find the value of −log(2.5):
pH ≈ − log(2.5) + 8 ≈ −0.3979 + 8 ≈7.6021
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.6021.
Question 34
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 5.8×
10−4M.
Solution
Step 1: Use the relationship between pOH and pH.
pOH =−log[OH−] and pH = 14 −pOH
Step 2: Calculate the pOH of the solution using the given hydroxide ion
concentration.
pOH =−log5.8×10−4= 3.24
Step 3: Calculate the pH of the solution using the pOH value.
pH = 14 −3.24 = 10.76
Therefore, the pH of the solution is 10.76.
20
Question 35
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+].
Given that [H3O+] = 3.2×10−4M, we can calculate the pH using the formula:
pH = −log3.2×10−4
Step 2: Substitute the value of [H3O+] into the formula:
pH = −log3.2×10−4
Step 3: Calculate the pH:
pH = −log3.2×10−4=−log(3.2) −log10−4
Step 4: Simplify the expression:
pH = −log(3.2) −(−4) = −log(3.2) + 4
Step 5: Using a calculator, find the value of −log(3.2):
−log(3.2) ≈ −0.5052
Step 6: Substitute this value back into the formula for pH:
pH = −0.5052 + 4 = 3.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−4M is approximately 3.49.
21
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 pH is defined as −log[H+]. Given that the hydrogen ion
concentration is 2.5×10−5M, we can plug this into the formula to find the pH.
pH = −log2.5×10−5
Step 2: Calculate the pH using the formula.
pH = −log2.5×10−5=−log(2.5) + log10−5
Step 3: Recall that −log(2.5) ≈ −0.3979, so the previous expression simpli-
fies to:
pH ≈ −(−0.3979) −5=0.3979 −5
Step 4: Finally, calculate the pH of the solution.
pH ≈0.3979 −5 = −4.6021
Therefore, the pH of the solution is approximately 4.60.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5 ×10−4
M.
Solution
Step 1: Write the expression for pOH and convert the given hydroxide ion
concentration to pOH. We know that pOH =−log[OH−].
pOH =−log5×10−4
pOH ≈3.3
Step 2: Use the relationship between pH and pOH to find pH. Since pH +
pOH = 14, we have pH = 14 −pOH.
pH = 14 −3.3
pH ≈10.7
Thus, the pH of the solution is approximately 10.7.
2
Question 4
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the pH is calculated using the formula
pH = −log[H+].
Given that the hydrogen ion concentration is 3.2×10−5M, we can substitute
this value into the formula to find the pH.
Step 2: Calculate the pH using the formula:
pH = −log3.2×10−5=−log(3.2) −log10−5.
Step 3: Since log10−5=−5, the expression simplifies to
pH = −log(3.2) −(−5) = −log(3.2) + 5.
Step 4: Using a calculator, we find that log(3.2) ≈0.505. Therefore,
pH ≈ −0.505 + 5 = 4.495.
Step 5: To find the pOH, we can use the relationship between pH and pOH
in a neutral solution:
pH + pOH = 14.
Step 6: Since the solution is acidic, the pOH can be calculated by rearranging
the equation:
pOH = 14 −pH.
Step 7: Plug in the calculated pH value to find the pOH:
pOH = 14 −4.495 = 9.505.
Step 8: Therefore, the pH of the solution is approximately 4.495 and the
pOH is approximately 9.505.
Question 5
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.6×10−3
M.
3
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Given that [OH−]=5.6×10−3M, we have:
pOH =−log5.6×10−3
pOH =−log(5.6) + log10−3
pOH =−(−0.7482) + (−3)
pOH = 0.7482 −3
pOH =−2.2518
Step 2: Calculate the pH of the solution using the relationship between pH
and pOH:
pH +pOH = 14
Substitute the known value of pOH into the equation to solve for pH:
pH −2.2518 = 14
pH = 14 + 2.2518
pH = 16.2518
Therefore, the pH of the solution with a hydroxide ion concentration of
5.6×10−3M is approximately 16.25.
Question 6
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 base-10 logarithm of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given value of the hydronium ion concentration into
the formula:
pH = −log2.5×10−3
4
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) + log10−3=−log(2.5) −3
Step 4: Use a calculator to find the value of log(2.5) ≈0.3979:
pH ≈ −(0.3979) −3≈ −0.3979 −3≈ −3.3979
Step 5: Therefore, the pH of the solution is approximately 3.40.
Question 7
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration given to find the concentration
of hydrogen ions.
Kw= [H+][3.2×10−5] = 1.0×10−14
[H+] = 1.0×10−14
3.2×10−5
[H+] = 3.125 ×10−10
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions.
pH = −log[H+]=−log3.125 ×10−10
pH = −(log(3.125) + log10−10)
pH = −(−0.505 + (−10))
pH = 0.505 + 10 = 10.505
Therefore, the pH of the solution is 10.505.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
5
Solution
Step 1: Recall that pH is defined as −log[H3O+] where [H3O+] is the concen-
tration of hydronium ions in the solution.
Step 2: Given that the concentration of hydronium ions is 3.2×10−5M, we
can calculate the pH as follows:
pH = −log3.2×10−5
Step 3: Performing the calculation:
pH = −log3.2×10−5=−log 3.2−log 10−5=−log 3.2+5
Step 4: Using the property of logarithms that log AB = log A+ log B, we
simplify the expression further:
pH = −log 3.2 + 5 = −(log 3 + log 10) + 5 = −(log 3 + 1) + 5
Step 5: Finally, evaluating the expression:
pH = −(log 3 + 1) + 5 ≈ −(≈0.48 + 1) + 5 ≈ −(1.48) + 5 ≈ −1.48 + 5 ≈3.52
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 3.52.
Question 9
Question
Calculate the pH of a 0.025 M hydrochloric acid solution. (Kw= 1.0×10−14 )
Solution
Step 1: Write the balanced chemical equation for the ionization of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Identify the initial concentration of the acid, which is 0.025 M. Since
hydrochloric acid is a strong acid, it completely ionizes to form H+ions and
Cl−ions.
Step 3: Calculate the concentration of H+ions in the solution:
[H+]=0.025 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
Step 5: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
6
Step 6: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−(−1.6) = 1.6
Therefore, the pH of the 0.025 M hydrochloric acid solution is 1.6.
Question 10
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
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 = −log2.5×10−8
Step 3: Calculate the pH using a calculator:
pH ≈ − log2.5×10−8≈ −(−7.60) ≈7.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.60.
Question 11
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+]. Given that the concentration
of H3O+is 3.5×10−4M, we can plug this value into the formula to find the
pH.
pH = −log3.5×10−4
Step 2: Calculate the pH using the given concentration.
pH = −log3.5×10−4=−log(3.5)+log10−4=−(−0.5441)+(−4) = 0.5441−4 = −3.4559
Step 3: Therefore, the pH of the solution is −3.46.
7
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−5
M.
Solution
Step 1: Write the chemical equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Calculate the concentration of hydrogen ions using the ion product
constant for water:
Kw= [H+][OH−]=1.0×10−14
[H+] = Kw
[OH−]=1.0×10−14
3.5×10−5= 2.857 ×10−10 M
Step 3: Calculate the pH using the formula:
pH = −log[H+] = −log2.857 ×10−10=−(log 2.857+log 10−10 ) = −(log 2.857−10) = −(−9.545) = 9.545
Therefore, the pH of the solution is 9.545.
Question 13
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH is defined as the negative base-10 logarithm of the
hydrogen ion concentration. The formula for pH is given by:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−5≈ −(log 3.2 + log 10−5)
pH ≈ −(log 3.2−5) ≈ −(0.5051 −5) ≈ −(−4.4949)
pH ≈4.4949
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately 4.49.
8
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
where [H+] represents the concentration of hydronium ions in the solution.
Step 2: Substituting the given hydronium ion concentration into the formula,
we get:
pH = −log1.5×10−3
Step 3: Use a calculator to evaluate the logarithm:
pH = −log1.5×10−3=−log(1.5) + log10−3
Step 4: Given that log(1.5) ≈0.1761 and log10−3=−3, we have:
pH = −0.1761 −3
Step 5: Simplifying, we get:
pH = −3.1761
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 3.1761.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9≈ − log(3.2) + 9 ≈ −0.5052 + 9 ≈8.4948
Step 4: Therefore, the pH of the solution is approximately 8.49.
9
Question 16
Question
Calculate the pH of a solution that has a concentration of hydroxide ions, OH−,
of 1.5×10−4M.
Solution
Given that the concentration of hydroxide ions is 1.5×10−4M, we can use the
relationship between pOH and pH to find the pH of the solution.
Step 1: Calculate the pOH of the solution using the formula:
pOH = −logOH−=−log1.5×10−4
pOH ≈3.82
Step 2: Use the following relationship between pH and pOH to find the pH
of the solution:
pH + pOH = 14
pH = 14 −3.82
pH ≈10.18
Therefore, the pH of the solution with a concentration of hydroxide ions of
1.5×10−4M is approximately 10.18.
Question 17
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in moles per liter.
Step 2: Given that the hydrogen ion concentration is 3.5×10−5M, we can
plug this value into the pH formula:
pH = −log3.5×10−5
Step 3: Calculate the pH:
pH = −log3.5×10−5=−log(3.5) + log10−5
Step 4: Recall that log10−5=−5, so we have:
pH = −log(3.5) −5
10
Step 5: Using a calculator, find log(3.5) ≈0.5441. Therefore:
pH = −0.5441 −5
Step 6: Finally, calculate the pH:
pH ≈ −5.5441
Step 7: Therefore, the pH of the solution is approximately 5.54.
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration, [H3O+]. The formula for calculating pH is:
pH = −log [H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log 3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−5
Step 4: Recall that log(10n) = n, we simplify the expression further:
pH = −log(3.2) −(−5)
Step 5: Calculate log(3.2) ≈0.5052 using a calculator:
pH = −0.5052 + 5
Step 6: Finally, calculate the pH of the solution:
pH ≈4.4948
Thus, the pH of the solution with a hydronium ion concentration of 3.2×10−5
M is approximately 4.49.
11
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.75×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. First, determine the concen-
tration of hydronium ions given in the problem.
[H3O+]=3.75 ×10−5M
Step 2: Substitute the given concentration into the formula for pH.
pH = −log3.75 ×10−5
Step 3: Calculate the pH using a calculator.
pH = −log3.75 ×10−5≈ − log(3.75) = −(−0.425) ≈0.425
Answer: The pH of the solution is approximately 0.425.
Question 20
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+]. Given that the hydrogen ion
concentration is 1.5×10−9M, we can calculate the pH as follows:
pH = −log1.5×10−9
Step 2: Substitute the given value into the formula and calculate the pH:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 3: Now, calculate the pH:
pH = −log(1.5) −log10−9=−0.1761 −(−9) = 8.8239
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 1.5×10−9M is 8.82.
12
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. In this case, the concentration of
H3O+is 3.2×10−5M. We can calculate the pH by taking the negative logarithm
of this concentration.
pH = −log3.2×10−5
pH = −log(3.2) −log10−5
pH = −log(3.2) −(−5)
pH = −0.5052 −(−5)
pH ≈4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
Question 22
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.0×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Given that [H+] = 3.0×10−4
M, we can calculate the pH using the formula −log3.0×10−4.
Step 2: Substitute the concentration of hydronium ions into the formula:
pH = −log3.0×10−4
Step 3: Calculate the pH:
pH = −log3.0×10−4=−log(3.0) + log10−4=−0.4771 + 4 = 3.5229
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 3.0×10−4M is approximately 3.52.
13
Question 23
Question
A 0.025 M solution of hydrochloric acid (HCl) has a pH of 2.85. Calculate the
pOH of the solution.
Solution
Step 1: Recall the definition of pH and pOH.
The pH of a solution is given by the formula pH = −log[H+].
The pOH of a solution is related to pH by the formula pOH = 14 −pH.
Step 2: Calculate the concentration of H+ions in the solution using the pH
value.
pH = −log[H+]
2.85 = −log[H+]
[H+] = 10−2.85
[H+] = 1.41 ×10−3M
Step 3: Calculate the pOH of the solution using the concentration of H+
ions.
pOH = 14 −pH
pOH = 14 −2.85
pOH = 11.15
Step 4: Therefore, the pOH of the 0.025 M hydrochloric acid solution with
a pH of 2.85 is 11.15.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
14
Solution
Step 1: Write the expression for the ion product constant of water.
Kw = [H+][OH−]
Step 2: Since Kw is a constant at a given temperature (25
°
C), we can use it
to find the hydrogen ion concentration.
Kw = (1.0×10−14) = [H+](2.5×10−5)
Step 3: Solve for the hydrogen ion concentration.
∴[H+] = 1.0×10−14
2.5×10−5
Step 4: Calculate the hydrogen ion concentration.
∴[H+] = 4.0×10−10 M
Step 5: Calculate the pH using the formula pH =−log[H+].
∴pH =−log4.0×10−10
Step 6: Calculate the pH of the solution.
∴pH =−(log 4.0 + log 10−10) = −(−9.39794000867)
Step 7: Round the pH to two decimal places.
∴pH ≈9.40
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−5M is approximately 9.40.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Write the expression for the ion product constant of water (Kw).
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the hydroxide ion concentration given to calculate the concen-
tration of hydronium ions.
[OH−]=1.5×10−3M
15
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−3≈6.67 ×10−12 M
Step 3: Calculate the pH of the solution.
pH = −log [H+] = −log (6.67 ×10−12)≈11.18
Therefore, the pH of the solution is approximately 11.18.
Question 26
Question
Calculate the pOH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pOH of a solution is defined as the negative base-10
logarithm of the hydroxide ion concentration (OH −) in moles per liter.
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the equation.
pOH = −log2.5×10−3
Step 3: Calculate the pOH.
pOH = −log2.5×10−3=−log(2.5) −log10−3=−0.3979 −(−3) = 2.6021
Step 4: Therefore, the pOH of the solution is 2.6021.
Question 27
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH = −log[OH−]
Given that [OH−]=3.5×10−4M, we have:
pOH = −log3.5×10−4
16
pOH ≈ − log(3.5) + 4
pOH ≈3.46
Step 2: Calculate the pH of the solution using the formula:
pH + pOH = 14
Since we know the pOH from Step 1, we can find the pH:
pH + 3.46 = 14
pH = 14 −3.46
pH ≈10.54
Therefore, the pH of the solution is approximately 10.54.
Question 28
Question
A solution has a hydroxide ion concentration of 7.5×10−6M. Calculate the pH
of the solution.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −log7.5×10−6
pOH ≈5.12
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH = 14 −5.12
pH ≈8.88
Therefore, the pH of the solution is approximately 8.88.
Question 29
Question
Calculate the pH of a solution with a concentration of hydroxide ions [OH−] =
2.0×10−5M.
17
Solution
Step 1: Use the relationship between [OH−] and [H+] to find the concentration
of hydronium ions.
Kw= [H+][OH−]=1.0×10−14
[H+] = 1.0×10−14
2.0×10−5= 5.0×10−10 M
Step 2: Calculate the pH using the formula pH =−log[H+].
pH =−log5.0×10−10=−(log(5.0)+log10−10) = −(0.69897−10) = 9.30103
Therefore, the pH of the solution is 9.30103.
Question 30
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration, so we can use the formula:
pH = −log[H+]
Step 2: Plug in the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using the given concentration:
pH = −log3.2×10−5=−log(3.2)+log10−5=−(−0.505)−5=0.505−5 = −4.495
Step 4: Therefore, the pH of a solution with a hydrogen ion concentration
of 3.2×10−5M is −4.495 .
Question 31
Question
Find the pH and pOH of a solution with a hydroxide ion concentration of 3.98×
10−6M.
18
Solution
Step 1: Start by using the equation Kw= [H+][OH−] to find the concentration
of H+ions in the solution:
Kw= (1.0×10−14) = [H+][OH−]
1.0×10−14 = [H+](3.98 ×10−6)
[H+] = 1.0×10−14
3.98 ×10−6
[H+]=2.51 ×10−9M
Step 2: Calculate the pH using the formula pH =−log [H+].
pH =−log2.51 ×10−9
pH ≈8.60
Step 3: Calculate the pOH using the formula pOH =−log [OH−].
pOH =−log3.98 ×10−6
pOH ≈5.40
Therefore, the pH of the solution is approximately 8.60 and the pOH of the
solution is approximately 5.40.
Question 32
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl).
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 dissociates completely
into ions. Therefore, the concentration of H+ions in the solution is equal to the
initial concentration of HCl, which is 0.025 M.
Step 3: Calculate the pH of the solution using the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
Step 5: Calculate the pH:
pH = −log(0.025) = 1.6
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.6.
19
Question 33
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. So, we can calculate the pH
using the given hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) −log10−8
Step 4: Since log10−8=−8, we have:
pH = −log(2.5) −(−8) = −log(2.5) + 8
Step 5: Now, using a calculator, find the value of −log(2.5):
pH ≈ − log(2.5) + 8 ≈ −0.3979 + 8 ≈7.6021
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.6021.
Question 34
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 5.8×
10−4M.
Solution
Step 1: Use the relationship between pOH and pH.
pOH =−log[OH−] and pH = 14 −pOH
Step 2: Calculate the pOH of the solution using the given hydroxide ion
concentration.
pOH =−log5.8×10−4= 3.24
Step 3: Calculate the pH of the solution using the pOH value.
pH = 14 −3.24 = 10.76
Therefore, the pH of the solution is 10.76.
20
Question 35
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+].
Given that [H3O+] = 3.2×10−4M, we can calculate the pH using the formula:
pH = −log3.2×10−4
Step 2: Substitute the value of [H3O+] into the formula:
pH = −log3.2×10−4
Step 3: Calculate the pH:
pH = −log3.2×10−4=−log(3.2) −log10−4
Step 4: Simplify the expression:
pH = −log(3.2) −(−4) = −log(3.2) + 4
Step 5: Using a calculator, find the value of −log(3.2):
−log(3.2) ≈ −0.5052
Step 6: Substitute this value back into the formula for pH:
pH = −0.5052 + 4 = 3.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−4M is approximately 3.49.
21
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 pH is defined as −log[H+]. Given that the hydrogen ion
concentration is 2.5×10−5M, we can plug this into the formula to find the pH.
pH = −log2.5×10−5
Step 2: Calculate the pH using the formula.
pH = −log2.5×10−5=−log(2.5) + log10−5
Step 3: Recall that −log(2.5) ≈ −0.3979, so the previous expression simpli-
fies to:
pH ≈ −(−0.3979) −5=0.3979 −5
Step 4: Finally, calculate the pH of the solution.
pH ≈0.3979 −5 = −4.6021
Therefore, the pH of the solution is approximately 4.60.
Question 3
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5 ×10−4
M.
Solution
Step 1: Write the expression for pOH and convert the given hydroxide ion
concentration to pOH. We know that pOH =−log[OH−].
pOH =−log5×10−4
pOH ≈3.3
Step 2: Use the relationship between pH and pOH to find pH. Since pH +
pOH = 14, we have pH = 14 −pOH.
pH = 14 −3.3
pH ≈10.7
Thus, the pH of the solution is approximately 10.7.
2
Question 4
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the pH is calculated using the formula
pH = −log[H+].
Given that the hydrogen ion concentration is 3.2×10−5M, we can substitute
this value into the formula to find the pH.
Step 2: Calculate the pH using the formula:
pH = −log3.2×10−5=−log(3.2) −log10−5.
Step 3: Since log10−5=−5, the expression simplifies to
pH = −log(3.2) −(−5) = −log(3.2) + 5.
Step 4: Using a calculator, we find that log(3.2) ≈0.505. Therefore,
pH ≈ −0.505 + 5 = 4.495.
Step 5: To find the pOH, we can use the relationship between pH and pOH
in a neutral solution:
pH + pOH = 14.
Step 6: Since the solution is acidic, the pOH can be calculated by rearranging
the equation:
pOH = 14 −pH.
Step 7: Plug in the calculated pH value to find the pOH:
pOH = 14 −4.495 = 9.505.
Step 8: Therefore, the pH of the solution is approximately 4.495 and the
pOH is approximately 9.505.
Question 5
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.6×10−3
M.
3
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Given that [OH−]=5.6×10−3M, we have:
pOH =−log5.6×10−3
pOH =−log(5.6) + log10−3
pOH =−(−0.7482) + (−3)
pOH = 0.7482 −3
pOH =−2.2518
Step 2: Calculate the pH of the solution using the relationship between pH
and pOH:
pH +pOH = 14
Substitute the known value of pOH into the equation to solve for pH:
pH −2.2518 = 14
pH = 14 + 2.2518
pH = 16.2518
Therefore, the pH of the solution with a hydroxide ion concentration of
5.6×10−3M is approximately 16.25.
Question 6
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 base-10 logarithm of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given value of the hydronium ion concentration into
the formula:
pH = −log2.5×10−3
4
Step 3: Calculate the pH:
pH = −log2.5×10−3=−log(2.5) + log10−3=−log(2.5) −3
Step 4: Use a calculator to find the value of log(2.5) ≈0.3979:
pH ≈ −(0.3979) −3≈ −0.3979 −3≈ −3.3979
Step 5: Therefore, the pH of the solution is approximately 3.40.
Question 7
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration given to find the concentration
of hydrogen ions.
Kw= [H+][3.2×10−5] = 1.0×10−14
[H+] = 1.0×10−14
3.2×10−5
[H+] = 3.125 ×10−10
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions.
pH = −log[H+]=−log3.125 ×10−10
pH = −(log(3.125) + log10−10)
pH = −(−0.505 + (−10))
pH = 0.505 + 10 = 10.505
Therefore, the pH of the solution is 10.505.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
5
Solution
Step 1: Recall that pH is defined as −log[H3O+] where [H3O+] is the concen-
tration of hydronium ions in the solution.
Step 2: Given that the concentration of hydronium ions is 3.2×10−5M, we
can calculate the pH as follows:
pH = −log3.2×10−5
Step 3: Performing the calculation:
pH = −log3.2×10−5=−log 3.2−log 10−5=−log 3.2+5
Step 4: Using the property of logarithms that log AB = log A+ log B, we
simplify the expression further:
pH = −log 3.2 + 5 = −(log 3 + log 10) + 5 = −(log 3 + 1) + 5
Step 5: Finally, evaluating the expression:
pH = −(log 3 + 1) + 5 ≈ −(≈0.48 + 1) + 5 ≈ −(1.48) + 5 ≈ −1.48 + 5 ≈3.52
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 3.52.
Question 9
Question
Calculate the pH of a 0.025 M hydrochloric acid solution. (Kw= 1.0×10−14 )
Solution
Step 1: Write the balanced chemical equation for the ionization of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Identify the initial concentration of the acid, which is 0.025 M. Since
hydrochloric acid is a strong acid, it completely ionizes to form H+ions and
Cl−ions.
Step 3: Calculate the concentration of H+ions in the solution:
[H+]=0.025 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
Step 5: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
6
Step 6: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−(−1.6) = 1.6
Therefore, the pH of the 0.025 M hydrochloric acid solution is 1.6.
Question 10
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
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 = −log2.5×10−8
Step 3: Calculate the pH using a calculator:
pH ≈ − log2.5×10−8≈ −(−7.60) ≈7.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.60.
Question 11
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+]. Given that the concentration
of H3O+is 3.5×10−4M, we can plug this value into the formula to find the
pH.
pH = −log3.5×10−4
Step 2: Calculate the pH using the given concentration.
pH = −log3.5×10−4=−log(3.5)+log10−4=−(−0.5441)+(−4) = 0.5441−4 = −3.4559
Step 3: Therefore, the pH of the solution is −3.46.
7
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−5
M.
Solution
Step 1: Write the chemical equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Calculate the concentration of hydrogen ions using the ion product
constant for water:
Kw= [H+][OH−]=1.0×10−14
[H+] = Kw
[OH−]=1.0×10−14
3.5×10−5= 2.857 ×10−10 M
Step 3: Calculate the pH using the formula:
pH = −log[H+] = −log2.857 ×10−10=−(log 2.857+log 10−10 ) = −(log 2.857−10) = −(−9.545) = 9.545
Therefore, the pH of the solution is 9.545.
Question 13
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH is defined as the negative base-10 logarithm of the
hydrogen ion concentration. The formula for pH is given by:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−5≈ −(log 3.2 + log 10−5)
pH ≈ −(log 3.2−5) ≈ −(0.5051 −5) ≈ −(−4.4949)
pH ≈4.4949
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately 4.49.
8
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
where [H+] represents the concentration of hydronium ions in the solution.
Step 2: Substituting the given hydronium ion concentration into the formula,
we get:
pH = −log1.5×10−3
Step 3: Use a calculator to evaluate the logarithm:
pH = −log1.5×10−3=−log(1.5) + log10−3
Step 4: Given that log(1.5) ≈0.1761 and log10−3=−3, we have:
pH = −0.1761 −3
Step 5: Simplifying, we get:
pH = −3.1761
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 3.1761.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula to
find the pH:
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−9≈ − log(3.2) + 9 ≈ −0.5052 + 9 ≈8.4948
Step 4: Therefore, the pH of the solution is approximately 8.49.
9
Question 16
Question
Calculate the pH of a solution that has a concentration of hydroxide ions, OH−,
of 1.5×10−4M.
Solution
Given that the concentration of hydroxide ions is 1.5×10−4M, we can use the
relationship between pOH and pH to find the pH of the solution.
Step 1: Calculate the pOH of the solution using the formula:
pOH = −logOH−=−log1.5×10−4
pOH ≈3.82
Step 2: Use the following relationship between pH and pOH to find the pH
of the solution:
pH + pOH = 14
pH = 14 −3.82
pH ≈10.18
Therefore, the pH of the solution with a concentration of hydroxide ions of
1.5×10−4M is approximately 10.18.
Question 17
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.5×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in moles per liter.
Step 2: Given that the hydrogen ion concentration is 3.5×10−5M, we can
plug this value into the pH formula:
pH = −log3.5×10−5
Step 3: Calculate the pH:
pH = −log3.5×10−5=−log(3.5) + log10−5
Step 4: Recall that log10−5=−5, so we have:
pH = −log(3.5) −5
10
Step 5: Using a calculator, find log(3.5) ≈0.5441. Therefore:
pH = −0.5441 −5
Step 6: Finally, calculate the pH:
pH ≈ −5.5441
Step 7: Therefore, the pH of the solution is approximately 5.54.
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration, [H3O+]. The formula for calculating pH is:
pH = −log [H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log 3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−5
Step 4: Recall that log(10n) = n, we simplify the expression further:
pH = −log(3.2) −(−5)
Step 5: Calculate log(3.2) ≈0.5052 using a calculator:
pH = −0.5052 + 5
Step 6: Finally, calculate the pH of the solution:
pH ≈4.4948
Thus, the pH of the solution with a hydronium ion concentration of 3.2×10−5
M is approximately 4.49.
11
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.75×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. First, determine the concen-
tration of hydronium ions given in the problem.
[H3O+]=3.75 ×10−5M
Step 2: Substitute the given concentration into the formula for pH.
pH = −log3.75 ×10−5
Step 3: Calculate the pH using a calculator.
pH = −log3.75 ×10−5≈ − log(3.75) = −(−0.425) ≈0.425
Answer: The pH of the solution is approximately 0.425.
Question 20
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+]. Given that the hydrogen ion
concentration is 1.5×10−9M, we can calculate the pH as follows:
pH = −log1.5×10−9
Step 2: Substitute the given value into the formula and calculate the pH:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 3: Now, calculate the pH:
pH = −log(1.5) −log10−9=−0.1761 −(−9) = 8.8239
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 1.5×10−9M is 8.82.
12
Question 21
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. In this case, the concentration of
H3O+is 3.2×10−5M. We can calculate the pH by taking the negative logarithm
of this concentration.
pH = −log3.2×10−5
pH = −log(3.2) −log10−5
pH = −log(3.2) −(−5)
pH = −0.5052 −(−5)
pH ≈4.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−5M is approximately 4.49.
Question 22
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.0×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Given that [H+] = 3.0×10−4
M, we can calculate the pH using the formula −log3.0×10−4.
Step 2: Substitute the concentration of hydronium ions into the formula:
pH = −log3.0×10−4
Step 3: Calculate the pH:
pH = −log3.0×10−4=−log(3.0) + log10−4=−0.4771 + 4 = 3.5229
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 3.0×10−4M is approximately 3.52.
13
Question 23
Question
A 0.025 M solution of hydrochloric acid (HCl) has a pH of 2.85. Calculate the
pOH of the solution.
Solution
Step 1: Recall the definition of pH and pOH.
The pH of a solution is given by the formula pH = −log[H+].
The pOH of a solution is related to pH by the formula pOH = 14 −pH.
Step 2: Calculate the concentration of H+ions in the solution using the pH
value.
pH = −log[H+]
2.85 = −log[H+]
[H+] = 10−2.85
[H+] = 1.41 ×10−3M
Step 3: Calculate the pOH of the solution using the concentration of H+
ions.
pOH = 14 −pH
pOH = 14 −2.85
pOH = 11.15
Step 4: Therefore, the pOH of the 0.025 M hydrochloric acid solution with
a pH of 2.85 is 11.15.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
14
Solution
Step 1: Write the expression for the ion product constant of water.
Kw = [H+][OH−]
Step 2: Since Kw is a constant at a given temperature (25
°
C), we can use it
to find the hydrogen ion concentration.
Kw = (1.0×10−14) = [H+](2.5×10−5)
Step 3: Solve for the hydrogen ion concentration.
∴[H+] = 1.0×10−14
2.5×10−5
Step 4: Calculate the hydrogen ion concentration.
∴[H+] = 4.0×10−10 M
Step 5: Calculate the pH using the formula pH =−log[H+].
∴pH =−log4.0×10−10
Step 6: Calculate the pH of the solution.
∴pH =−(log 4.0 + log 10−10) = −(−9.39794000867)
Step 7: Round the pH to two decimal places.
∴pH ≈9.40
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−5M is approximately 9.40.
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Write the expression for the ion product constant of water (Kw).
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the hydroxide ion concentration given to calculate the concen-
tration of hydronium ions.
[OH−]=1.5×10−3M
15
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−3≈6.67 ×10−12 M
Step 3: Calculate the pH of the solution.
pH = −log [H+] = −log (6.67 ×10−12)≈11.18
Therefore, the pH of the solution is approximately 11.18.
Question 26
Question
Calculate the pOH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pOH of a solution is defined as the negative base-10
logarithm of the hydroxide ion concentration (OH −) in moles per liter.
pOH = −log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the equation.
pOH = −log2.5×10−3
Step 3: Calculate the pOH.
pOH = −log2.5×10−3=−log(2.5) −log10−3=−0.3979 −(−3) = 2.6021
Step 4: Therefore, the pOH of the solution is 2.6021.
Question 27
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−4
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH = −log[OH−]
Given that [OH−]=3.5×10−4M, we have:
pOH = −log3.5×10−4
16
pOH ≈ − log(3.5) + 4
pOH ≈3.46
Step 2: Calculate the pH of the solution using the formula:
pH + pOH = 14
Since we know the pOH from Step 1, we can find the pH:
pH + 3.46 = 14
pH = 14 −3.46
pH ≈10.54
Therefore, the pH of the solution is approximately 10.54.
Question 28
Question
A solution has a hydroxide ion concentration of 7.5×10−6M. Calculate the pH
of the solution.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −log7.5×10−6
pOH ≈5.12
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH = 14 −5.12
pH ≈8.88
Therefore, the pH of the solution is approximately 8.88.
Question 29
Question
Calculate the pH of a solution with a concentration of hydroxide ions [OH−] =
2.0×10−5M.
17
Solution
Step 1: Use the relationship between [OH−] and [H+] to find the concentration
of hydronium ions.
Kw= [H+][OH−]=1.0×10−14
[H+] = 1.0×10−14
2.0×10−5= 5.0×10−10 M
Step 2: Calculate the pH using the formula pH =−log[H+].
pH =−log5.0×10−10=−(log(5.0)+log10−10) = −(0.69897−10) = 9.30103
Therefore, the pH of the solution is 9.30103.
Question 30
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration, so we can use the formula:
pH = −log[H+]
Step 2: Plug in the given hydrogen ion concentration into the formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using the given concentration:
pH = −log3.2×10−5=−log(3.2)+log10−5=−(−0.505)−5=0.505−5 = −4.495
Step 4: Therefore, the pH of a solution with a hydrogen ion concentration
of 3.2×10−5M is −4.495 .
Question 31
Question
Find the pH and pOH of a solution with a hydroxide ion concentration of 3.98×
10−6M.
18
Solution
Step 1: Start by using the equation Kw= [H+][OH−] to find the concentration
of H+ions in the solution:
Kw= (1.0×10−14) = [H+][OH−]
1.0×10−14 = [H+](3.98 ×10−6)
[H+] = 1.0×10−14
3.98 ×10−6
[H+]=2.51 ×10−9M
Step 2: Calculate the pH using the formula pH =−log [H+].
pH =−log2.51 ×10−9
pH ≈8.60
Step 3: Calculate the pOH using the formula pOH =−log [OH−].
pOH =−log3.98 ×10−6
pOH ≈5.40
Therefore, the pH of the solution is approximately 8.60 and the pOH of the
solution is approximately 5.40.
Question 32
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl).
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 dissociates completely
into ions. Therefore, the concentration of H+ions in the solution is equal to the
initial concentration of HCl, which is 0.025 M.
Step 3: Calculate the pH of the solution using the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
Step 5: Calculate the pH:
pH = −log(0.025) = 1.6
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.6.
19
Question 33
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. So, we can calculate the pH
using the given hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−8
Step 3: Calculate the pH:
pH = −log2.5×10−8=−log(2.5) −log10−8
Step 4: Since log10−8=−8, we have:
pH = −log(2.5) −(−8) = −log(2.5) + 8
Step 5: Now, using a calculator, find the value of −log(2.5):
pH ≈ − log(2.5) + 8 ≈ −0.3979 + 8 ≈7.6021
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−8M is approximately 7.6021.
Question 34
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 5.8×
10−4M.
Solution
Step 1: Use the relationship between pOH and pH.
pOH =−log[OH−] and pH = 14 −pOH
Step 2: Calculate the pOH of the solution using the given hydroxide ion
concentration.
pOH =−log5.8×10−4= 3.24
Step 3: Calculate the pH of the solution using the pOH value.
pH = 14 −3.24 = 10.76
Therefore, the pH of the solution is 10.76.
20
Question 35
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+].
Given that [H3O+] = 3.2×10−4M, we can calculate the pH using the formula:
pH = −log3.2×10−4
Step 2: Substitute the value of [H3O+] into the formula:
pH = −log3.2×10−4
Step 3: Calculate the pH:
pH = −log3.2×10−4=−log(3.2) −log10−4
Step 4: Simplify the expression:
pH = −log(3.2) −(−4) = −log(3.2) + 4
Step 5: Using a calculator, find the value of −log(3.2):
−log(3.2) ≈ −0.5052
Step 6: Substitute this value back into the formula for pH:
pH = −0.5052 + 4 = 3.4948
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−4M is approximately 3.49.
21
