CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 9
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH is calculated using the formula: pH = −log[H+],
where [H+] is the concentration of hydronium ions in the solution.
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
substitute this value into the formula to find the pH:
pH = −log3.2×10−5
Step 3: Using the properties of logarithms, we can simplify this expression:
pH = −log(3.2) −log10−5
Step 4: We know that log10−5=−5, so we can further simplify the
expression:
pH = −log(3.2) −(−5)
Step 5: Continuing to simplify, we have:
pH = −log(3.2) + 5
Step 6: Finally, using a calculator to evaluate log(3.2), we find:
pH ≈ −0.5052 + 5
Step 7: Therefore, the pH of the solution is approximately pH ≈4.495.
Question 2
Question
Calculate the pH and pOH of a solution with a hydroxide ion concentration of
1.5×10−8M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −logOH−=−log1.5×10−8
Step 2: Solve for pOH:
pOH = −log1.5×10−8=−(log(1.5) + log10−8) = −(log(1.5) −8) ≈6.82
Step 3: Use the relationship between pH and pOH to find the pH of the
solution:
pH + pOH = 14
Step 4: Calculate pH:
pH = 14 −pOH = 14 −6.82 ≈7.18
Therefore, the pH of the solution is approximately 7.18 and the pOH is
approximately 6.82.
Question 3
Question
Calculate the pH of a solution with a hydrogen ion concentration of 5.0×10−4
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log5.0×10−4
Step 3: Calculate the pH using a calculator:
pH = −log5.0×10−4
2
pH = −log(5.0) −log10−4
pH = −(log(5.0) + log10−4)
pH = −(log(5.0) −4)
pH = −(log(5.0) −4) ≈3.3
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 5.0×10−4M is approximately 3.3.
Question 4
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+], where [H+] is the hydrogen ion
concentration.
pH = −log2.5×10−8
Step 2: Substitute the given hydrogen ion concentration into the formula.
pH = −log2.5×10−8
Step 3: Use the properties of logarithms to simplify the expression.
pH = −log(2.5) −log10−8
Step 4: Recall that log(10x) = x, so log10−8=−8.
pH = −log(2.5) −(−8)
Step 5: Use a calculator to find the value of log(2.5) ≈0.39794.
pH = −0.39794 + 8
Step 6: Finally, calculate the pH of the solution.
pH ≈7.60
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−8M is approximately 7.60.
3
Question 5
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+].
Step 2: Given that the hydronium ion concentration is 2.5×10−6M, we can
plug this value into the pH formula.
pH = −log2.5×10−6
Step 3: Calculate the pH.
pH = −log2.5×10−6=−log(2.5) −log10−6
Step 4: Use the property of logarithms log(a×b) = log(a) + log(b).
pH = −log(2.5) −log10−6=−log(2.5) −(−6) = −log(2.5) + 6
Step 5: Calculate the final value of pH.
pH ≈ −0.3979 + 6 ≈5.6021
Therefore, the pH of a solution with a hydronium ion concentration of 2.5×
10−6M is approximately 5.60.
Question 6
Question
Calculate the pH of a solution with a hydroxide ion concentration of 8.25×10−4
M.
Solution
Step 1: Write the expression for Kw.
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration using Kw.
Kw= (8.25 ×10−4)[H+]
1.0×10−14 = (8.25 ×10−4)[H+]
4
[H+] = 1.0×10−14
8.25 ×10−4
[H+] = 1.21 ×10−11 M
Step 3: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+]
pH = −log1.21 ×10−11
pH = 10.9
Therefore, the pH of the solution is 10.9.
Question 7
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 1.5×10−8M.
Solution
Step 1: Recall that the pH and pOH of a solution are related to the hydrogen ion
concentration ([H+]) and hydroxide ion concentration ([OH−]) by the equations:
pH = −log[H+]
pOH = −log[OH−]
and
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 1.5×10−8M, we can
calculate the pH as follows:
pH = −log1.5×10−8
Step 3: Using a calculator, we find:
pH ≈ − log1.5×10−8≈ −(−7.823130) ≈7.823
Step 4: Now, we can calculate the pOH using the relation pH + pOH = 14:
pOH = 14 −pH
Step 5: Substituting the calculated pH value, we get:
pOH = 14 −7.823
Step 6: Therefore, using a calculator, we find:
pOH = 14 −7.823 = 6.177
Step 7: The pH of the solution is approximately 7.823 and the pOH is
approximately 6.177.
5
Question 8
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1 ×10−3
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH =−log[H+]. Since [H+] = 1 ×10−3M, we can calculate the pH as follows:
Step 1: pH =−log1×10−3=−log10−3=−(−3) = 3
Therefore, the pH of the solution is 3.
Question 9
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−9
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to calculate the concen-
tration of hydronium ions.
[OH−] = 3.5×10−9M
[H+] = Kw
[OH−]=1.0×10−14
3.5×10−9
[H+] = 2.857 ×10−6M
Step 3: Calculate the pH of the solution.
pH = −log[H+]=−log2.857 ×10−6
pH = −log(2.857) + log10−6
pH = 5.545 + 6
pH = 11.545
Therefore, the pH of the solution is 11.545.
6
Question 10
Question
Calculate the pH of a solution with a 5.0×10−3M concentration of hydrochloric
acid (HCl).
Solution
Step 1: Write the balanced equation for the dissociation of hydrochloric acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Determine the concentration of H+ions formed from the dissociation
of HCl. Since HCl is a strong acid, it dissociates completely. Therefore, the
concentration of H+ions is equal to the initial concentration of HCl, which is
5.0×10−3M.
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
Step 4: Substitute the value of [H+] into the equation:
pH = −log5.0×10−3
pH = −log(5.0) + log10−3
pH = −log(5.0) −3 log(10)
pH = −log(5.0) −3×1
pH = −log(5.0) −3
pH = −0.69897 −3
pH = −3.69897
Therefore, the pH of a solution with 5.0×10−3M HCl is approximately 3.70.
Question 11
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
7
Solution
Step 1: Recall the relationship between pH, pOH, hydrogen ion concentration,
and hydroxide ion concentration:
pH = −log[H+]
pOH = −log[OH−]
Also, for water at 25
°
C, [H+]×[OH−] = 1.0×10−14 M2.
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9
pH = −(log(2.5) + 9) ≈ −12.60
Step 3: Next, we can calculate the pOH using the relationship between pH
and pOH:
pH + pOH = 14
pOH = 14 −pH = 14 + 12.60 ≈1.40
Therefore, the pH of the solution is approximately 12.60 and the pOH is
approximately 1.40.
Question 12
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= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the expression.
Kw= 1.0×10−14 = (x)(1.5×10−3)
Step 3: Solve for the concentration of hydronium ions (x).
x=1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 4: Calculate the pH using the formula pH =−logH+.
pH =−log6.67 ×10−12=−log(6.67) −log10−12= 11.18
Therefore, the pH of the solution is 11.18.
8
Question 13
Question
Calculate the pH of a solution with a pOH of 2.83.
Solution
Step 1: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 2.83 = 14
Step 3: Solve for pH:
pH = 14 −2.83
pH = 11.17
Step 4: Therefore, the pH of the solution is 11.17.
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the definition of pH. The pH 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 formula.
Plugging in the given hydronium ion concentration:
pH = −log3.2×10−5
Step 3: Calculate the pH. Using a calculator, find the pH value:
pH = −log3.2×10−5≈4.495
Therefore, the pH of the solution is approximately 4.495.
9
Question 15
Question
Calculate the pH of a 0.025 M nitric acid (HNO3) solution. Given that the
dissociation constant (Ka) of nitric acid is 1.2×10−5.
Solution
Step 1: Write the balanced chemical equation for the dissociation of nitric acid:
HNO3→H++ NO−
3
Step 2: Write the expression for the acid dissociation constant (Ka):
Ka=[H+][NO−
3]
[HNO3]
Step 3: Since nitric acid is a strong acid, it completely dissociates in solution.
Therefore, the concentration of HNO3is equal to the concentration of H+ions
which is 0.025 M.
Step 4: Substitute the given values into the Kaexpression:
1.2×10−5=x×x
0.025
1.2×10−5=x2
0.025
Step 5: Solve for x, the concentration of H+ions:
x2= 0.025 ×1.2×10−5
x2= 3 ×10−7
x=p3×10−7
x= 5.48 ×10−4M
Step 6: Calculate the pH using the concentration of H+ions:
pH = −log5.48 ×10−4
pH = −log(5.48) + log10−4
pH = −(log(5.48) −4)
pH ≈3.26
Therefore, the pH of a 0.025 M nitric acid solution is approximately 3.26.
10
Question 16
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−9
Step 3: Calculate the pH:
pH = −log2.5×10−9=−(log(2.5) + log10−9)
Step 4: Remember that log10−9=−9:
pH = −(0.3979 + (−9)) = 9 −0.3979 = 8.6021
Step 5: Therefore, the pH of a solution with a hydrogen ion concentration
of 2.5×10−9M is approximately 8.60.
Question 17
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.2×10−9
Step 3: Use a calculator to evaluate the logarithm:
pH ≈ − log(3.2) + log10−9
pH ≈ −0.5052 −9
pH ≈ −9.5052
Step 4: Round the pH value to the appropriate number of significant figures:
pH ≈ −9.5
Therefore, the pH of the solution is approximately 9.5.
11
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall that the pH is defined as −log[H+]. We are given the concentra-
tion of hydronium ions, so we can directly substitute this value into the formula
to find the pH.
pH = −log2.5×10−8
Step 2: Calculate the pH by taking the negative logarithm of the given
hydronium ion concentration.
pH = −log2.5×10−8=−(log 2.5 + log 10−8)
Step 3: Keep in mind that log 10−8=−8 due to the logarithmic property
log10 x=−y⇐⇒ x= 10−y. Substitute this back into the equation to simplify
further.
pH = −(log 2.5−8)
Step 4: Use a calculator to find the pH of the solution.
pH ≈ −(log 2.5−8) ≈ −0.3979 ≈0.40
Therefore, the pH of the solution is approximately 0.40.
Question 19
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the relationship between pH, pOH, and hydronium ion
concentration is given by:
pH = −log[H3O+]
pOH = −log[OH−]
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
directly substitute this value into the formula for pH:
pH = −log3.2×10−5
12
Step 3: Calculate the pH:
pH = −log3.2×10−5=−(log 3.2 + log 10−5) = −(log 3.2−5)
Step 4: Evaluate the pH:
pH = −(log 3.2−5) ≈ −(≈0.505 −5) ≈ −(−4.495) ≈4.495
Step 5: Now, calculate the pOH using the hydronium ion concentration:
[OH−] = 1 mol
Kw[H3O+]=1 mol
10−14/3.2×10−5
Step 6: Calculate the pOH:
pOH = −log 1
10−14/3.2×10−5=−log3.125 ×109
Step 7: Evaluate the pOH:
pOH = −log3.125 ×109=−(log 3.125 + log 109) = −(log 3.125 + 9)
Step 8: Final calculation of pOH:
pOH = −(log 3.125 + 9) ≈ −(≈0.496 + 9) ≈ −(9.496) ≈9.496
Step 9: The pH of the solution is approximately 4.495 and the pOH is
approximately 9.496.
Question 20
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−8M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula pH =
−log[H+]. Since the hydroxide ion concentration (OH−) is given, we need to
first find the hydrogen ion concentration (H+) using the ion product constant
of water (Kw= 1.0×10−14).
Step 2: The relationship between [OH−] and [H+] is given by [OH−]×
[H+] = Kw. Given [OH−] = 2.5×10−8M, we can solve for [H+] as follows:
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−8= 4.0×10−7M
Step 3: Now that we have found [H+]=4.0×10−7M, we can calculate the
pH using the formula pH =−log4.0×10−7.
pH =−log4.0×10−7=−(−6.4) = 6.4
Therefore, the pH of the solution is 6.4.
13
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[H3O+]. Given that the hydronium ion
concentration is 3.2×10−5M, we can substitute this value into the pH formula
to find the pH.
pH = −log3.2×10−5
Step 2: Use the properties of logarithms to simplify the expression.
pH = −log(3.2) −log10−5
Step 3: We know that log10−5=−5.
pH = −log(3.2) −(−5)
Step 4: Finally, evaluate the logarithm.
pH = −log(3.2) + 5
Step 5: Use a calculator to find the pH.
pH ≈4.494875
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 that has a hydroxide ion concentration of 1.5×
10−4M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration:
[OH−] = 1.5×10−4M
14
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−4
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion:
pH = −log[H+]
Step 4: Plug in the values and solve for pH:
pH = −log 1.0×10−14
1.5×10−4
Step 5: Calculate the pH of the solution using a calculator:
pH ≈10.52
Therefore, the pH of the solution is approximately 10.52.
Question 23
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall the relationship between pH and hydrogen ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the equation
to find the pH:
pH = −log2.5×10−9
pH = −log(2.5) −log10−9
pH = −log(2.5) −(−9)
Step 3: Calculate the pH:
pH ≈ −0.398 −(−9)
pH ≈9.398
Step 4: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 5: Use the relationship between pH and pOH to find the pOH:
pH + pOH = 14
15
9.398 + pOH = 14
Step 6: Calculate the pOH:
pOH = 14 −9.398
pOH ≈4.602
Therefore, the pH of the solution is approximately 9.398 and the pOH is
approximately 4.602.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Identify the relationship between pH and [OH−] The relationship be-
tween the concentration of hydroxide ions [OH−] and the pH of a solution is
given by the formula:
pOH = −log[OH−]
Step 2: Calculate the pOH of the solution Given that [OH−] = 3.2×10−5
M, we can calculate the pOH as follows:
pOH = −log3.2×10−5
pOH ≈ − log(3.2) + log10−5
pOH ≈ −0.5052 + (−5)
pOH ≈ −5.5052
Step 3: Calculate the pH of the solution The pH of a solution can be deter-
mined using the relationship:
pH + pOH = 14
Since we have already calculated the pOH as −5.5052, we can find the pH:
pH = 14 −(−5.5052)
pH = 14 + 5.5052
pH ≈19.5052
Therefore, the pH of the solution with a hydroxide ion concentration of
3.2×10−5M is approximately 19.5052.
16
Question 25
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 calculated using the formula:
pH = −log[H+]
where [H+] represents the concentration of hydrogen ions in the solution.
Step 2: Given that the hydrogen ion concentration is 3.2×10−5M, we can
substitute this value into the pH formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−5≈ − log(3.2) + log10−5
Step 4: Use the fact that log10−5=−5 to simplify the expression further:
pH ≈ − log(3.2) −5
Step 5: Finally, calculate the pH:
pH ≈ − log(3.2) −5≈ −0.5051 −5≈ −5.5051
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately -5.51.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−7
M.
Solution
Step 1: Recall that the pH of a solution is given by the formula:
pH = −log[H+]
where [H+] is the concentration of hydrogen ions in the solution.
17
Step 2: Substituting the given hydrogen ion concentration into the formula,
we have:
pH = −log3.2×10−7
Step 3: Use a calculator to find the value of log3.2×10−7:
log3.2×10−7≈ −6.49485
Step 4: Calculate the pH:
pH ≈ −(−6.49485)
pH ≈6.49485
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−7M is approximately 6.49.
Question 27
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−5M.
Solution
Step 1: Recall that the pH and pOH of a solution can be calculated using the
following formulas:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−5M, we can
calculate the pH as:
pH = −log2.5×10−5
Step 3: Calculate the pH using the formula:
pH = −log2.5×10−5=−log(2.5) −log10−5=−0.3979 −(−5) = 4.6021
Step 4: Therefore, the pH of the solution is 4.60.
Step 5: Since the solution is neutral, the pOH can be calculated as:
pOH = 14 −pH
Step 6: Substitute the pH value into the formula to find the pOH:
pOH = 14 −4.60 = 9.40
Step 7: Thus, the pOH of the solution is 9.40.
18
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
Step 2: Use the relationship between pH and pOH to find the pH of the solution.
Step 1: Given: [OH−]=2.5×10−9M
The pOH of the solution can be calculated using the formula:
pOH = −log[OH−]
pOH = −log2.5×10−9
pOH = −log(2.5) −log10−9
pOH ≈ −(log(2.5) + 9)
pOH ≈ −(0.3979 + 9)
pOH ≈ −9.3979
Step 2: The pH of the solution can be calculated using the relationship
between pH and pOH:
pH + pOH = 14
pH = 14 −pOH
pH = 14 −(−9.3979)
pH ≈14 + 9.3979
pH ≈23.3979
Therefore, the pH of the solution is approximately 23.4.
Question 29
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−5M.
19
Solution
Step 1: Write the expression for Kw.
Kw= [H+]×[OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration by rearranging the Kwexpression.
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
2.5×10−5
[H+] = 4 ×10−10 M
Step 3: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+]
pH = −log4×10−10
pH = 9.4
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−3
M.
Solution
Step 1: Write the equilibrium expression for water.
H2O⇌H++ OH−
Step 2: Calculate the concentration of hydrogen ions in the solution using
the ion product constant of water (Kw= 1.0×10−14 at 25
°
C).
Kw= [H+][OH−]
[H+] = Kw
[OH−]=1.0×10−14
3.0×10−3= 3.33 ×10−12 M
Step 3: Calculate the pH of the solution using the formula pH =−log [H+].
pH =−log 3.33 ×10−12 =−log 3.33 + log 10−12 = 11.48
Therefore, the pH of the solution is 11.48.
20
Question 31
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+]. We are given the hydrogen ion
concentration, so we can directly substitute this value into the pH formula.
pH = −log3.2×10−9
Step 2: Now, we can calculate the pH of the solution.
pH = −log3.2×10−9=−log(3.2) −log10−9
Step 3: Recall that log10−9=−9. Therefore, we can simplify the expres-
sion further.
pH = −log(3.2) −(−9) = −log(3.2) + 9
Step 4: Finally, we can calculate the pH value using a calculator.
pH ≈ − log(3.2) + 9 ≈8.49
Therefore, the pH of the solution with a hydrogen ion concentration of 3.2×
10−9M is approximately 8.49.
Question 32
Question
Calculate the pH of a solution with a pOH of 4.76.
Solution
Step 1: Recall the relationship between pH and pOH in a solution:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 4.76 = 14
Step 3: Solve for pH:
pH = 14 −4.76
pH = 9.24
Step 4: Therefore, the pH of the solution is 9.24.
21
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall that the hydroxide ion concentration and the pH of a solution
are related through the equation:
pOH =−log[OH−]
Step 2: We are given the hydroxide ion concentration as 1.5×10−3M. Let’s
substitute this into the equation to find the pOH:
pOH =−log1.5×10−3
Step 3: Calculate the pOH:
pOH =−log1.5×10−3=−log(1.5) −log10−3
Step 4: Further simplify the expression:
pOH =−log(1.5) −(−3) = −log(1.5) + 3
Step 5: Using a calculator, find the value of −log(1.5):
pOH ≈ −0.1761 + 3
Step 6: Finally, calculate the pOH:
pOH ≈2.8239
Step 7: Recall that the pH and pOH of a solution are related through the
equation:
pH +pOH = 14
Step 8: Calculate the pH using the pOH value we found:
pH + 2.8239 = 14
Step 9: Solve for pH:
pH = 14 −2.8239
Step 10: Calculate the pH:
pH ≈11.1761
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 11.18.
22
Question 34
Question
Calculate the pH of a 0.005 M hydrochloric acid solution.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid, HCl, in water.
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Calculate the concentration of H+ions in the solution. Since hy-
drochloric acid is a strong acid that completely dissociates in water, its concen-
tration will be equal to the initial concentration of the acid.
[H+]=0.005 M
Step 3: Calculate the pH of the solution using the formula for pH.
pH = −log[H+]
Step 4: Substitute the given concentration of H+ions into the formula for
pH and solve for the pH.
pH = −log(0.005) = −(−2.3) = 2.3
Answer: The pH of a 0.005 M hydrochloric acid solution is 2.3.
Question 35
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−4
23
Question 2
Question
Calculate the pH and pOH of a solution with a hydroxide ion concentration of
1.5×10−8M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −logOH−=−log1.5×10−8
Step 2: Solve for pOH:
pOH = −log1.5×10−8=−(log(1.5) + log10−8) = −(log(1.5) −8) ≈6.82
Step 3: Use the relationship between pH and pOH to find the pH of the
solution:
pH + pOH = 14
Step 4: Calculate pH:
pH = 14 −pOH = 14 −6.82 ≈7.18
Therefore, the pH of the solution is approximately 7.18 and the pOH is
approximately 6.82.
Question 3
Question
Calculate the pH of a solution with a hydrogen ion concentration of 5.0×10−4
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log5.0×10−4
Step 3: Calculate the pH using a calculator:
pH = −log5.0×10−4
2
pH = −log(5.0) −log10−4
pH = −(log(5.0) + log10−4)
pH = −(log(5.0) −4)
pH = −(log(5.0) −4) ≈3.3
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 5.0×10−4M is approximately 3.3.
Question 4
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+], where [H+] is the hydrogen ion
concentration.
pH = −log2.5×10−8
Step 2: Substitute the given hydrogen ion concentration into the formula.
pH = −log2.5×10−8
Step 3: Use the properties of logarithms to simplify the expression.
pH = −log(2.5) −log10−8
Step 4: Recall that log(10x) = x, so log10−8=−8.
pH = −log(2.5) −(−8)
Step 5: Use a calculator to find the value of log(2.5) ≈0.39794.
pH = −0.39794 + 8
Step 6: Finally, calculate the pH of the solution.
pH ≈7.60
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−8M is approximately 7.60.
3
Question 5
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+].
Step 2: Given that the hydronium ion concentration is 2.5×10−6M, we can
plug this value into the pH formula.
pH = −log2.5×10−6
Step 3: Calculate the pH.
pH = −log2.5×10−6=−log(2.5) −log10−6
Step 4: Use the property of logarithms log(a×b) = log(a) + log(b).
pH = −log(2.5) −log10−6=−log(2.5) −(−6) = −log(2.5) + 6
Step 5: Calculate the final value of pH.
pH ≈ −0.3979 + 6 ≈5.6021
Therefore, the pH of a solution with a hydronium ion concentration of 2.5×
10−6M is approximately 5.60.
Question 6
Question
Calculate the pH of a solution with a hydroxide ion concentration of 8.25×10−4
M.
Solution
Step 1: Write the expression for Kw.
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration using Kw.
Kw= (8.25 ×10−4)[H+]
1.0×10−14 = (8.25 ×10−4)[H+]
4
[H+] = 1.0×10−14
8.25 ×10−4
[H+] = 1.21 ×10−11 M
Step 3: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+]
pH = −log1.21 ×10−11
pH = 10.9
Therefore, the pH of the solution is 10.9.
Question 7
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 1.5×10−8M.
Solution
Step 1: Recall that the pH and pOH of a solution are related to the hydrogen ion
concentration ([H+]) and hydroxide ion concentration ([OH−]) by the equations:
pH = −log[H+]
pOH = −log[OH−]
and
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 1.5×10−8M, we can
calculate the pH as follows:
pH = −log1.5×10−8
Step 3: Using a calculator, we find:
pH ≈ − log1.5×10−8≈ −(−7.823130) ≈7.823
Step 4: Now, we can calculate the pOH using the relation pH + pOH = 14:
pOH = 14 −pH
Step 5: Substituting the calculated pH value, we get:
pOH = 14 −7.823
Step 6: Therefore, using a calculator, we find:
pOH = 14 −7.823 = 6.177
Step 7: The pH of the solution is approximately 7.823 and the pOH is
approximately 6.177.
5
Question 8
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1 ×10−3
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH =−log[H+]. Since [H+] = 1 ×10−3M, we can calculate the pH as follows:
Step 1: pH =−log1×10−3=−log10−3=−(−3) = 3
Therefore, the pH of the solution is 3.
Question 9
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−9
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to calculate the concen-
tration of hydronium ions.
[OH−] = 3.5×10−9M
[H+] = Kw
[OH−]=1.0×10−14
3.5×10−9
[H+] = 2.857 ×10−6M
Step 3: Calculate the pH of the solution.
pH = −log[H+]=−log2.857 ×10−6
pH = −log(2.857) + log10−6
pH = 5.545 + 6
pH = 11.545
Therefore, the pH of the solution is 11.545.
6
Question 10
Question
Calculate the pH of a solution with a 5.0×10−3M concentration of hydrochloric
acid (HCl).
Solution
Step 1: Write the balanced equation for the dissociation of hydrochloric acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Determine the concentration of H+ions formed from the dissociation
of HCl. Since HCl is a strong acid, it dissociates completely. Therefore, the
concentration of H+ions is equal to the initial concentration of HCl, which is
5.0×10−3M.
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
Step 4: Substitute the value of [H+] into the equation:
pH = −log5.0×10−3
pH = −log(5.0) + log10−3
pH = −log(5.0) −3 log(10)
pH = −log(5.0) −3×1
pH = −log(5.0) −3
pH = −0.69897 −3
pH = −3.69897
Therefore, the pH of a solution with 5.0×10−3M HCl is approximately 3.70.
Question 11
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
7
Solution
Step 1: Recall the relationship between pH, pOH, hydrogen ion concentration,
and hydroxide ion concentration:
pH = −log[H+]
pOH = −log[OH−]
Also, for water at 25
°
C, [H+]×[OH−] = 1.0×10−14 M2.
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9
pH = −(log(2.5) + 9) ≈ −12.60
Step 3: Next, we can calculate the pOH using the relationship between pH
and pOH:
pH + pOH = 14
pOH = 14 −pH = 14 + 12.60 ≈1.40
Therefore, the pH of the solution is approximately 12.60 and the pOH is
approximately 1.40.
Question 12
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= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the expression.
Kw= 1.0×10−14 = (x)(1.5×10−3)
Step 3: Solve for the concentration of hydronium ions (x).
x=1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 4: Calculate the pH using the formula pH =−logH+.
pH =−log6.67 ×10−12=−log(6.67) −log10−12= 11.18
Therefore, the pH of the solution is 11.18.
8
Question 13
Question
Calculate the pH of a solution with a pOH of 2.83.
Solution
Step 1: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 2.83 = 14
Step 3: Solve for pH:
pH = 14 −2.83
pH = 11.17
Step 4: Therefore, the pH of the solution is 11.17.
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the definition of pH. The pH 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 formula.
Plugging in the given hydronium ion concentration:
pH = −log3.2×10−5
Step 3: Calculate the pH. Using a calculator, find the pH value:
pH = −log3.2×10−5≈4.495
Therefore, the pH of the solution is approximately 4.495.
9
Question 15
Question
Calculate the pH of a 0.025 M nitric acid (HNO3) solution. Given that the
dissociation constant (Ka) of nitric acid is 1.2×10−5.
Solution
Step 1: Write the balanced chemical equation for the dissociation of nitric acid:
HNO3→H++ NO−
3
Step 2: Write the expression for the acid dissociation constant (Ka):
Ka=[H+][NO−
3]
[HNO3]
Step 3: Since nitric acid is a strong acid, it completely dissociates in solution.
Therefore, the concentration of HNO3is equal to the concentration of H+ions
which is 0.025 M.
Step 4: Substitute the given values into the Kaexpression:
1.2×10−5=x×x
0.025
1.2×10−5=x2
0.025
Step 5: Solve for x, the concentration of H+ions:
x2= 0.025 ×1.2×10−5
x2= 3 ×10−7
x=p3×10−7
x= 5.48 ×10−4M
Step 6: Calculate the pH using the concentration of H+ions:
pH = −log5.48 ×10−4
pH = −log(5.48) + log10−4
pH = −(log(5.48) −4)
pH ≈3.26
Therefore, the pH of a 0.025 M nitric acid solution is approximately 3.26.
10
Question 16
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−9
Step 3: Calculate the pH:
pH = −log2.5×10−9=−(log(2.5) + log10−9)
Step 4: Remember that log10−9=−9:
pH = −(0.3979 + (−9)) = 9 −0.3979 = 8.6021
Step 5: Therefore, the pH of a solution with a hydrogen ion concentration
of 2.5×10−9M is approximately 8.60.
Question 17
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.2×10−9
Step 3: Use a calculator to evaluate the logarithm:
pH ≈ − log(3.2) + log10−9
pH ≈ −0.5052 −9
pH ≈ −9.5052
Step 4: Round the pH value to the appropriate number of significant figures:
pH ≈ −9.5
Therefore, the pH of the solution is approximately 9.5.
11
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall that the pH is defined as −log[H+]. We are given the concentra-
tion of hydronium ions, so we can directly substitute this value into the formula
to find the pH.
pH = −log2.5×10−8
Step 2: Calculate the pH by taking the negative logarithm of the given
hydronium ion concentration.
pH = −log2.5×10−8=−(log 2.5 + log 10−8)
Step 3: Keep in mind that log 10−8=−8 due to the logarithmic property
log10 x=−y⇐⇒ x= 10−y. Substitute this back into the equation to simplify
further.
pH = −(log 2.5−8)
Step 4: Use a calculator to find the pH of the solution.
pH ≈ −(log 2.5−8) ≈ −0.3979 ≈0.40
Therefore, the pH of the solution is approximately 0.40.
Question 19
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the relationship between pH, pOH, and hydronium ion
concentration is given by:
pH = −log[H3O+]
pOH = −log[OH−]
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
directly substitute this value into the formula for pH:
pH = −log3.2×10−5
12
Step 3: Calculate the pH:
pH = −log3.2×10−5=−(log 3.2 + log 10−5) = −(log 3.2−5)
Step 4: Evaluate the pH:
pH = −(log 3.2−5) ≈ −(≈0.505 −5) ≈ −(−4.495) ≈4.495
Step 5: Now, calculate the pOH using the hydronium ion concentration:
[OH−] = 1 mol
Kw[H3O+]=1 mol
10−14/3.2×10−5
Step 6: Calculate the pOH:
pOH = −log 1
10−14/3.2×10−5=−log3.125 ×109
Step 7: Evaluate the pOH:
pOH = −log3.125 ×109=−(log 3.125 + log 109) = −(log 3.125 + 9)
Step 8: Final calculation of pOH:
pOH = −(log 3.125 + 9) ≈ −(≈0.496 + 9) ≈ −(9.496) ≈9.496
Step 9: The pH of the solution is approximately 4.495 and the pOH is
approximately 9.496.
Question 20
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−8M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula pH =
−log[H+]. Since the hydroxide ion concentration (OH−) is given, we need to
first find the hydrogen ion concentration (H+) using the ion product constant
of water (Kw= 1.0×10−14).
Step 2: The relationship between [OH−] and [H+] is given by [OH−]×
[H+] = Kw. Given [OH−] = 2.5×10−8M, we can solve for [H+] as follows:
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−8= 4.0×10−7M
Step 3: Now that we have found [H+]=4.0×10−7M, we can calculate the
pH using the formula pH =−log4.0×10−7.
pH =−log4.0×10−7=−(−6.4) = 6.4
Therefore, the pH of the solution is 6.4.
13
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[H3O+]. Given that the hydronium ion
concentration is 3.2×10−5M, we can substitute this value into the pH formula
to find the pH.
pH = −log3.2×10−5
Step 2: Use the properties of logarithms to simplify the expression.
pH = −log(3.2) −log10−5
Step 3: We know that log10−5=−5.
pH = −log(3.2) −(−5)
Step 4: Finally, evaluate the logarithm.
pH = −log(3.2) + 5
Step 5: Use a calculator to find the pH.
pH ≈4.494875
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 that has a hydroxide ion concentration of 1.5×
10−4M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration:
[OH−] = 1.5×10−4M
14
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−4
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion:
pH = −log[H+]
Step 4: Plug in the values and solve for pH:
pH = −log 1.0×10−14
1.5×10−4
Step 5: Calculate the pH of the solution using a calculator:
pH ≈10.52
Therefore, the pH of the solution is approximately 10.52.
Question 23
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall the relationship between pH and hydrogen ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the equation
to find the pH:
pH = −log2.5×10−9
pH = −log(2.5) −log10−9
pH = −log(2.5) −(−9)
Step 3: Calculate the pH:
pH ≈ −0.398 −(−9)
pH ≈9.398
Step 4: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 5: Use the relationship between pH and pOH to find the pOH:
pH + pOH = 14
15
9.398 + pOH = 14
Step 6: Calculate the pOH:
pOH = 14 −9.398
pOH ≈4.602
Therefore, the pH of the solution is approximately 9.398 and the pOH is
approximately 4.602.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Identify the relationship between pH and [OH−] The relationship be-
tween the concentration of hydroxide ions [OH−] and the pH of a solution is
given by the formula:
pOH = −log[OH−]
Step 2: Calculate the pOH of the solution Given that [OH−] = 3.2×10−5
M, we can calculate the pOH as follows:
pOH = −log3.2×10−5
pOH ≈ − log(3.2) + log10−5
pOH ≈ −0.5052 + (−5)
pOH ≈ −5.5052
Step 3: Calculate the pH of the solution The pH of a solution can be deter-
mined using the relationship:
pH + pOH = 14
Since we have already calculated the pOH as −5.5052, we can find the pH:
pH = 14 −(−5.5052)
pH = 14 + 5.5052
pH ≈19.5052
Therefore, the pH of the solution with a hydroxide ion concentration of
3.2×10−5M is approximately 19.5052.
16
Question 25
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 calculated using the formula:
pH = −log[H+]
where [H+] represents the concentration of hydrogen ions in the solution.
Step 2: Given that the hydrogen ion concentration is 3.2×10−5M, we can
substitute this value into the pH formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−5≈ − log(3.2) + log10−5
Step 4: Use the fact that log10−5=−5 to simplify the expression further:
pH ≈ − log(3.2) −5
Step 5: Finally, calculate the pH:
pH ≈ − log(3.2) −5≈ −0.5051 −5≈ −5.5051
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately -5.51.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−7
M.
Solution
Step 1: Recall that the pH of a solution is given by the formula:
pH = −log[H+]
where [H+] is the concentration of hydrogen ions in the solution.
17
Step 2: Substituting the given hydrogen ion concentration into the formula,
we have:
pH = −log3.2×10−7
Step 3: Use a calculator to find the value of log3.2×10−7:
log3.2×10−7≈ −6.49485
Step 4: Calculate the pH:
pH ≈ −(−6.49485)
pH ≈6.49485
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−7M is approximately 6.49.
Question 27
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−5M.
Solution
Step 1: Recall that the pH and pOH of a solution can be calculated using the
following formulas:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−5M, we can
calculate the pH as:
pH = −log2.5×10−5
Step 3: Calculate the pH using the formula:
pH = −log2.5×10−5=−log(2.5) −log10−5=−0.3979 −(−5) = 4.6021
Step 4: Therefore, the pH of the solution is 4.60.
Step 5: Since the solution is neutral, the pOH can be calculated as:
pOH = 14 −pH
Step 6: Substitute the pH value into the formula to find the pOH:
pOH = 14 −4.60 = 9.40
Step 7: Thus, the pOH of the solution is 9.40.
18
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
Step 2: Use the relationship between pH and pOH to find the pH of the solution.
Step 1: Given: [OH−]=2.5×10−9M
The pOH of the solution can be calculated using the formula:
pOH = −log[OH−]
pOH = −log2.5×10−9
pOH = −log(2.5) −log10−9
pOH ≈ −(log(2.5) + 9)
pOH ≈ −(0.3979 + 9)
pOH ≈ −9.3979
Step 2: The pH of the solution can be calculated using the relationship
between pH and pOH:
pH + pOH = 14
pH = 14 −pOH
pH = 14 −(−9.3979)
pH ≈14 + 9.3979
pH ≈23.3979
Therefore, the pH of the solution is approximately 23.4.
Question 29
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−5M.
19
Solution
Step 1: Write the expression for Kw.
Kw= [H+]×[OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration by rearranging the Kwexpression.
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
2.5×10−5
[H+] = 4 ×10−10 M
Step 3: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+]
pH = −log4×10−10
pH = 9.4
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−3
M.
Solution
Step 1: Write the equilibrium expression for water.
H2O⇌H++ OH−
Step 2: Calculate the concentration of hydrogen ions in the solution using
the ion product constant of water (Kw= 1.0×10−14 at 25
°
C).
Kw= [H+][OH−]
[H+] = Kw
[OH−]=1.0×10−14
3.0×10−3= 3.33 ×10−12 M
Step 3: Calculate the pH of the solution using the formula pH =−log [H+].
pH =−log 3.33 ×10−12 =−log 3.33 + log 10−12 = 11.48
Therefore, the pH of the solution is 11.48.
20
Question 31
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+]. We are given the hydrogen ion
concentration, so we can directly substitute this value into the pH formula.
pH = −log3.2×10−9
Step 2: Now, we can calculate the pH of the solution.
pH = −log3.2×10−9=−log(3.2) −log10−9
Step 3: Recall that log10−9=−9. Therefore, we can simplify the expres-
sion further.
pH = −log(3.2) −(−9) = −log(3.2) + 9
Step 4: Finally, we can calculate the pH value using a calculator.
pH ≈ − log(3.2) + 9 ≈8.49
Therefore, the pH of the solution with a hydrogen ion concentration of 3.2×
10−9M is approximately 8.49.
Question 32
Question
Calculate the pH of a solution with a pOH of 4.76.
Solution
Step 1: Recall the relationship between pH and pOH in a solution:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 4.76 = 14
Step 3: Solve for pH:
pH = 14 −4.76
pH = 9.24
Step 4: Therefore, the pH of the solution is 9.24.
21
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall that the hydroxide ion concentration and the pH of a solution
are related through the equation:
pOH =−log[OH−]
Step 2: We are given the hydroxide ion concentration as 1.5×10−3M. Let’s
substitute this into the equation to find the pOH:
pOH =−log1.5×10−3
Step 3: Calculate the pOH:
pOH =−log1.5×10−3=−log(1.5) −log10−3
Step 4: Further simplify the expression:
pOH =−log(1.5) −(−3) = −log(1.5) + 3
Step 5: Using a calculator, find the value of −log(1.5):
pOH ≈ −0.1761 + 3
Step 6: Finally, calculate the pOH:
pOH ≈2.8239
Step 7: Recall that the pH and pOH of a solution are related through the
equation:
pH +pOH = 14
Step 8: Calculate the pH using the pOH value we found:
pH + 2.8239 = 14
Step 9: Solve for pH:
pH = 14 −2.8239
Step 10: Calculate the pH:
pH ≈11.1761
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 11.18.
22
Question 34
Question
Calculate the pH of a 0.005 M hydrochloric acid solution.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid, HCl, in water.
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Calculate the concentration of H+ions in the solution. Since hy-
drochloric acid is a strong acid that completely dissociates in water, its concen-
tration will be equal to the initial concentration of the acid.
[H+]=0.005 M
Step 3: Calculate the pH of the solution using the formula for pH.
pH = −log[H+]
Step 4: Substitute the given concentration of H+ions into the formula for
pH and solve for the pH.
pH = −log(0.005) = −(−2.3) = 2.3
Answer: The pH of a 0.005 M hydrochloric acid solution is 2.3.
Question 35
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−4
23
Question 2
Question
Calculate the pH and pOH of a solution with a hydroxide ion concentration of
1.5×10−8M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −logOH−=−log1.5×10−8
Step 2: Solve for pOH:
pOH = −log1.5×10−8=−(log(1.5) + log10−8) = −(log(1.5) −8) ≈6.82
Step 3: Use the relationship between pH and pOH to find the pH of the
solution:
pH + pOH = 14
Step 4: Calculate pH:
pH = 14 −pOH = 14 −6.82 ≈7.18
Therefore, the pH of the solution is approximately 7.18 and the pOH is
approximately 6.82.
Question 3
Question
Calculate the pH of a solution with a hydrogen ion concentration of 5.0×10−4
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log5.0×10−4
Step 3: Calculate the pH using a calculator:
pH = −log5.0×10−4
2
pH = −log(5.0) −log10−4
pH = −(log(5.0) + log10−4)
pH = −(log(5.0) −4)
pH = −(log(5.0) −4) ≈3.3
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 5.0×10−4M is approximately 3.3.
Question 4
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+], where [H+] is the hydrogen ion
concentration.
pH = −log2.5×10−8
Step 2: Substitute the given hydrogen ion concentration into the formula.
pH = −log2.5×10−8
Step 3: Use the properties of logarithms to simplify the expression.
pH = −log(2.5) −log10−8
Step 4: Recall that log(10x) = x, so log10−8=−8.
pH = −log(2.5) −(−8)
Step 5: Use a calculator to find the value of log(2.5) ≈0.39794.
pH = −0.39794 + 8
Step 6: Finally, calculate the pH of the solution.
pH ≈7.60
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−8M is approximately 7.60.
3
Question 5
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+].
Step 2: Given that the hydronium ion concentration is 2.5×10−6M, we can
plug this value into the pH formula.
pH = −log2.5×10−6
Step 3: Calculate the pH.
pH = −log2.5×10−6=−log(2.5) −log10−6
Step 4: Use the property of logarithms log(a×b) = log(a) + log(b).
pH = −log(2.5) −log10−6=−log(2.5) −(−6) = −log(2.5) + 6
Step 5: Calculate the final value of pH.
pH ≈ −0.3979 + 6 ≈5.6021
Therefore, the pH of a solution with a hydronium ion concentration of 2.5×
10−6M is approximately 5.60.
Question 6
Question
Calculate the pH of a solution with a hydroxide ion concentration of 8.25×10−4
M.
Solution
Step 1: Write the expression for Kw.
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration using Kw.
Kw= (8.25 ×10−4)[H+]
1.0×10−14 = (8.25 ×10−4)[H+]
4
[H+] = 1.0×10−14
8.25 ×10−4
[H+] = 1.21 ×10−11 M
Step 3: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+]
pH = −log1.21 ×10−11
pH = 10.9
Therefore, the pH of the solution is 10.9.
Question 7
Question
Calculate the pH and pOH of a solution that has a hydrogen ion concentration
of 1.5×10−8M.
Solution
Step 1: Recall that the pH and pOH of a solution are related to the hydrogen ion
concentration ([H+]) and hydroxide ion concentration ([OH−]) by the equations:
pH = −log[H+]
pOH = −log[OH−]
and
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 1.5×10−8M, we can
calculate the pH as follows:
pH = −log1.5×10−8
Step 3: Using a calculator, we find:
pH ≈ − log1.5×10−8≈ −(−7.823130) ≈7.823
Step 4: Now, we can calculate the pOH using the relation pH + pOH = 14:
pOH = 14 −pH
Step 5: Substituting the calculated pH value, we get:
pOH = 14 −7.823
Step 6: Therefore, using a calculator, we find:
pOH = 14 −7.823 = 6.177
Step 7: The pH of the solution is approximately 7.823 and the pOH is
approximately 6.177.
5
Question 8
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1 ×10−3
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH =−log[H+]. Since [H+] = 1 ×10−3M, we can calculate the pH as follows:
Step 1: pH =−log1×10−3=−log10−3=−(−3) = 3
Therefore, the pH of the solution is 3.
Question 9
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.5×10−9
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to calculate the concen-
tration of hydronium ions.
[OH−] = 3.5×10−9M
[H+] = Kw
[OH−]=1.0×10−14
3.5×10−9
[H+] = 2.857 ×10−6M
Step 3: Calculate the pH of the solution.
pH = −log[H+]=−log2.857 ×10−6
pH = −log(2.857) + log10−6
pH = 5.545 + 6
pH = 11.545
Therefore, the pH of the solution is 11.545.
6
Question 10
Question
Calculate the pH of a solution with a 5.0×10−3M concentration of hydrochloric
acid (HCl).
Solution
Step 1: Write the balanced equation for the dissociation of hydrochloric acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Determine the concentration of H+ions formed from the dissociation
of HCl. Since HCl is a strong acid, it dissociates completely. Therefore, the
concentration of H+ions is equal to the initial concentration of HCl, which is
5.0×10−3M.
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
Step 4: Substitute the value of [H+] into the equation:
pH = −log5.0×10−3
pH = −log(5.0) + log10−3
pH = −log(5.0) −3 log(10)
pH = −log(5.0) −3×1
pH = −log(5.0) −3
pH = −0.69897 −3
pH = −3.69897
Therefore, the pH of a solution with 5.0×10−3M HCl is approximately 3.70.
Question 11
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
7
Solution
Step 1: Recall the relationship between pH, pOH, hydrogen ion concentration,
and hydroxide ion concentration:
pH = −log[H+]
pOH = −log[OH−]
Also, for water at 25
°
C, [H+]×[OH−] = 1.0×10−14 M2.
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH:
pH = −log2.5×10−9=−log(2.5) −log10−9
pH = −(log(2.5) + 9) ≈ −12.60
Step 3: Next, we can calculate the pOH using the relationship between pH
and pOH:
pH + pOH = 14
pOH = 14 −pH = 14 + 12.60 ≈1.40
Therefore, the pH of the solution is approximately 12.60 and the pOH is
approximately 1.40.
Question 12
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= [H+][OH−]
Step 2: Substitute the given hydroxide ion concentration into the expression.
Kw= 1.0×10−14 = (x)(1.5×10−3)
Step 3: Solve for the concentration of hydronium ions (x).
x=1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 4: Calculate the pH using the formula pH =−logH+.
pH =−log6.67 ×10−12=−log(6.67) −log10−12= 11.18
Therefore, the pH of the solution is 11.18.
8
Question 13
Question
Calculate the pH of a solution with a pOH of 2.83.
Solution
Step 1: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 2.83 = 14
Step 3: Solve for pH:
pH = 14 −2.83
pH = 11.17
Step 4: Therefore, the pH of the solution is 11.17.
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall the definition of pH. The pH 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 formula.
Plugging in the given hydronium ion concentration:
pH = −log3.2×10−5
Step 3: Calculate the pH. Using a calculator, find the pH value:
pH = −log3.2×10−5≈4.495
Therefore, the pH of the solution is approximately 4.495.
9
Question 15
Question
Calculate the pH of a 0.025 M nitric acid (HNO3) solution. Given that the
dissociation constant (Ka) of nitric acid is 1.2×10−5.
Solution
Step 1: Write the balanced chemical equation for the dissociation of nitric acid:
HNO3→H++ NO−
3
Step 2: Write the expression for the acid dissociation constant (Ka):
Ka=[H+][NO−
3]
[HNO3]
Step 3: Since nitric acid is a strong acid, it completely dissociates in solution.
Therefore, the concentration of HNO3is equal to the concentration of H+ions
which is 0.025 M.
Step 4: Substitute the given values into the Kaexpression:
1.2×10−5=x×x
0.025
1.2×10−5=x2
0.025
Step 5: Solve for x, the concentration of H+ions:
x2= 0.025 ×1.2×10−5
x2= 3 ×10−7
x=p3×10−7
x= 5.48 ×10−4M
Step 6: Calculate the pH using the concentration of H+ions:
pH = −log5.48 ×10−4
pH = −log(5.48) + log10−4
pH = −(log(5.48) −4)
pH ≈3.26
Therefore, the pH of a 0.025 M nitric acid solution is approximately 3.26.
10
Question 16
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−9
Step 3: Calculate the pH:
pH = −log2.5×10−9=−(log(2.5) + log10−9)
Step 4: Remember that log10−9=−9:
pH = −(0.3979 + (−9)) = 9 −0.3979 = 8.6021
Step 5: Therefore, the pH of a solution with a hydrogen ion concentration
of 2.5×10−9M is approximately 8.60.
Question 17
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.2×10−9
Step 3: Use a calculator to evaluate the logarithm:
pH ≈ − log(3.2) + log10−9
pH ≈ −0.5052 −9
pH ≈ −9.5052
Step 4: Round the pH value to the appropriate number of significant figures:
pH ≈ −9.5
Therefore, the pH of the solution is approximately 9.5.
11
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−8
M.
Solution
Step 1: Recall that the pH is defined as −log[H+]. We are given the concentra-
tion of hydronium ions, so we can directly substitute this value into the formula
to find the pH.
pH = −log2.5×10−8
Step 2: Calculate the pH by taking the negative logarithm of the given
hydronium ion concentration.
pH = −log2.5×10−8=−(log 2.5 + log 10−8)
Step 3: Keep in mind that log 10−8=−8 due to the logarithmic property
log10 x=−y⇐⇒ x= 10−y. Substitute this back into the equation to simplify
further.
pH = −(log 2.5−8)
Step 4: Use a calculator to find the pH of the solution.
pH ≈ −(log 2.5−8) ≈ −0.3979 ≈0.40
Therefore, the pH of the solution is approximately 0.40.
Question 19
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall that the relationship between pH, pOH, and hydronium ion
concentration is given by:
pH = −log[H3O+]
pOH = −log[OH−]
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
directly substitute this value into the formula for pH:
pH = −log3.2×10−5
12
Step 3: Calculate the pH:
pH = −log3.2×10−5=−(log 3.2 + log 10−5) = −(log 3.2−5)
Step 4: Evaluate the pH:
pH = −(log 3.2−5) ≈ −(≈0.505 −5) ≈ −(−4.495) ≈4.495
Step 5: Now, calculate the pOH using the hydronium ion concentration:
[OH−] = 1 mol
Kw[H3O+]=1 mol
10−14/3.2×10−5
Step 6: Calculate the pOH:
pOH = −log 1
10−14/3.2×10−5=−log3.125 ×109
Step 7: Evaluate the pOH:
pOH = −log3.125 ×109=−(log 3.125 + log 109) = −(log 3.125 + 9)
Step 8: Final calculation of pOH:
pOH = −(log 3.125 + 9) ≈ −(≈0.496 + 9) ≈ −(9.496) ≈9.496
Step 9: The pH of the solution is approximately 4.495 and the pOH is
approximately 9.496.
Question 20
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−8M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula pH =
−log[H+]. Since the hydroxide ion concentration (OH−) is given, we need to
first find the hydrogen ion concentration (H+) using the ion product constant
of water (Kw= 1.0×10−14).
Step 2: The relationship between [OH−] and [H+] is given by [OH−]×
[H+] = Kw. Given [OH−] = 2.5×10−8M, we can solve for [H+] as follows:
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−8= 4.0×10−7M
Step 3: Now that we have found [H+]=4.0×10−7M, we can calculate the
pH using the formula pH =−log4.0×10−7.
pH =−log4.0×10−7=−(−6.4) = 6.4
Therefore, the pH of the solution is 6.4.
13
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[H3O+]. Given that the hydronium ion
concentration is 3.2×10−5M, we can substitute this value into the pH formula
to find the pH.
pH = −log3.2×10−5
Step 2: Use the properties of logarithms to simplify the expression.
pH = −log(3.2) −log10−5
Step 3: We know that log10−5=−5.
pH = −log(3.2) −(−5)
Step 4: Finally, evaluate the logarithm.
pH = −log(3.2) + 5
Step 5: Use a calculator to find the pH.
pH ≈4.494875
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 that has a hydroxide ion concentration of 1.5×
10−4M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−]=1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration:
[OH−] = 1.5×10−4M
14
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−4
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion:
pH = −log[H+]
Step 4: Plug in the values and solve for pH:
pH = −log 1.0×10−14
1.5×10−4
Step 5: Calculate the pH of the solution using a calculator:
pH ≈10.52
Therefore, the pH of the solution is approximately 10.52.
Question 23
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall the relationship between pH and hydrogen ion concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the equation
to find the pH:
pH = −log2.5×10−9
pH = −log(2.5) −log10−9
pH = −log(2.5) −(−9)
Step 3: Calculate the pH:
pH ≈ −0.398 −(−9)
pH ≈9.398
Step 4: Recall that pH and pOH are related by the equation:
pH + pOH = 14
Step 5: Use the relationship between pH and pOH to find the pOH:
pH + pOH = 14
15
9.398 + pOH = 14
Step 6: Calculate the pOH:
pOH = 14 −9.398
pOH ≈4.602
Therefore, the pH of the solution is approximately 9.398 and the pOH is
approximately 4.602.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Identify the relationship between pH and [OH−] The relationship be-
tween the concentration of hydroxide ions [OH−] and the pH of a solution is
given by the formula:
pOH = −log[OH−]
Step 2: Calculate the pOH of the solution Given that [OH−] = 3.2×10−5
M, we can calculate the pOH as follows:
pOH = −log3.2×10−5
pOH ≈ − log(3.2) + log10−5
pOH ≈ −0.5052 + (−5)
pOH ≈ −5.5052
Step 3: Calculate the pH of the solution The pH of a solution can be deter-
mined using the relationship:
pH + pOH = 14
Since we have already calculated the pOH as −5.5052, we can find the pH:
pH = 14 −(−5.5052)
pH = 14 + 5.5052
pH ≈19.5052
Therefore, the pH of the solution with a hydroxide ion concentration of
3.2×10−5M is approximately 19.5052.
16
Question 25
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 calculated using the formula:
pH = −log[H+]
where [H+] represents the concentration of hydrogen ions in the solution.
Step 2: Given that the hydrogen ion concentration is 3.2×10−5M, we can
substitute this value into the pH formula:
pH = −log3.2×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.2×10−5≈ − log(3.2) + log10−5
Step 4: Use the fact that log10−5=−5 to simplify the expression further:
pH ≈ − log(3.2) −5
Step 5: Finally, calculate the pH:
pH ≈ − log(3.2) −5≈ −0.5051 −5≈ −5.5051
Step 6: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−5M is approximately -5.51.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.2×10−7
M.
Solution
Step 1: Recall that the pH of a solution is given by the formula:
pH = −log[H+]
where [H+] is the concentration of hydrogen ions in the solution.
17
Step 2: Substituting the given hydrogen ion concentration into the formula,
we have:
pH = −log3.2×10−7
Step 3: Use a calculator to find the value of log3.2×10−7:
log3.2×10−7≈ −6.49485
Step 4: Calculate the pH:
pH ≈ −(−6.49485)
pH ≈6.49485
Step 5: Therefore, the pH of the solution with a hydrogen ion concentration
of 3.2×10−7M is approximately 6.49.
Question 27
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−5M.
Solution
Step 1: Recall that the pH and pOH of a solution can be calculated using the
following formulas:
pH = −log[H+]
pOH = −log[OH−]
Step 2: Given that the hydrogen ion concentration is 2.5×10−5M, we can
calculate the pH as:
pH = −log2.5×10−5
Step 3: Calculate the pH using the formula:
pH = −log2.5×10−5=−log(2.5) −log10−5=−0.3979 −(−5) = 4.6021
Step 4: Therefore, the pH of the solution is 4.60.
Step 5: Since the solution is neutral, the pOH can be calculated as:
pOH = 14 −pH
Step 6: Substitute the pH value into the formula to find the pOH:
pOH = 14 −4.60 = 9.40
Step 7: Thus, the pOH of the solution is 9.40.
18
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−9
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration.
Step 2: Use the relationship between pH and pOH to find the pH of the solution.
Step 1: Given: [OH−]=2.5×10−9M
The pOH of the solution can be calculated using the formula:
pOH = −log[OH−]
pOH = −log2.5×10−9
pOH = −log(2.5) −log10−9
pOH ≈ −(log(2.5) + 9)
pOH ≈ −(0.3979 + 9)
pOH ≈ −9.3979
Step 2: The pH of the solution can be calculated using the relationship
between pH and pOH:
pH + pOH = 14
pH = 14 −pOH
pH = 14 −(−9.3979)
pH ≈14 + 9.3979
pH ≈23.3979
Therefore, the pH of the solution is approximately 23.4.
Question 29
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 2.5×
10−5M.
19
Solution
Step 1: Write the expression for Kw.
Kw= [H+]×[OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration by rearranging the Kwexpression.
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
2.5×10−5
[H+] = 4 ×10−10 M
Step 3: Calculate the pH using the hydrogen ion concentration.
pH = −log[H+]
pH = −log4×10−10
pH = 9.4
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−3
M.
Solution
Step 1: Write the equilibrium expression for water.
H2O⇌H++ OH−
Step 2: Calculate the concentration of hydrogen ions in the solution using
the ion product constant of water (Kw= 1.0×10−14 at 25
°
C).
Kw= [H+][OH−]
[H+] = Kw
[OH−]=1.0×10−14
3.0×10−3= 3.33 ×10−12 M
Step 3: Calculate the pH of the solution using the formula pH =−log [H+].
pH =−log 3.33 ×10−12 =−log 3.33 + log 10−12 = 11.48
Therefore, the pH of the solution is 11.48.
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Question 31
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+]. We are given the hydrogen ion
concentration, so we can directly substitute this value into the pH formula.
pH = −log3.2×10−9
Step 2: Now, we can calculate the pH of the solution.
pH = −log3.2×10−9=−log(3.2) −log10−9
Step 3: Recall that log10−9=−9. Therefore, we can simplify the expres-
sion further.
pH = −log(3.2) −(−9) = −log(3.2) + 9
Step 4: Finally, we can calculate the pH value using a calculator.
pH ≈ − log(3.2) + 9 ≈8.49
Therefore, the pH of the solution with a hydrogen ion concentration of 3.2×
10−9M is approximately 8.49.
Question 32
Question
Calculate the pH of a solution with a pOH of 4.76.
Solution
Step 1: Recall the relationship between pH and pOH in a solution:
pH + pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH + 4.76 = 14
Step 3: Solve for pH:
pH = 14 −4.76
pH = 9.24
Step 4: Therefore, the pH of the solution is 9.24.
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Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall that the hydroxide ion concentration and the pH of a solution
are related through the equation:
pOH =−log[OH−]
Step 2: We are given the hydroxide ion concentration as 1.5×10−3M. Let’s
substitute this into the equation to find the pOH:
pOH =−log1.5×10−3
Step 3: Calculate the pOH:
pOH =−log1.5×10−3=−log(1.5) −log10−3
Step 4: Further simplify the expression:
pOH =−log(1.5) −(−3) = −log(1.5) + 3
Step 5: Using a calculator, find the value of −log(1.5):
pOH ≈ −0.1761 + 3
Step 6: Finally, calculate the pOH:
pOH ≈2.8239
Step 7: Recall that the pH and pOH of a solution are related through the
equation:
pH +pOH = 14
Step 8: Calculate the pH using the pOH value we found:
pH + 2.8239 = 14
Step 9: Solve for pH:
pH = 14 −2.8239
Step 10: Calculate the pH:
pH ≈11.1761
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 11.18.
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Question 34
Question
Calculate the pH of a 0.005 M hydrochloric acid solution.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid, HCl, in water.
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Calculate the concentration of H+ions in the solution. Since hy-
drochloric acid is a strong acid that completely dissociates in water, its concen-
tration will be equal to the initial concentration of the acid.
[H+]=0.005 M
Step 3: Calculate the pH of the solution using the formula for pH.
pH = −log[H+]
Step 4: Substitute the given concentration of H+ions into the formula for
pH and solve for the pH.
pH = −log(0.005) = −(−2.3) = 2.3
Answer: The pH of a 0.005 M hydrochloric acid solution is 2.3.
Question 35
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall the relationship between pH and hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−4
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pH = −(−3.6)
pH ≈3.6
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−4M is approximately 3.6.
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