CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 1
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×
10−4M.
Solution
Step 1: Recall that pH is defined as −log[H+] where [H+] is the concentration
of hydronium ions in the solution.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−4=−(−3.60) = 3.60
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−4M is 3.60 .
Question 2
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3 ×10−5
M.
Solution
Step 1: Recall that pH is defined as −log10([H+]). Therefore, to find the pH of
the solution, we need to calculate −log10(3 ×10−5).
Step 2: Substitute the hydrogen ion concentration into the formula:
−log10(3 ×10−5)
Step 3: Simplify the expression:
−log10(3) −log10(10−5)
−log10(3) + 5
Step 4: Recall that log10(3) ≈0.4771. Substitute this value back into the
expression:
−0.4771 + 5
Step 5: Calculate the final value:
5−0.4771 = 4.5229
Step 6: Therefore, the pH of the solution is approximately 4.52.
Question 3
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+]. Therefore, to find the pH
of the solution, we first need to calculate [H+] from the given hydronium ion
concentration.
Step 2: The concentration of hydronium ions, [H+], is given as 3.2×10−5
M.
Step 3: Substituting the given value of [H+] into the formula for pH, we
have:
pH = −log3.2×10−5
Step 4: Calculate the pH:
pH = −log3.2×10−5=−log(3.2) −log10−5
Step 5: Simplify the expression:
pH = −log(3.2) + 5 = −0.5052 + 5 = 4.4948
Step 6: Therefore, the pH of the solution with a hydronium ion concentra-
tion of 3.2×10−5M is 4.49.
2
Question 4
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Given that [OH−]=1.5×10−10 M,
pOH =−log1.5×10−10
pOH =−(log 1.5 + log 10−10)
pOH =−(0.17609 + (−10))
pOH = 9.82391 ≈9.82
Step 2: Calculate the pH of the solution using the formula:
pH = 14 −pOH
Substitute the calculated pOH value into the formula:
pH = 14 −9.82
pH = 4.18
Therefore, the pH of the solution is 4.18.
Question 5
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+]
pOH = −log[OH−]
3
pH + pOH = 14
Step 2: Given that [H+] = 3.2×10−5M, we can calculate the pH using the
formula:
pH = −log3.2×10−5
Step 3: Calculating the pH:
pH = −log3.2×10−5=−log(3.2)+log10−5=−(−0.4948)+(−5) = 0.4948−5 = 4.5052
Therefore, the pH of the solution is 4.5052.
Step 4: Using the relationship between pH and pOH, we can find the pOH:
pH + pOH = 14
4.5052 + pOH = 14
Step 5: Solving for pOH:
pOH = 14 −4.5052 = 9.4948
Therefore, the pOH of the solution is 9.4948.
Question 6
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−4
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
pH formula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−4=−(−3.6) = 3.6
Step 4: Therefore, the pH of the solution is 3.6.
Question 7
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl).
(Given: Kw= 1.0×10−14 at 25
°
C)
4
Solution
Step 1: Write the dissociation equation for HCl:
HCl →H++ Cl−
Step 2: Calculate the concentration of H+ions produced: Since HCl is a
strong acid, it dissociates completely. Therefore, the concentration of H+ions
will be the same as the initial concentration of HCl.
[H+]=0.025 M
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log(0.025)
pH = −log2.5×10−2
pH = −(−1.60)
pH = 1.60
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.60.
Question 8
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −log[OH−] = −log1.5×10−3
Step 2: Solve for pOH:
pOH = −log1.5×10−3=−log(1.5)+log10−3=−log(1.5)−3=0.1761−3 = −2.8239
Step 3: Use the relationship between pH and pOH:
pH + pOH = 14
Step 4: Solve for pH:
pH = 14 −pOH = 14 −(−2.8239) = 16.8239
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 16.8239.
5
Question 9
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 of water.
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
Kw= [H+][OH−] = 1.0×10−14 (at 25
°
C)
Since the solution is neutral, the hydrogen ion concentration is equal to the
hydroxide ion concentration. Therefore, [H+]=1.5×10−3M.
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log1.5×10−3≈2.82
Question 10
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. We are given the concentration
of hydronium ions, so we can use this formula to calculate the pH:
pH = −log[H+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log1.5×10−9
Step 3: Calculate the pH using a calculator:
pH ≈ − log1.5×10−9≈ −(−8.82) ≈8.82
Step 4: Therefore, the pH of the solution is approximately 8.82.
6
Question 11
Question
A solution has a hydrogen ion concentration of 2.3×10−5M. Calculate the pH
and pOH of the solution.
Solution
Step 1: Recall the definitions of pH and pOH.
pH = −log[H+]
pOH = −log[OH−]
Step 2: Calculate the pH using the hydrogen ion concentration given.
pH = −log2.3×10−5
pH = −log(2.3) + log10−5
pH ≈ −(log(2.3) −5)
pH ≈ −(0.3617 −5)
pH ≈ −(4.6383)
pH ≈4.64
Step 3: Use the relationship pH + pOH = 14 to find the pOH.
pOH = 14 −pH
pOH = 14 −4.64
pOH ≈9.36
Therefore, the pH of the solution is approximately 4.64 and the pOH is
approximately 9.36.
Question 12
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.78 ×10−6
M.
Solution
Step 1: The pH of a solution is calculated using the formula:
pH = −log[H+]
7
Given that the hydrogen ion concentration is 3.78 ×10−6M, we can substitute
this value into the formula to find the pH.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.78 ×10−6
Step 3: Calculate the pH:
pH = −log3.78 ×10−6
pH = −(log 3.78 + log 10−6)
pH = −(0.5775 + (−6))
pH = −0.5775 + 6
pH = 5.4225
Therefore, the pH of the solution with a hydrogen ion concentration of 3.78×
10−6M is 5.4225.
Question 13
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
1.5×10−4M.
Solution
Step 1: Recall that pH is calculated using the formula pH =−log[H3O+],
where [H3O+] represents the concentration of hydronium ions.
Step 2: Substitute the given concentration of hydronium ions into the for-
mula:
pH = −log1.5×10−4
Step 3: Calculate the pH:
pH = −log1.5×10−4=−(−3.823) = 3.823
Step 4: Now, since pH +pOH = 14, we can calculate the pOH using the
formula pOH = 14 −pH.
Step 5: Substitute the calculated pH into the formula to find the pOH:
pOH = 14 −3.823 = 10.177
Step 6: Therefore, the pH of the solution is 3.823 and the pOH is 10.177.
8
Question 14
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.22 ×10−5M.
Solution
Step 1: Recall the relationship between hydronium ion concentration ([H3O+]),
pH, and pOH:
pH = −log[H3O+],pOH = −log[OH−]
Step 2: Given the hydronium ion concentration [H3O+]=3.22 ×10−5M,
we can calculate the pH:
pH = −log3.22 ×10−5
pH = −log(3.22) −log10−5
pH = −(log(3.22) + (−5))
pH = −(log(3.22) −5)
pH ≈ −(−0.4906 −5)
pH ≈5.49
Step 3: Now, we can calculate the pOH using the relationship:
pOH = 14 −pH
pOH = 14 −5.49
pOH ≈8.51
Therefore, the pH of the solution is approximately 5.49 and the pOH is
approximately 8.51.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−6
M.
9
Solution
Step 1: Write out the formula for calculating pH.
pH = −log[H+]
where [H+] is the hydrogen ion concentration in moles per liter.
Step 2: Substitute the given hydrogen ion concentration into the formula.
pH = −log2.5×10−6
Step 3: Calculate the pH.
pH = −log2.5×10−6=−log(2.5) + log10−6
Step 4: Simplify the expression.
pH = −(log(2.5)−6) = −(log(2.5)−log106) = −(log(2.5)−6) = −(log(2.5)−6) = −(log(2.5)−6)
Step 5: Use the properties of logarithms to further simplify the expression.
pH = −(0.3979 −6) = −(−5.6021) = 5.6021
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−6M is 5.6021.
Question 16
Question
Calculate the pH of a solution with a pOH of 2.4.
Solution
Step 1: Recall the relationship between pH and pOH:
pH +pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH = 14 −2.4
Step 3: Calculate the pH:
pH = 11.6
Therefore, the pH of the solution is 11.6.
10
Question 17
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
pH = −log2.5×10−9
Step 2: Calculate the pH using a calculator.
pH = −log2.5×10−9≈ − log(2.5) + 9 ≈9.60
Step 3: Remember that pOH is defined as −log[OH−], where [OH−] is the
hydroxide ion concentration. Since pH + pOH = 14, we can find the pOH.
pOH = 14 −pH
pOH = 14 −9.60
Step 4: Calculate the pOH using the pH value obtained in Step 2.
pOH = 14 −9.60 = 4.40
Therefore, the pH of the solution is 9.60 and the pOH is 4.40.
Question 18
Question
Calculate the pH of a solution with a H+concentration of 3.2×10−5M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula: pH =
−log[H+].
Step 2: Substitute the given H+concentration into the formula:
pH =−log3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH =−log(3.2) −log10−5
pH =−log(3.2) −(−5)
11
Step 4: Calculate the logarithm of 3.2 using a calculator:
log(3.2) ≈0.505
Step 5: Substitute the approximate value back into the equation:
pH ≈ −0.505 + 5
pH ≈4.495
Step 6: Therefore, the pH of the solution is approximately 4.495.
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.6×10−4
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration ([H3O+]):
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.6×10−4
Step 3: Use a calculator to find the value of −log3.6×10−4:
pH ≈ − log3.6×10−4≈ −(−3.44) ≈3.44
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.6×10−4M is approximately 3.44.
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
12
Solution
Step 1: Recall the relationship between pH and the hydronium ion concentra-
tion:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−4
Step 3: Calculate the pH:
pH = −log2.5×10−4=−log(2.5) −log10−4
Step 4: Recall that −log10−4= 4:
pH = −log(2.5) −4
Step 5: Use a calculator to find −log(2.5) ≈ −0.3979:
pH ≈ −0.3979 −4 = 3.6021
Therefore, the pH of the solution is approximately 3.60.
Question 21
Question
Calculate the pH of a solution that has a hydrogen ion concentration of 3.5×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Thus, we need to first find the
hydrogen ion concentration from the given pH. Given [H+]=3.5×10−6M, we
can now calculate the pH as follows:
pH = −log3.5×10−6
Step 2: Use the properties of logarithms to simplify the calculation.
pH = −log(3.5) −log10−6
pH = −log(3.5) −(−6)
pH = −log(3.5) + 6
Step 3: Evaluate the logarithmic term using a calculator.
pH ≈ −(−0.455932) + 6
pH ≈0.455932 + 6
pH ≈6.455932
Therefore, the pH of the solution is approximately 6.46.
13
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M. (Assume complete dissociation of hydroxide ions in solution.)
Solution
Step 1: Write out the dissociation of hydroxide ions in water:
OH−(aq)→H2O(l)+O2−(aq)
Step 2: Determine the concentration of hydrogen ions ([H+]) using the hy-
droxide ion concentration:
Kw= [H+]×[OH−]
Since Kw= 1.0×10−14 at 25
°
C, and we are given [OH−] = 2.5×10−5M:
[H+] = 1.0×10−14
2.5×10−5= 4.0×10−10
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions:
pH = −log [H+] = −log 4.0×10−10 = 9.4
Therefore, the pH of the solution is 9.4.
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.7×10−5
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. Therefore,
in this case, we have:
pH = −log3.7×10−5
Step 2: Calculate the pH by plugging in the given hydronium ion concen-
tration:
pH = −log3.7×10−5
pH = −log(3.7) + log10−5
14
pH = −(log(3.7) −5)
pH ≈ −(0.5682 −5)
Step 3: Further solve for the pH value:
pH ≈ −(0.5682 −5)
pH ≈ −(−4.4318)
pH ≈4.4318
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 3.7×10−5M is approximately 4.43.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−]
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration.
Kw= 1.0×10−14 (at 25
°
C)
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
Step 3: Calculate the hydrogen ion concentration and then the pH.
[H+]=4.0×10−11 M
pH = −log[H+]=−log4.0×10−11
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
15
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Use the relationship between Kwand the concentrations of hydro-
nium and hydroxide ions:
Kw= [H+][OH−]=1.0×10−14
Step 3: Given the hydroxide ion concentration is 2.5×10−4M, we can
determine the hydronium ion concentration:
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
[H+] = 4.0×10−11 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log4.0×10−11
pH = −(log(4.0) + log10−11)
pH = −(0.6021 + (−11))
pH = 10.6021
Therefore, the pH of the solution is 10.6021.
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 pH is defined as −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log3.2×10−7
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−7
16
pH = −log(3.2) −(−7)
Step 4: Use a calculator to find the pH:
pH ≈ −0.5051 −(−7)
pH ≈6.4949
Step 5: Therefore, the pH of the solution is approximately 6.49.
Question 27
Question
Calculate the pH of a solution that is 0.020 M in hydrochloric acid (HCl). (Hint:
HCl is a strong acid.)
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 in
water. Therefore, the concentration of H+ions in the solution will be equal to
the initial concentration of HCl, which is 0.020 M.
Step 3: Calculate the pH using the formula:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.020)
Step 5: Calculate the pH:
pH = −log(0.020) = −(−1.69897) = 1.69897
Therefore, the pH of the solution that is 0.020 M in hydrochloric acid is
approximately 1.70.
Question 28
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
17
Solution
Step 1: Recall the relationship between pH, pOH, and the concentrations of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH:
pH = −log2.5×10−9
pH = −log(2.5) −log10−9
pH = −log(2.5) −(−9)
pH = 9 −log(2.5)
pH ≈9−0.3979
pH ≈8.6021
Step 3: Using the relationship pH + pOH = 14, we can find the pOH:
pOH = 14 −pH
pOH = 14 −8.6021
pOH ≈5.3979
Therefore, the pH of the solution is approximately 8.6021 and the pOH is
approximately 5.3979.
Question 29
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
18
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration given to find the hydrogen ion
concentration.
[OH−] = 2.5×10−5M
1.0×10−14
2.5×10−5= [H+]
[H+] = 4.0×10−10 M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log4.0×10−10
pH = −log(4.0) −log10−10
pH = −0.6021 −(−10)
pH = 9.3979
Therefore, the pH of the solution is 9.40.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−5
M.
Solution
Step 1: Use the relationship between [OH−] and pOH to find pOH.
pOH = −log[OH−]
pOH = −log1.5×10−5
pOH = −(−4.82)
pOH = 4.82
Step 2: Use the fact that pOH + pH = 14 to find pH.
pH = 14 −pOH
pH = 14 −4.82
pH = 9.18
Therefore, the pH of the solution is 9.18.
19
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall the definition of pH and the relationship between hydronium ion
concentration and 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 pH for-
mula.
pH = −log1.5×10−3
Step 3: Calculate the pH.
pH = −log1.5×10−3=−(−2.82) = 2.82
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 2.82.
Question 32
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall the relation between [H3O+] and pH:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the equation:
pH = −log1.5×10−3
Step 3: Solve for pH:
pH = −log1.5×10−3=−log(1.5) −log10−3
Step 4: Use the property −log(10n) = −n:
pH = −log(1.5) −log10−3=−log(1.5) −(−3)
20
Step 5: Calculate the value of −log(1.5):
pH ≈ −0.176 −(−3) = 2.824
Step 6: Therefore, the pH of a solution with a hydronium ion concentration
of 1.5×10−3M is approximately 2.824.
Question 33
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log2.5×10−6
Step 3: Calculate the pH using a calculator:
pH ≈ −(−5.60)
pH ≈5.60
Step 4: Therefore, the pH of the solution is approximately 5.60.
Question 34
Question
Calculate the pH of a solution if the concentration of hydronium ions is 2.5×10−5
M.
Solution
Step 1: Recall that the pH is defined as the negative base-10 logarithm of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−5
21
Step 3: Use the properties of logarithms to simplify:
pH = −log(2.5) −log10−5
pH = −log(2.5) −(−5)
Step 4: Calculate the pH:
pH = −log(2.5) + 5 ≈4.60
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−5M is approximately 4.60.
Question 35
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that the relationship between pH, pOH, and the ion concentra-
tions is given by:
pH + pOH = 14
Step 2: First, calculate the pOH of the solution using the given hydroxide ion
concentration:
pOH = −logOH−=−log2.5×10−5
Step 3: Calculate pOH:
pOH = −log2.5×10−5=−(−4.60) = 4.60
Step 4: Use the relationship between pH and pOH to find the pH of the solution:
pH = 14 −pOH = 14 −4.60
Step 5: Calculate pH:
pH = 14 −4.60 = 9.40
Step 6: Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−5M is pH = 9.40.
22
Question 4
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Given that [OH−]=1.5×10−10 M,
pOH =−log1.5×10−10
pOH =−(log 1.5 + log 10−10)
pOH =−(0.17609 + (−10))
pOH = 9.82391 ≈9.82
Step 2: Calculate the pH of the solution using the formula:
pH = 14 −pOH
Substitute the calculated pOH value into the formula:
pH = 14 −9.82
pH = 4.18
Therefore, the pH of the solution is 4.18.
Question 5
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+]
pOH = −log[OH−]
3
pH + pOH = 14
Step 2: Given that [H+] = 3.2×10−5M, we can calculate the pH using the
formula:
pH = −log3.2×10−5
Step 3: Calculating the pH:
pH = −log3.2×10−5=−log(3.2)+log10−5=−(−0.4948)+(−5) = 0.4948−5 = 4.5052
Therefore, the pH of the solution is 4.5052.
Step 4: Using the relationship between pH and pOH, we can find the pOH:
pH + pOH = 14
4.5052 + pOH = 14
Step 5: Solving for pOH:
pOH = 14 −4.5052 = 9.4948
Therefore, the pOH of the solution is 9.4948.
Question 6
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−4
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
pH formula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−4=−(−3.6) = 3.6
Step 4: Therefore, the pH of the solution is 3.6.
Question 7
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl).
(Given: Kw= 1.0×10−14 at 25
°
C)
4
Solution
Step 1: Write the dissociation equation for HCl:
HCl →H++ Cl−
Step 2: Calculate the concentration of H+ions produced: Since HCl is a
strong acid, it dissociates completely. Therefore, the concentration of H+ions
will be the same as the initial concentration of HCl.
[H+]=0.025 M
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log(0.025)
pH = −log2.5×10−2
pH = −(−1.60)
pH = 1.60
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.60.
Question 8
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −log[OH−] = −log1.5×10−3
Step 2: Solve for pOH:
pOH = −log1.5×10−3=−log(1.5)+log10−3=−log(1.5)−3=0.1761−3 = −2.8239
Step 3: Use the relationship between pH and pOH:
pH + pOH = 14
Step 4: Solve for pH:
pH = 14 −pOH = 14 −(−2.8239) = 16.8239
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 16.8239.
5
Question 9
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 of water.
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
Kw= [H+][OH−] = 1.0×10−14 (at 25
°
C)
Since the solution is neutral, the hydrogen ion concentration is equal to the
hydroxide ion concentration. Therefore, [H+]=1.5×10−3M.
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log1.5×10−3≈2.82
Question 10
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. We are given the concentration
of hydronium ions, so we can use this formula to calculate the pH:
pH = −log[H+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log1.5×10−9
Step 3: Calculate the pH using a calculator:
pH ≈ − log1.5×10−9≈ −(−8.82) ≈8.82
Step 4: Therefore, the pH of the solution is approximately 8.82.
6
Question 11
Question
A solution has a hydrogen ion concentration of 2.3×10−5M. Calculate the pH
and pOH of the solution.
Solution
Step 1: Recall the definitions of pH and pOH.
pH = −log[H+]
pOH = −log[OH−]
Step 2: Calculate the pH using the hydrogen ion concentration given.
pH = −log2.3×10−5
pH = −log(2.3) + log10−5
pH ≈ −(log(2.3) −5)
pH ≈ −(0.3617 −5)
pH ≈ −(4.6383)
pH ≈4.64
Step 3: Use the relationship pH + pOH = 14 to find the pOH.
pOH = 14 −pH
pOH = 14 −4.64
pOH ≈9.36
Therefore, the pH of the solution is approximately 4.64 and the pOH is
approximately 9.36.
Question 12
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.78 ×10−6
M.
Solution
Step 1: The pH of a solution is calculated using the formula:
pH = −log[H+]
7
Given that the hydrogen ion concentration is 3.78 ×10−6M, we can substitute
this value into the formula to find the pH.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.78 ×10−6
Step 3: Calculate the pH:
pH = −log3.78 ×10−6
pH = −(log 3.78 + log 10−6)
pH = −(0.5775 + (−6))
pH = −0.5775 + 6
pH = 5.4225
Therefore, the pH of the solution with a hydrogen ion concentration of 3.78×
10−6M is 5.4225.
Question 13
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
1.5×10−4M.
Solution
Step 1: Recall that pH is calculated using the formula pH =−log[H3O+],
where [H3O+] represents the concentration of hydronium ions.
Step 2: Substitute the given concentration of hydronium ions into the for-
mula:
pH = −log1.5×10−4
Step 3: Calculate the pH:
pH = −log1.5×10−4=−(−3.823) = 3.823
Step 4: Now, since pH +pOH = 14, we can calculate the pOH using the
formula pOH = 14 −pH.
Step 5: Substitute the calculated pH into the formula to find the pOH:
pOH = 14 −3.823 = 10.177
Step 6: Therefore, the pH of the solution is 3.823 and the pOH is 10.177.
8
Question 14
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.22 ×10−5M.
Solution
Step 1: Recall the relationship between hydronium ion concentration ([H3O+]),
pH, and pOH:
pH = −log[H3O+],pOH = −log[OH−]
Step 2: Given the hydronium ion concentration [H3O+]=3.22 ×10−5M,
we can calculate the pH:
pH = −log3.22 ×10−5
pH = −log(3.22) −log10−5
pH = −(log(3.22) + (−5))
pH = −(log(3.22) −5)
pH ≈ −(−0.4906 −5)
pH ≈5.49
Step 3: Now, we can calculate the pOH using the relationship:
pOH = 14 −pH
pOH = 14 −5.49
pOH ≈8.51
Therefore, the pH of the solution is approximately 5.49 and the pOH is
approximately 8.51.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−6
M.
9
Solution
Step 1: Write out the formula for calculating pH.
pH = −log[H+]
where [H+] is the hydrogen ion concentration in moles per liter.
Step 2: Substitute the given hydrogen ion concentration into the formula.
pH = −log2.5×10−6
Step 3: Calculate the pH.
pH = −log2.5×10−6=−log(2.5) + log10−6
Step 4: Simplify the expression.
pH = −(log(2.5)−6) = −(log(2.5)−log106) = −(log(2.5)−6) = −(log(2.5)−6) = −(log(2.5)−6)
Step 5: Use the properties of logarithms to further simplify the expression.
pH = −(0.3979 −6) = −(−5.6021) = 5.6021
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−6M is 5.6021.
Question 16
Question
Calculate the pH of a solution with a pOH of 2.4.
Solution
Step 1: Recall the relationship between pH and pOH:
pH +pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH = 14 −2.4
Step 3: Calculate the pH:
pH = 11.6
Therefore, the pH of the solution is 11.6.
10
Question 17
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
pH = −log2.5×10−9
Step 2: Calculate the pH using a calculator.
pH = −log2.5×10−9≈ − log(2.5) + 9 ≈9.60
Step 3: Remember that pOH is defined as −log[OH−], where [OH−] is the
hydroxide ion concentration. Since pH + pOH = 14, we can find the pOH.
pOH = 14 −pH
pOH = 14 −9.60
Step 4: Calculate the pOH using the pH value obtained in Step 2.
pOH = 14 −9.60 = 4.40
Therefore, the pH of the solution is 9.60 and the pOH is 4.40.
Question 18
Question
Calculate the pH of a solution with a H+concentration of 3.2×10−5M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula: pH =
−log[H+].
Step 2: Substitute the given H+concentration into the formula:
pH =−log3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH =−log(3.2) −log10−5
pH =−log(3.2) −(−5)
11
Step 4: Calculate the logarithm of 3.2 using a calculator:
log(3.2) ≈0.505
Step 5: Substitute the approximate value back into the equation:
pH ≈ −0.505 + 5
pH ≈4.495
Step 6: Therefore, the pH of the solution is approximately 4.495.
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.6×10−4
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration ([H3O+]):
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.6×10−4
Step 3: Use a calculator to find the value of −log3.6×10−4:
pH ≈ − log3.6×10−4≈ −(−3.44) ≈3.44
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.6×10−4M is approximately 3.44.
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
12
Solution
Step 1: Recall the relationship between pH and the hydronium ion concentra-
tion:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−4
Step 3: Calculate the pH:
pH = −log2.5×10−4=−log(2.5) −log10−4
Step 4: Recall that −log10−4= 4:
pH = −log(2.5) −4
Step 5: Use a calculator to find −log(2.5) ≈ −0.3979:
pH ≈ −0.3979 −4 = 3.6021
Therefore, the pH of the solution is approximately 3.60.
Question 21
Question
Calculate the pH of a solution that has a hydrogen ion concentration of 3.5×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Thus, we need to first find the
hydrogen ion concentration from the given pH. Given [H+]=3.5×10−6M, we
can now calculate the pH as follows:
pH = −log3.5×10−6
Step 2: Use the properties of logarithms to simplify the calculation.
pH = −log(3.5) −log10−6
pH = −log(3.5) −(−6)
pH = −log(3.5) + 6
Step 3: Evaluate the logarithmic term using a calculator.
pH ≈ −(−0.455932) + 6
pH ≈0.455932 + 6
pH ≈6.455932
Therefore, the pH of the solution is approximately 6.46.
13
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M. (Assume complete dissociation of hydroxide ions in solution.)
Solution
Step 1: Write out the dissociation of hydroxide ions in water:
OH−(aq)→H2O(l)+O2−(aq)
Step 2: Determine the concentration of hydrogen ions ([H+]) using the hy-
droxide ion concentration:
Kw= [H+]×[OH−]
Since Kw= 1.0×10−14 at 25
°
C, and we are given [OH−] = 2.5×10−5M:
[H+] = 1.0×10−14
2.5×10−5= 4.0×10−10
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions:
pH = −log [H+] = −log 4.0×10−10 = 9.4
Therefore, the pH of the solution is 9.4.
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.7×10−5
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. Therefore,
in this case, we have:
pH = −log3.7×10−5
Step 2: Calculate the pH by plugging in the given hydronium ion concen-
tration:
pH = −log3.7×10−5
pH = −log(3.7) + log10−5
14
pH = −(log(3.7) −5)
pH ≈ −(0.5682 −5)
Step 3: Further solve for the pH value:
pH ≈ −(0.5682 −5)
pH ≈ −(−4.4318)
pH ≈4.4318
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 3.7×10−5M is approximately 4.43.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−]
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration.
Kw= 1.0×10−14 (at 25
°
C)
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
Step 3: Calculate the hydrogen ion concentration and then the pH.
[H+]=4.0×10−11 M
pH = −log[H+]=−log4.0×10−11
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
15
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Use the relationship between Kwand the concentrations of hydro-
nium and hydroxide ions:
Kw= [H+][OH−]=1.0×10−14
Step 3: Given the hydroxide ion concentration is 2.5×10−4M, we can
determine the hydronium ion concentration:
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
[H+] = 4.0×10−11 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log4.0×10−11
pH = −(log(4.0) + log10−11)
pH = −(0.6021 + (−11))
pH = 10.6021
Therefore, the pH of the solution is 10.6021.
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 pH is defined as −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log3.2×10−7
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−7
16
pH = −log(3.2) −(−7)
Step 4: Use a calculator to find the pH:
pH ≈ −0.5051 −(−7)
pH ≈6.4949
Step 5: Therefore, the pH of the solution is approximately 6.49.
Question 27
Question
Calculate the pH of a solution that is 0.020 M in hydrochloric acid (HCl). (Hint:
HCl is a strong acid.)
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 in
water. Therefore, the concentration of H+ions in the solution will be equal to
the initial concentration of HCl, which is 0.020 M.
Step 3: Calculate the pH using the formula:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.020)
Step 5: Calculate the pH:
pH = −log(0.020) = −(−1.69897) = 1.69897
Therefore, the pH of the solution that is 0.020 M in hydrochloric acid is
approximately 1.70.
Question 28
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
17
Solution
Step 1: Recall the relationship between pH, pOH, and the concentrations of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH:
pH = −log2.5×10−9
pH = −log(2.5) −log10−9
pH = −log(2.5) −(−9)
pH = 9 −log(2.5)
pH ≈9−0.3979
pH ≈8.6021
Step 3: Using the relationship pH + pOH = 14, we can find the pOH:
pOH = 14 −pH
pOH = 14 −8.6021
pOH ≈5.3979
Therefore, the pH of the solution is approximately 8.6021 and the pOH is
approximately 5.3979.
Question 29
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
18
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration given to find the hydrogen ion
concentration.
[OH−] = 2.5×10−5M
1.0×10−14
2.5×10−5= [H+]
[H+] = 4.0×10−10 M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log4.0×10−10
pH = −log(4.0) −log10−10
pH = −0.6021 −(−10)
pH = 9.3979
Therefore, the pH of the solution is 9.40.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−5
M.
Solution
Step 1: Use the relationship between [OH−] and pOH to find pOH.
pOH = −log[OH−]
pOH = −log1.5×10−5
pOH = −(−4.82)
pOH = 4.82
Step 2: Use the fact that pOH + pH = 14 to find pH.
pH = 14 −pOH
pH = 14 −4.82
pH = 9.18
Therefore, the pH of the solution is 9.18.
19
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall the definition of pH and the relationship between hydronium ion
concentration and 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 pH for-
mula.
pH = −log1.5×10−3
Step 3: Calculate the pH.
pH = −log1.5×10−3=−(−2.82) = 2.82
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 2.82.
Question 32
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall the relation between [H3O+] and pH:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the equation:
pH = −log1.5×10−3
Step 3: Solve for pH:
pH = −log1.5×10−3=−log(1.5) −log10−3
Step 4: Use the property −log(10n) = −n:
pH = −log(1.5) −log10−3=−log(1.5) −(−3)
20
Step 5: Calculate the value of −log(1.5):
pH ≈ −0.176 −(−3) = 2.824
Step 6: Therefore, the pH of a solution with a hydronium ion concentration
of 1.5×10−3M is approximately 2.824.
Question 33
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log2.5×10−6
Step 3: Calculate the pH using a calculator:
pH ≈ −(−5.60)
pH ≈5.60
Step 4: Therefore, the pH of the solution is approximately 5.60.
Question 34
Question
Calculate the pH of a solution if the concentration of hydronium ions is 2.5×10−5
M.
Solution
Step 1: Recall that the pH is defined as the negative base-10 logarithm of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−5
21
Step 3: Use the properties of logarithms to simplify:
pH = −log(2.5) −log10−5
pH = −log(2.5) −(−5)
Step 4: Calculate the pH:
pH = −log(2.5) + 5 ≈4.60
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−5M is approximately 4.60.
Question 35
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that the relationship between pH, pOH, and the ion concentra-
tions is given by:
pH + pOH = 14
Step 2: First, calculate the pOH of the solution using the given hydroxide ion
concentration:
pOH = −logOH−=−log2.5×10−5
Step 3: Calculate pOH:
pOH = −log2.5×10−5=−(−4.60) = 4.60
Step 4: Use the relationship between pH and pOH to find the pH of the solution:
pH = 14 −pOH = 14 −4.60
Step 5: Calculate pH:
pH = 14 −4.60 = 9.40
Step 6: Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−5M is pH = 9.40.
22
Question 4
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−10
M.
Solution
Step 1: Calculate the pOH of the solution using the formula:
pOH =−log[OH−]
Given that [OH−]=1.5×10−10 M,
pOH =−log1.5×10−10
pOH =−(log 1.5 + log 10−10)
pOH =−(0.17609 + (−10))
pOH = 9.82391 ≈9.82
Step 2: Calculate the pH of the solution using the formula:
pH = 14 −pOH
Substitute the calculated pOH value into the formula:
pH = 14 −9.82
pH = 4.18
Therefore, the pH of the solution is 4.18.
Question 5
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−5M.
Solution
Step 1: Recall the relationship between pH, pOH, and the concentration of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+]
pOH = −log[OH−]
3
pH + pOH = 14
Step 2: Given that [H+] = 3.2×10−5M, we can calculate the pH using the
formula:
pH = −log3.2×10−5
Step 3: Calculating the pH:
pH = −log3.2×10−5=−log(3.2)+log10−5=−(−0.4948)+(−5) = 0.4948−5 = 4.5052
Therefore, the pH of the solution is 4.5052.
Step 4: Using the relationship between pH and pOH, we can find the pOH:
pH + pOH = 14
4.5052 + pOH = 14
Step 5: Solving for pOH:
pOH = 14 −4.5052 = 9.4948
Therefore, the pOH of the solution is 9.4948.
Question 6
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−4
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
pH formula:
pH = −log2.5×10−4
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−4=−(−3.6) = 3.6
Step 4: Therefore, the pH of the solution is 3.6.
Question 7
Question
Calculate the pH of a solution that is 0.025 M in hydrochloric acid (HCl).
(Given: Kw= 1.0×10−14 at 25
°
C)
4
Solution
Step 1: Write the dissociation equation for HCl:
HCl →H++ Cl−
Step 2: Calculate the concentration of H+ions produced: Since HCl is a
strong acid, it dissociates completely. Therefore, the concentration of H+ions
will be the same as the initial concentration of HCl.
[H+]=0.025 M
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log(0.025)
pH = −log2.5×10−2
pH = −(−1.60)
pH = 1.60
Therefore, the pH of a 0.025 M hydrochloric acid solution is 1.60.
Question 8
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH = −log[OH−] = −log1.5×10−3
Step 2: Solve for pOH:
pOH = −log1.5×10−3=−log(1.5)+log10−3=−log(1.5)−3=0.1761−3 = −2.8239
Step 3: Use the relationship between pH and pOH:
pH + pOH = 14
Step 4: Solve for pH:
pH = 14 −pOH = 14 −(−2.8239) = 16.8239
Therefore, the pH of the solution with a hydroxide ion concentration of
1.5×10−3M is approximately 16.8239.
5
Question 9
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 of water.
Kw= [H+][OH−]
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
Kw= [H+][OH−] = 1.0×10−14 (at 25
°
C)
Since the solution is neutral, the hydrogen ion concentration is equal to the
hydroxide ion concentration. Therefore, [H+]=1.5×10−3M.
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log1.5×10−3≈2.82
Question 10
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. We are given the concentration
of hydronium ions, so we can use this formula to calculate the pH:
pH = −log[H+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log1.5×10−9
Step 3: Calculate the pH using a calculator:
pH ≈ − log1.5×10−9≈ −(−8.82) ≈8.82
Step 4: Therefore, the pH of the solution is approximately 8.82.
6
Question 11
Question
A solution has a hydrogen ion concentration of 2.3×10−5M. Calculate the pH
and pOH of the solution.
Solution
Step 1: Recall the definitions of pH and pOH.
pH = −log[H+]
pOH = −log[OH−]
Step 2: Calculate the pH using the hydrogen ion concentration given.
pH = −log2.3×10−5
pH = −log(2.3) + log10−5
pH ≈ −(log(2.3) −5)
pH ≈ −(0.3617 −5)
pH ≈ −(4.6383)
pH ≈4.64
Step 3: Use the relationship pH + pOH = 14 to find the pOH.
pOH = 14 −pH
pOH = 14 −4.64
pOH ≈9.36
Therefore, the pH of the solution is approximately 4.64 and the pOH is
approximately 9.36.
Question 12
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.78 ×10−6
M.
Solution
Step 1: The pH of a solution is calculated using the formula:
pH = −log[H+]
7
Given that the hydrogen ion concentration is 3.78 ×10−6M, we can substitute
this value into the formula to find the pH.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.78 ×10−6
Step 3: Calculate the pH:
pH = −log3.78 ×10−6
pH = −(log 3.78 + log 10−6)
pH = −(0.5775 + (−6))
pH = −0.5775 + 6
pH = 5.4225
Therefore, the pH of the solution with a hydrogen ion concentration of 3.78×
10−6M is 5.4225.
Question 13
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
1.5×10−4M.
Solution
Step 1: Recall that pH is calculated using the formula pH =−log[H3O+],
where [H3O+] represents the concentration of hydronium ions.
Step 2: Substitute the given concentration of hydronium ions into the for-
mula:
pH = −log1.5×10−4
Step 3: Calculate the pH:
pH = −log1.5×10−4=−(−3.823) = 3.823
Step 4: Now, since pH +pOH = 14, we can calculate the pOH using the
formula pOH = 14 −pH.
Step 5: Substitute the calculated pH into the formula to find the pOH:
pOH = 14 −3.823 = 10.177
Step 6: Therefore, the pH of the solution is 3.823 and the pOH is 10.177.
8
Question 14
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.22 ×10−5M.
Solution
Step 1: Recall the relationship between hydronium ion concentration ([H3O+]),
pH, and pOH:
pH = −log[H3O+],pOH = −log[OH−]
Step 2: Given the hydronium ion concentration [H3O+]=3.22 ×10−5M,
we can calculate the pH:
pH = −log3.22 ×10−5
pH = −log(3.22) −log10−5
pH = −(log(3.22) + (−5))
pH = −(log(3.22) −5)
pH ≈ −(−0.4906 −5)
pH ≈5.49
Step 3: Now, we can calculate the pOH using the relationship:
pOH = 14 −pH
pOH = 14 −5.49
pOH ≈8.51
Therefore, the pH of the solution is approximately 5.49 and the pOH is
approximately 8.51.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−6
M.
9
Solution
Step 1: Write out the formula for calculating pH.
pH = −log[H+]
where [H+] is the hydrogen ion concentration in moles per liter.
Step 2: Substitute the given hydrogen ion concentration into the formula.
pH = −log2.5×10−6
Step 3: Calculate the pH.
pH = −log2.5×10−6=−log(2.5) + log10−6
Step 4: Simplify the expression.
pH = −(log(2.5)−6) = −(log(2.5)−log106) = −(log(2.5)−6) = −(log(2.5)−6) = −(log(2.5)−6)
Step 5: Use the properties of logarithms to further simplify the expression.
pH = −(0.3979 −6) = −(−5.6021) = 5.6021
Therefore, the pH of the solution with a hydrogen ion concentration of 2.5×
10−6M is 5.6021.
Question 16
Question
Calculate the pH of a solution with a pOH of 2.4.
Solution
Step 1: Recall the relationship between pH and pOH:
pH +pOH = 14
Step 2: Substitute the given pOH value into the equation to find the pH:
pH = 14 −2.4
Step 3: Calculate the pH:
pH = 11.6
Therefore, the pH of the solution is 11.6.
10
Question 17
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the hydrogen ion
concentration.
pH = −log2.5×10−9
Step 2: Calculate the pH using a calculator.
pH = −log2.5×10−9≈ − log(2.5) + 9 ≈9.60
Step 3: Remember that pOH is defined as −log[OH−], where [OH−] is the
hydroxide ion concentration. Since pH + pOH = 14, we can find the pOH.
pOH = 14 −pH
pOH = 14 −9.60
Step 4: Calculate the pOH using the pH value obtained in Step 2.
pOH = 14 −9.60 = 4.40
Therefore, the pH of the solution is 9.60 and the pOH is 4.40.
Question 18
Question
Calculate the pH of a solution with a H+concentration of 3.2×10−5M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula: pH =
−log[H+].
Step 2: Substitute the given H+concentration into the formula:
pH =−log3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH =−log(3.2) −log10−5
pH =−log(3.2) −(−5)
11
Step 4: Calculate the logarithm of 3.2 using a calculator:
log(3.2) ≈0.505
Step 5: Substitute the approximate value back into the equation:
pH ≈ −0.505 + 5
pH ≈4.495
Step 6: Therefore, the pH of the solution is approximately 4.495.
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.6×10−4
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydronium
ion concentration ([H3O+]):
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log3.6×10−4
Step 3: Use a calculator to find the value of −log3.6×10−4:
pH ≈ − log3.6×10−4≈ −(−3.44) ≈3.44
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.6×10−4M is approximately 3.44.
Question 20
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
12
Solution
Step 1: Recall the relationship between pH and the hydronium ion concentra-
tion:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−4
Step 3: Calculate the pH:
pH = −log2.5×10−4=−log(2.5) −log10−4
Step 4: Recall that −log10−4= 4:
pH = −log(2.5) −4
Step 5: Use a calculator to find −log(2.5) ≈ −0.3979:
pH ≈ −0.3979 −4 = 3.6021
Therefore, the pH of the solution is approximately 3.60.
Question 21
Question
Calculate the pH of a solution that has a hydrogen ion concentration of 3.5×10−6
M.
Solution
Step 1: Recall that pH is defined as −log[H+]. Thus, we need to first find the
hydrogen ion concentration from the given pH. Given [H+]=3.5×10−6M, we
can now calculate the pH as follows:
pH = −log3.5×10−6
Step 2: Use the properties of logarithms to simplify the calculation.
pH = −log(3.5) −log10−6
pH = −log(3.5) −(−6)
pH = −log(3.5) + 6
Step 3: Evaluate the logarithmic term using a calculator.
pH ≈ −(−0.455932) + 6
pH ≈0.455932 + 6
pH ≈6.455932
Therefore, the pH of the solution is approximately 6.46.
13
Question 22
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M. (Assume complete dissociation of hydroxide ions in solution.)
Solution
Step 1: Write out the dissociation of hydroxide ions in water:
OH−(aq)→H2O(l)+O2−(aq)
Step 2: Determine the concentration of hydrogen ions ([H+]) using the hy-
droxide ion concentration:
Kw= [H+]×[OH−]
Since Kw= 1.0×10−14 at 25
°
C, and we are given [OH−] = 2.5×10−5M:
[H+] = 1.0×10−14
2.5×10−5= 4.0×10−10
Step 3: Calculate the pH of the solution using the concentration of hydrogen
ions:
pH = −log [H+] = −log 4.0×10−10 = 9.4
Therefore, the pH of the solution is 9.4.
Question 23
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.7×10−5
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+]. Therefore,
in this case, we have:
pH = −log3.7×10−5
Step 2: Calculate the pH by plugging in the given hydronium ion concen-
tration:
pH = −log3.7×10−5
pH = −log(3.7) + log10−5
14
pH = −(log(3.7) −5)
pH ≈ −(0.5682 −5)
Step 3: Further solve for the pH value:
pH ≈ −(0.5682 −5)
pH ≈ −(−4.4318)
pH ≈4.4318
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 3.7×10−5M is approximately 4.43.
Question 24
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−]
Step 2: Use the hydroxide ion concentration to find the hydrogen ion con-
centration.
Kw= 1.0×10−14 (at 25
°
C)
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
Step 3: Calculate the hydrogen ion concentration and then the pH.
[H+]=4.0×10−11 M
pH = −log[H+]=−log4.0×10−11
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
15
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Use the relationship between Kwand the concentrations of hydro-
nium and hydroxide ions:
Kw= [H+][OH−]=1.0×10−14
Step 3: Given the hydroxide ion concentration is 2.5×10−4M, we can
determine the hydronium ion concentration:
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4
[H+] = 4.0×10−11 M
Step 4: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log4.0×10−11
pH = −(log(4.0) + log10−11)
pH = −(0.6021 + (−11))
pH = 10.6021
Therefore, the pH of the solution is 10.6021.
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 pH is defined as −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log3.2×10−7
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−7
16
pH = −log(3.2) −(−7)
Step 4: Use a calculator to find the pH:
pH ≈ −0.5051 −(−7)
pH ≈6.4949
Step 5: Therefore, the pH of the solution is approximately 6.49.
Question 27
Question
Calculate the pH of a solution that is 0.020 M in hydrochloric acid (HCl). (Hint:
HCl is a strong acid.)
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 in
water. Therefore, the concentration of H+ions in the solution will be equal to
the initial concentration of HCl, which is 0.020 M.
Step 3: Calculate the pH using the formula:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.020)
Step 5: Calculate the pH:
pH = −log(0.020) = −(−1.69897) = 1.69897
Therefore, the pH of the solution that is 0.020 M in hydrochloric acid is
approximately 1.70.
Question 28
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−9M.
17
Solution
Step 1: Recall the relationship between pH, pOH, and the concentrations of
hydrogen ions ([H+]) and hydroxide ions ([OH−]):
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 2.5×10−9M, we can
calculate the pH:
pH = −log2.5×10−9
pH = −log(2.5) −log10−9
pH = −log(2.5) −(−9)
pH = 9 −log(2.5)
pH ≈9−0.3979
pH ≈8.6021
Step 3: Using the relationship pH + pOH = 14, we can find the pOH:
pOH = 14 −pH
pOH = 14 −8.6021
pOH ≈5.3979
Therefore, the pH of the solution is approximately 8.6021 and the pOH is
approximately 5.3979.
Question 29
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
18
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the hydroxide ion concentration given to find the hydrogen ion
concentration.
[OH−] = 2.5×10−5M
1.0×10−14
2.5×10−5= [H+]
[H+] = 4.0×10−10 M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log4.0×10−10
pH = −log(4.0) −log10−10
pH = −0.6021 −(−10)
pH = 9.3979
Therefore, the pH of the solution is 9.40.
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−5
M.
Solution
Step 1: Use the relationship between [OH−] and pOH to find pOH.
pOH = −log[OH−]
pOH = −log1.5×10−5
pOH = −(−4.82)
pOH = 4.82
Step 2: Use the fact that pOH + pH = 14 to find pH.
pH = 14 −pOH
pH = 14 −4.82
pH = 9.18
Therefore, the pH of the solution is 9.18.
19
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall the definition of pH and the relationship between hydronium ion
concentration and 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 pH for-
mula.
pH = −log1.5×10−3
Step 3: Calculate the pH.
pH = −log1.5×10−3=−(−2.82) = 2.82
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−3M is 2.82.
Question 32
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Step 1: Recall the relation between [H3O+] and pH:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the equation:
pH = −log1.5×10−3
Step 3: Solve for pH:
pH = −log1.5×10−3=−log(1.5) −log10−3
Step 4: Use the property −log(10n) = −n:
pH = −log(1.5) −log10−3=−log(1.5) −(−3)
20
Step 5: Calculate the value of −log(1.5):
pH ≈ −0.176 −(−3) = 2.824
Step 6: Therefore, the pH of a solution with a hydronium ion concentration
of 1.5×10−3M is approximately 2.824.
Question 33
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−6
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm of the hydrogen ion
concentration:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log2.5×10−6
Step 3: Calculate the pH using a calculator:
pH ≈ −(−5.60)
pH ≈5.60
Step 4: Therefore, the pH of the solution is approximately 5.60.
Question 34
Question
Calculate the pH of a solution if the concentration of hydronium ions is 2.5×10−5
M.
Solution
Step 1: Recall that the pH is defined as the negative base-10 logarithm of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−5
21
Step 3: Use the properties of logarithms to simplify:
pH = −log(2.5) −log10−5
pH = −log(2.5) −(−5)
Step 4: Calculate the pH:
pH = −log(2.5) + 5 ≈4.60
Step 5: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−5M is approximately 4.60.
Question 35
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that the relationship between pH, pOH, and the ion concentra-
tions is given by:
pH + pOH = 14
Step 2: First, calculate the pOH of the solution using the given hydroxide ion
concentration:
pOH = −logOH−=−log2.5×10−5
Step 3: Calculate pOH:
pOH = −log2.5×10−5=−(−4.60) = 4.60
Step 4: Use the relationship between pH and pOH to find the pH of the solution:
pH = 14 −pOH = 14 −4.60
Step 5: Calculate pH:
pH = 14 −4.60 = 9.40
Step 6: Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−5M is pH = 9.40.
22
