CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 4
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−4
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. We are given that [H3O+] =
1.5×10−4M. To find the pH, we use the formula:
pH = −log1.5×10−4
Step 2: Calculate the pH:
pH = −log1.5×10−4=−(−3.823) = 3.823
Therefore, the pH of the solution is 3.823.
Question 2
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
2.5×10−10 M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 2.5×10−10 M, we can
calculate the pH:
pH = −log2.5×10−10
pH = −log(2.5) −log10−10
pH = −(log(2.5) + (−10 log(10)))
pH = −(log(2.5) + (−10))
pH = −(0.3979 + (−10))
pH = −(−9.6021)
pH = 9.6021
Step 3: Now, we can calculate the pOH using the relationship pH + pOH =
14:
pOH = 14 −9.6021
pOH = 4.3979
Therefore, the pH of the solution is 9.6021 and the pOH of the solution is
4.3979.
Question 3
Question
Calculate the pH of a solution with a hydrogen ion concentration of 5.8×10−4
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 to
find the pH:
pH = −log5.8×10−4
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(5.8) −log10−4=−log(5.8) + 4
2
Step 4: Use a calculator to find the value of log(5.8) and then calculate the
pH:
pH ≈ −(log 5.8) + 4 ≈ −0.763 −4≈3.237
Step 5: Therefore, the pH of the solution is approximately 3.24.
Question 4
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 pOH.
pOH =−log[OH−]
Step 2: Calculate pOH using the given hydroxide ion concentration.
pOH =−log1.5×10−3
pOH =−log(1.5) + log10−3
pOH =−0.176 + 3 = 2.824
Step 3: Use the relationship between pOH and pH to find pH.
pOH +pH = 14
pH = 14 −pOH
pH = 14 −2.824 = 11.176
Therefore, the pH of a solution with a hydroxide ion concentration of 1.5×
10−3M is 11.176.
Question 5
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−4
M.
3
Solution
Step 1: Recall that the pH is related to the hydronium ion concentration by the
formula: pH = -log[H3O+]. Thus, we have:
pH = −log1.5×10−4
Step 2: Substitute the given hydronium ion concentration into the formula
and solve for the pH:
pH = −log1.5×10−4
pH = −log(1.5) + log10−4
pH = −(log(1.5) −4)
Step 3: Use a calculator to determine the numerical value of log(1.5):
pH = −(log(1.5) −4)
pH ≈ −(0.1761 −4)
pH ≈ −(−3.8239)
pH ≈3.8239
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 1.5×10−4M is approximately 3.82.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log2.5×10−4
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(2.5) −log10−4
4
Step 4: Recall that log(10n) = n, so log10−4=−4:
pH = −log(2.5) −(−4)
Step 5: Calculate the pH value:
pH = −log(2.5) + 4
Step 6: Use a calculator to find the pH:
pH ≈ − log(2.5) + 4 ≈ −0.3979 + 4 ≈3.6021
Step 7: Therefore, the pH of the solution is approximately 3.60.
Question 7
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Given that the hydronium ion concentration is 1.5×10−3M, we can use the
formula pH =−log[H3O+] to find the pH of the solution.
Step 1: Calculate the pH using the given hydronium ion concentration.
pH = −log1.5×10−3
pH = −log(1.5) + log10−3
pH = −log(1.5) −3
Step 2: Use a calculator to find the pH.
pH ≈ −0.176 −3
pH ≈ −3.176
Therefore, the pH of the solution is approximately 3.176.
Question 8
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 1.5×
10−9M.
5
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
[OH−] = 1.5×10−9M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−9
[H+] = 6.67 ×10−6M
Step 3: Calculate the pH of the solution.
pH =−log[H+]=−log6.67 ×10−6
pH =−log(6.67) −log10−6
pH =−log(6.67) + 6
pH ≈5.18
Therefore, the pH of the solution is approximately 5.18.
Question 9
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is calculated using the formula: pH = -log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
and calculate the pH.
pH = −log2.5×10−4
Step 3: Use the properties of logarithms to simplify the calculation.
pH = −log(2.5) −log10−4
Step 4: Recall that log(10n) = nfor any real number n.
pH = −log(2.5) −(−4)
Step 5: Calculate the first term using a calculator.
log(2.5) ≈0.3979
6
Step 6: Substitute the values into the equation.
pH = −0.3979 + 4
Step 7: Calculate the final value of pH.
pH = 4 −0.3979 = 3.6021
Therefore, the pH of the solution with a hydronium ion concentration of
2.5×10−4M is approximately 3.60.
Question 10
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−4
M.
Solution
Step 1: Calculate the pOH of the solution.
Given: [OH−] = 3.0×10−4M
pOH =−log[OH−]
pOH =−log3.0×10−4
pOH ≈3.52
Step 2: Use the relationship
pH +pOH = 14
to find the pH of the solution.
pH = 14 −pOH
pH = 14 −3.52
pH ≈10.48
Therefore, the pH of the solution is approximately 10.48.
Question 11
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
7
Solution
Step 1: Write the expression for the autoionization of water and the equilibrium
expression for Kw.
Autoionization of water: 2H2O(l)⇌H3O+(aq) + OH−(aq)
Kw= [H3O+][OH−]=1.0×10−14
Step 2: Use Kwto find the [H3O+] based on the given [OH−].
Given [OH−] = 1.5×10−3M
Kw= [H3O+][OH−]=1.0×10−14
[H3O+] = Kw
[OH−]=1.0×10−14
1.5×10−3
Step 3: Calculate the concentration of [H3O+].
[H3O+] = 1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 4: Calculate the pH of the solution.
pH = −log[H3O+] = −log6.67 ×10−12
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula
pH =−log[H+]. To find the pH from hydroxide ion concentration, we first
need to find the hydrogen ion concentration using the relation [H+][OH−] =
1.0×10−14 for a neutral solution at 25
°
C.
Step 2: Given that [OH−] = 2.5×10−4M, we can substitute this value into
the equation [H+][OH−]=1.0×10−14 and solve for [H+].
[H+]×2.5×10−4= 1.0×10−14
[H+] = 1.0×10−14
2.5×10−4
[H+] = 4.0×10−11 M
8
Step 3: Now that we have the hydrogen ion concentration, we can calculate
the pH.
pH =−log4.0×10−11
pH =−(log 4.0 + log 10−11)
pH =−(0.6021 + (−11))
pH =−(−10.3979)
pH ≈10.4
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is approximately 10.4.
Question 13
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
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 = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−(−2.60) = 2.60
Step 4: Thus, the pH of the solution with a hydronium ion concentration of
2.5×10−3M is 2.60 .
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.72×10−5
M. Express the answer to two decimal places.
Solution
Step 1: Recall that pH is defined as the negative base 10 logarithm of the
hydronium ion concentration ([H3O+]) in a solution:
pH = −log[H3O+]
9
Step 2: Plug in the given hydronium ion concentration:
pH = −log3.72 ×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.72 ×10−5≈ − log(3.72)+log10−5≈ −(−0.571)−5≈0.571−5≈ −4.43
Step 4: Therefore, the pH of the solution is approximately −4.43.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
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 = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9=−(−8.60) = 8.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−9M is 8.60.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Use the relationship between pOH and [OH−] to find the pOH of the
solution.
pOH =−log[OH−]
pOH =−log2.5×10−3
10
pOH =−log 2.5−log 10−3
pOH =−log 2.5+3
pOH =−0.3979 + 3
pOH = 2.6021
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH +pOH = 14
pH = 14 −pOH
pH = 14 −2.6021
pH = 11.3979
Therefore, the pH of the solution is 11.4.
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Use the relationship between hydroxide ion concentration and pOH to
find the pOH of the solution.
pOH = −log[OH−] = −log3.2×10−5
Step 2: Calculate the pOH value.
pOH = −log3.2×10−5=−(−4.495) = 4.495
Step 3: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
Step 4: Calculate the pH value.
pH + 4.495 = 14
pH = 14 −4.495
pH ≈9.505
Therefore, the pH of the solution is approximately 9.505.
11
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that pH is calculated using the formula: pH =−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula:
pH =−log2.5×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH =−log(2.5) −log10−5
Step 4: Recall that log(10−n) = −nfor any positive value of n. So:
pH =−log(2.5) −(−5)
Step 5: Calculate the values inside the logarithms:
pH =−log(2.5) + 5
Step 6: Use a calculator to find the logarithm:
pH ≈ −0.3979 + 5
Step 7: Add the values to get the final result:
pH ≈4.6021
Therefore, the pH of the solution is approximately 4.6021.
Question 19
Question
Calculate the pH of a solution that has a hydronium ion concentration of 3.5×
10−4M.
12
Solution
Step 1: Recall that pH is defined as −log[H3O+]. First, determine the hydro-
nium ion concentration from the given information.
Given: [H3O+]=3.5×10−4M.
Step 2: Substitute the hydronium ion concentration into the pH formula and
solve for pH.
pH = −log3.5×10−4
Step 3: Calculate the pH.
pH = −log3.5×10−4=−log(3.5)+log10−4=−log(3.5)−4=3.46−4 = −0.54
Step 4: Therefore, the pH of the solution is −0.54.
Question 20
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−]=1.0×10−14
Step 2: Use the hydroxide ion concentration to solve for the hydrogen ion
concentration.
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4= 4.0×10−11 M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log4.0×10−11≈10.398
Therefore, the pH of the solution is approximately 10.40.
Question 21
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
1.5×10−3M.
13
Solution
Step 1: Calculate the pH of the solution. Given that the hydronium ion con-
centration is 1.5×10−3M, we can use the formula:
pH = −log[H3O+]
Substitute the given hydronium ion concentration into the formula to find
the pH:
pH = −log1.5×10−3
pH = −log(1.5) + log10−3
pH = −(log(1.5) −3)
pH = −(0.176 −3)
pH = −(−2.824)
pH = 2.824
Therefore, the pH of the solution is 2.824.
Step 2: Calculate the pOH of the solution. The relation between pH and
pOH is:
pH + pOH = 14
Substitute the calculated pH into the equation to find the pOH:
2.824 + pOH = 14
pOH = 14 −2.824
pOH = 11.176
Therefore, the pOH of the solution is 11.176.
Question 22
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid, HCl.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Identify the initial concentration of HCl as 0.025 M, which also
represents the initial concentration of H+ions.
14
Step 3: Since hydrochloric acid is a strong acid, it dissociates completely in
water, so the concentration of H+ions is equal to the initial concentration of
HCl.
Step 4: Calculate the pH using the formula:
pH = −log[H+]
Step 5: Substitute the concentration of H+ions into the formula to find the
pH:
pH = −log(0.025)
Step 6: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−(−1.602) = 1.602
Therefore, the pH of a 0.025 M solution of hydrochloric acid is 1.602.
Question 23
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Write the relationship between pOH and OH- concentration.
pOH = −log[OH-]
Step 2: Substitute the given hydroxide ion concentration into the equation
to find the pOH.
pOH = −log1.5×10−9
pOH = −log(1.5) −log10−9
pOH ≈8.82
Step 3: Use the relationship between pH and pOH.
pH + pOH = 14
Step 4: Calculate the pH by subtracting the pOH from 14.
pH = 14 −8.82
pH ≈5.18
Therefore, the pH of the solution is approximately 5.18.
15
Question 24
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.5×
10−5M.
Solution
Step 1: Write down the expression for calculating the pOH of the solution. The
pOH of a solution can be calculated using the formula:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula.
pOH =−log3.5×10−5
Step 3: Calculate the pOH.
pOH =−log3.5×10−5=−(log 3.5 + log 10−5) = −(log 3.5−5)
pOH ≈ −(log 3.5−5)
Step 4: Now, calculate the pH of the solution using the relationship between
pH and pOH in water. In water, pH +pOH = 14.
pH = 14 −pOH = 14 −(log 3.5−5)
Step 5: Calculate the pH of the solution.
pH ≈14 −(log 3.5−5)
Question 25
Question
Calculate the pH of a solution that has a pOH of 2.5.
Solution
Step 1: Recall that the pH and pOH of a solution are related by the equation:
pH + pOH = 14
Step 2: Given that the pOH of the solution is 2.5, we can calculate the pH
using the equation above:
pH + 2.5 = 14
16
Step 3: Subtracting 2.5 from both sides of the equation gives:
pH = 14 −2.5
Step 4: Therefore, the pH of the solution is:
pH = 11.5
Step 5: The pH of the solution with a pOH of 2.5 is 11.5.
Question 26
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−11
M.
Solution
Step 1: Write the expression for Kw, the ion product of water.
Kw= [H+][OH−]
Step 2: Since Kw= 1.0×10−14 at 25
°
C, and we have the concentration of
hydroxide ions, we can solve for the concentration of hydronium ions.
Kw= [H+]·1.5×10−11
1.0×10−14 = [H+]·1.5×10−11
[H+] = 1.0×10−14
1.5×10−11
[H+]≈6.67 ×10−4M
Step 3: Calculate the pH using the formula pH =−log [H+].
pH =−log 6.67 ×10−4
pH =−log 6.67 −log 10−4
pH ≈3.18
Therefore, the pH of the solution is approximately 3.18.
Question 27
Question
A solution is prepared by dissolving 0.050 moles of hydrochloric acid (HCl) in
enough water to make 500.0 mL of solution. Calculate the pH and pOH of the
resulting solution.
17
Solution
Step 1: Calculate the concentration of HCl in the solution. The concentration
(in M) of HCl can be calculated using the formula:
Concentration (M) = moles of solute
volume of solution (L)
Given: Moles of HCl = 0.050 mol Volume of solution = 500.0 mL = 0.500 L
Plugging in the values:
Concentration of HCl = 0.050 mol
0.500 L = 0.10 M
Step 2: Calculate the pH of the solution. Since HCl is a strong acid that fully
dissociates in water, the concentration of H+ ions is equal to the concentration
of HCl.
The pH can be calculated using the formula:
pH = −log[H+]
Given that [H+] = 0.10M: pH = −log(0.10) = 1.00
Therefore, the pH of the solution is 1.00.
Step 3: Calculate the pOH of the solution. The pOH can be calculated using
the formula:
pOH = −log[OH−]
Since the solution only contains HCl, there are no OH- ions present. There-
fore, the concentration of OH- ions is 0.
pOH = −log(0) = undefined
Therefore, the pOH of the solution is undefined.
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.6×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH =−log[OH−]
pOH =−log3.6×10−5
pOH ≈4.44
18
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.44
pH ≈9.56
Therefore, the pH of the solution with a hydroxide ion concentration of
3.6×10−5M is approximately 9.56.
Question 29
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
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 pH for-
mula:
pH = −log3.2×10−6
Step 3: Use the logarithm property log(a×b) = log a+ log bto simplify the
calculation:
pH = −(log 3.2 + log 10−6)
Step 4: Recall that log(10n) = n, then simplify further:
pH = −(log 3.2−6)
Step 5: Use a calculator to find log 3.2≈0.5051, then calculate the pH:
pH = −(0.5051 −6) = −(−5.4949) = 5.4949
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−6M is approximately 5.49.
Question 30
Question
A solution has a hydrogen ion concentration of 1.5×10−4M. Calculate the pH
and pOH of the solution.
19
Solution
Step 1: Recall that the pH is calculated using the formula: pH =−log[H+],
where [H+] is the hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log1.5×10−4
Step 3: Calculate the pH:
pH =−log1.5×10−4=−log 1.5−log 10−4=−0.1761 −(−4)
Step 4: Simplify the calculation:
pH = 3.8239
Step 5: Therefore, the pH of the solution is 3.82.
Step 6: Since pH + pOH = 14, we can calculate the pOH using the formula:
pOH = 14 −pH.
Step 7: Substitute the pH value into the formula to calculate pOH:
pOH = 14 −3.82
Step 8: Calculate the pOH:
pOH = 10.18
Step 9: Therefore, the pOH of the solution is 10.18.
Question 31
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid (HCl):
HCl →H++Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely
in water. This means that the concentration of H+ions is equal to the initial
concentration of the hydrochloric acid, which is 0.025 M.
Step 3: Calculate the pH using the formula:
pH =−log[H+]
Step 4: Substitute the given concentration of H+ions into the formula:
pH =−log(0.025)
20
Step 5: Calculate the pH:
pH =−log(0.025) = −log2.5×10−2=−(−1.602) = 1.602
Answer: The pH of a 0.025 M solution of hydrochloric acid is 1.602.
Question 32
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 and hydronium ion concentration. The pH
of a solution is defined as −log[H3O+], where [H3O+] is the concentration of
hydronium ions in the solution.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula.
pH = −log3.2×10−5
Step 3: Calculate the pH of the solution.
pH = −log3.2×10−5=−log(3.2) + log10−5=−(0.5051) −(−5) = 4.4949
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.49.
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.60×10−5
M.
Solution
Step 1: Use the relationship between pOH and the hydroxide ion concentration
to find the pOH of the solution.
pOH = −log[OH−]
pOH = −log5.60 ×10−5
pOH = −(−4.252)
pOH ≈4.25
21
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
pH + 4.25 = 14
pH = 14 −4.25
pH ≈9.75
The pH of the solution is approximately 9.75.
Question 34
Question
A solution is prepared by mixing 50.0 mL of 0.200 M hydrochloric acid (HCl)
with 75.0 mL of 0.150 M sodium hydroxide (NaOH). Calculate the pH of the
resulting solution. (Given: Kw= 1.0×10−14)
Solution
Step 1: Determine the moles of HCl and NaOH used.
Moles of HCl = Volume ×Molarity
= (0.050 L) ×(0.200 mol/L)
= 0.010 mol
Moles of NaOH = Volume ×Molarity
= (0.075 L) ×(0.150 mol/L)
= 0.01125 mol
Step 2: Calculate the limiting reactant by comparing the moles of HCl and
NaOH. Since HCl and NaOH react in a 1:1 ratio (1 mole of HCl reacts with
1 mole of NaOH), HCl is the limiting reactant as it produces fewer moles of
reactant.
Step 3: Calculate the excess moles of NaOH.
Excess moles of NaOH = Moles of NaOH −Moles of HCl
= 0.01125 mol −0.010 mol
= 0.00125 mol
Step 4: Calculate the moles of the resulting base, which is NaCl. Since 1
mole of NaOH produces 1 mole of NaCl, the moles of NaCl formed will equal
the excess moles of NaOH.
Moles of NaCl = Excess moles of NaOH
= 0.00125 mol
22
Step 5: Calculate the concentration of NaCl.
Volume of resulting solution = 50.0 mL + 75.0 mL
= 125.0 mL = 0.125 L
Molarity of NaCl = Moles of NaCl
Volume of resulting solution
=0.00125 mol
0.125 L
= 0.010 mol/L
Step 6: Calculate the pOH of the resulting solution.
pOH =−log[OH−]
=−log(0.010)
= 2
Step 7: Calculate the pH of the resulting solution. Since pH +pOH = 14,
pH = 14 −pOH
= 14 −2
= 12
Therefore, the pH of the resulting solution is 12.
Question 35
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−7
M.
Solution
Step 1: Use the formula pOH =−log[OH−] to find the pOH of the solution.
Given: [OH−]=2.5×10−7M
pOH =−log2.5×10−7
Step 2: Calculate the pOH.
pOH =−log2.5×10−7
pOH =−(log 2.5 + log 10−7)
pOH =−(0.3979 −7)
23
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 2.5×10−10 M, we can
calculate the pH:
pH = −log2.5×10−10
pH = −log(2.5) −log10−10
pH = −(log(2.5) + (−10 log(10)))
pH = −(log(2.5) + (−10))
pH = −(0.3979 + (−10))
pH = −(−9.6021)
pH = 9.6021
Step 3: Now, we can calculate the pOH using the relationship pH + pOH =
14:
pOH = 14 −9.6021
pOH = 4.3979
Therefore, the pH of the solution is 9.6021 and the pOH of the solution is
4.3979.
Question 3
Question
Calculate the pH of a solution with a hydrogen ion concentration of 5.8×10−4
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 to
find the pH:
pH = −log5.8×10−4
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(5.8) −log10−4=−log(5.8) + 4
2
Step 4: Use a calculator to find the value of log(5.8) and then calculate the
pH:
pH ≈ −(log 5.8) + 4 ≈ −0.763 −4≈3.237
Step 5: Therefore, the pH of the solution is approximately 3.24.
Question 4
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 pOH.
pOH =−log[OH−]
Step 2: Calculate pOH using the given hydroxide ion concentration.
pOH =−log1.5×10−3
pOH =−log(1.5) + log10−3
pOH =−0.176 + 3 = 2.824
Step 3: Use the relationship between pOH and pH to find pH.
pOH +pH = 14
pH = 14 −pOH
pH = 14 −2.824 = 11.176
Therefore, the pH of a solution with a hydroxide ion concentration of 1.5×
10−3M is 11.176.
Question 5
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−4
M.
3
Solution
Step 1: Recall that the pH is related to the hydronium ion concentration by the
formula: pH = -log[H3O+]. Thus, we have:
pH = −log1.5×10−4
Step 2: Substitute the given hydronium ion concentration into the formula
and solve for the pH:
pH = −log1.5×10−4
pH = −log(1.5) + log10−4
pH = −(log(1.5) −4)
Step 3: Use a calculator to determine the numerical value of log(1.5):
pH = −(log(1.5) −4)
pH ≈ −(0.1761 −4)
pH ≈ −(−3.8239)
pH ≈3.8239
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 1.5×10−4M is approximately 3.82.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log2.5×10−4
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(2.5) −log10−4
4
Step 4: Recall that log(10n) = n, so log10−4=−4:
pH = −log(2.5) −(−4)
Step 5: Calculate the pH value:
pH = −log(2.5) + 4
Step 6: Use a calculator to find the pH:
pH ≈ − log(2.5) + 4 ≈ −0.3979 + 4 ≈3.6021
Step 7: Therefore, the pH of the solution is approximately 3.60.
Question 7
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Given that the hydronium ion concentration is 1.5×10−3M, we can use the
formula pH =−log[H3O+] to find the pH of the solution.
Step 1: Calculate the pH using the given hydronium ion concentration.
pH = −log1.5×10−3
pH = −log(1.5) + log10−3
pH = −log(1.5) −3
Step 2: Use a calculator to find the pH.
pH ≈ −0.176 −3
pH ≈ −3.176
Therefore, the pH of the solution is approximately 3.176.
Question 8
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 1.5×
10−9M.
5
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
[OH−] = 1.5×10−9M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−9
[H+] = 6.67 ×10−6M
Step 3: Calculate the pH of the solution.
pH =−log[H+]=−log6.67 ×10−6
pH =−log(6.67) −log10−6
pH =−log(6.67) + 6
pH ≈5.18
Therefore, the pH of the solution is approximately 5.18.
Question 9
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is calculated using the formula: pH = -log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
and calculate the pH.
pH = −log2.5×10−4
Step 3: Use the properties of logarithms to simplify the calculation.
pH = −log(2.5) −log10−4
Step 4: Recall that log(10n) = nfor any real number n.
pH = −log(2.5) −(−4)
Step 5: Calculate the first term using a calculator.
log(2.5) ≈0.3979
6
Step 6: Substitute the values into the equation.
pH = −0.3979 + 4
Step 7: Calculate the final value of pH.
pH = 4 −0.3979 = 3.6021
Therefore, the pH of the solution with a hydronium ion concentration of
2.5×10−4M is approximately 3.60.
Question 10
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−4
M.
Solution
Step 1: Calculate the pOH of the solution.
Given: [OH−] = 3.0×10−4M
pOH =−log[OH−]
pOH =−log3.0×10−4
pOH ≈3.52
Step 2: Use the relationship
pH +pOH = 14
to find the pH of the solution.
pH = 14 −pOH
pH = 14 −3.52
pH ≈10.48
Therefore, the pH of the solution is approximately 10.48.
Question 11
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
7
Solution
Step 1: Write the expression for the autoionization of water and the equilibrium
expression for Kw.
Autoionization of water: 2H2O(l)⇌H3O+(aq) + OH−(aq)
Kw= [H3O+][OH−]=1.0×10−14
Step 2: Use Kwto find the [H3O+] based on the given [OH−].
Given [OH−] = 1.5×10−3M
Kw= [H3O+][OH−]=1.0×10−14
[H3O+] = Kw
[OH−]=1.0×10−14
1.5×10−3
Step 3: Calculate the concentration of [H3O+].
[H3O+] = 1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 4: Calculate the pH of the solution.
pH = −log[H3O+] = −log6.67 ×10−12
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula
pH =−log[H+]. To find the pH from hydroxide ion concentration, we first
need to find the hydrogen ion concentration using the relation [H+][OH−] =
1.0×10−14 for a neutral solution at 25
°
C.
Step 2: Given that [OH−] = 2.5×10−4M, we can substitute this value into
the equation [H+][OH−]=1.0×10−14 and solve for [H+].
[H+]×2.5×10−4= 1.0×10−14
[H+] = 1.0×10−14
2.5×10−4
[H+] = 4.0×10−11 M
8
Step 3: Now that we have the hydrogen ion concentration, we can calculate
the pH.
pH =−log4.0×10−11
pH =−(log 4.0 + log 10−11)
pH =−(0.6021 + (−11))
pH =−(−10.3979)
pH ≈10.4
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is approximately 10.4.
Question 13
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
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 = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−(−2.60) = 2.60
Step 4: Thus, the pH of the solution with a hydronium ion concentration of
2.5×10−3M is 2.60 .
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.72×10−5
M. Express the answer to two decimal places.
Solution
Step 1: Recall that pH is defined as the negative base 10 logarithm of the
hydronium ion concentration ([H3O+]) in a solution:
pH = −log[H3O+]
9
Step 2: Plug in the given hydronium ion concentration:
pH = −log3.72 ×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.72 ×10−5≈ − log(3.72)+log10−5≈ −(−0.571)−5≈0.571−5≈ −4.43
Step 4: Therefore, the pH of the solution is approximately −4.43.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
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 = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9=−(−8.60) = 8.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−9M is 8.60.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Use the relationship between pOH and [OH−] to find the pOH of the
solution.
pOH =−log[OH−]
pOH =−log2.5×10−3
10
pOH =−log 2.5−log 10−3
pOH =−log 2.5+3
pOH =−0.3979 + 3
pOH = 2.6021
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH +pOH = 14
pH = 14 −pOH
pH = 14 −2.6021
pH = 11.3979
Therefore, the pH of the solution is 11.4.
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Use the relationship between hydroxide ion concentration and pOH to
find the pOH of the solution.
pOH = −log[OH−] = −log3.2×10−5
Step 2: Calculate the pOH value.
pOH = −log3.2×10−5=−(−4.495) = 4.495
Step 3: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
Step 4: Calculate the pH value.
pH + 4.495 = 14
pH = 14 −4.495
pH ≈9.505
Therefore, the pH of the solution is approximately 9.505.
11
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that pH is calculated using the formula: pH =−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula:
pH =−log2.5×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH =−log(2.5) −log10−5
Step 4: Recall that log(10−n) = −nfor any positive value of n. So:
pH =−log(2.5) −(−5)
Step 5: Calculate the values inside the logarithms:
pH =−log(2.5) + 5
Step 6: Use a calculator to find the logarithm:
pH ≈ −0.3979 + 5
Step 7: Add the values to get the final result:
pH ≈4.6021
Therefore, the pH of the solution is approximately 4.6021.
Question 19
Question
Calculate the pH of a solution that has a hydronium ion concentration of 3.5×
10−4M.
12
Solution
Step 1: Recall that pH is defined as −log[H3O+]. First, determine the hydro-
nium ion concentration from the given information.
Given: [H3O+]=3.5×10−4M.
Step 2: Substitute the hydronium ion concentration into the pH formula and
solve for pH.
pH = −log3.5×10−4
Step 3: Calculate the pH.
pH = −log3.5×10−4=−log(3.5)+log10−4=−log(3.5)−4=3.46−4 = −0.54
Step 4: Therefore, the pH of the solution is −0.54.
Question 20
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−]=1.0×10−14
Step 2: Use the hydroxide ion concentration to solve for the hydrogen ion
concentration.
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4= 4.0×10−11 M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log4.0×10−11≈10.398
Therefore, the pH of the solution is approximately 10.40.
Question 21
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
1.5×10−3M.
13
Solution
Step 1: Calculate the pH of the solution. Given that the hydronium ion con-
centration is 1.5×10−3M, we can use the formula:
pH = −log[H3O+]
Substitute the given hydronium ion concentration into the formula to find
the pH:
pH = −log1.5×10−3
pH = −log(1.5) + log10−3
pH = −(log(1.5) −3)
pH = −(0.176 −3)
pH = −(−2.824)
pH = 2.824
Therefore, the pH of the solution is 2.824.
Step 2: Calculate the pOH of the solution. The relation between pH and
pOH is:
pH + pOH = 14
Substitute the calculated pH into the equation to find the pOH:
2.824 + pOH = 14
pOH = 14 −2.824
pOH = 11.176
Therefore, the pOH of the solution is 11.176.
Question 22
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid, HCl.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Identify the initial concentration of HCl as 0.025 M, which also
represents the initial concentration of H+ions.
14
Step 3: Since hydrochloric acid is a strong acid, it dissociates completely in
water, so the concentration of H+ions is equal to the initial concentration of
HCl.
Step 4: Calculate the pH using the formula:
pH = −log[H+]
Step 5: Substitute the concentration of H+ions into the formula to find the
pH:
pH = −log(0.025)
Step 6: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−(−1.602) = 1.602
Therefore, the pH of a 0.025 M solution of hydrochloric acid is 1.602.
Question 23
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Write the relationship between pOH and OH- concentration.
pOH = −log[OH-]
Step 2: Substitute the given hydroxide ion concentration into the equation
to find the pOH.
pOH = −log1.5×10−9
pOH = −log(1.5) −log10−9
pOH ≈8.82
Step 3: Use the relationship between pH and pOH.
pH + pOH = 14
Step 4: Calculate the pH by subtracting the pOH from 14.
pH = 14 −8.82
pH ≈5.18
Therefore, the pH of the solution is approximately 5.18.
15
Question 24
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.5×
10−5M.
Solution
Step 1: Write down the expression for calculating the pOH of the solution. The
pOH of a solution can be calculated using the formula:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula.
pOH =−log3.5×10−5
Step 3: Calculate the pOH.
pOH =−log3.5×10−5=−(log 3.5 + log 10−5) = −(log 3.5−5)
pOH ≈ −(log 3.5−5)
Step 4: Now, calculate the pH of the solution using the relationship between
pH and pOH in water. In water, pH +pOH = 14.
pH = 14 −pOH = 14 −(log 3.5−5)
Step 5: Calculate the pH of the solution.
pH ≈14 −(log 3.5−5)
Question 25
Question
Calculate the pH of a solution that has a pOH of 2.5.
Solution
Step 1: Recall that the pH and pOH of a solution are related by the equation:
pH + pOH = 14
Step 2: Given that the pOH of the solution is 2.5, we can calculate the pH
using the equation above:
pH + 2.5 = 14
16
Step 3: Subtracting 2.5 from both sides of the equation gives:
pH = 14 −2.5
Step 4: Therefore, the pH of the solution is:
pH = 11.5
Step 5: The pH of the solution with a pOH of 2.5 is 11.5.
Question 26
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−11
M.
Solution
Step 1: Write the expression for Kw, the ion product of water.
Kw= [H+][OH−]
Step 2: Since Kw= 1.0×10−14 at 25
°
C, and we have the concentration of
hydroxide ions, we can solve for the concentration of hydronium ions.
Kw= [H+]·1.5×10−11
1.0×10−14 = [H+]·1.5×10−11
[H+] = 1.0×10−14
1.5×10−11
[H+]≈6.67 ×10−4M
Step 3: Calculate the pH using the formula pH =−log [H+].
pH =−log 6.67 ×10−4
pH =−log 6.67 −log 10−4
pH ≈3.18
Therefore, the pH of the solution is approximately 3.18.
Question 27
Question
A solution is prepared by dissolving 0.050 moles of hydrochloric acid (HCl) in
enough water to make 500.0 mL of solution. Calculate the pH and pOH of the
resulting solution.
17
Solution
Step 1: Calculate the concentration of HCl in the solution. The concentration
(in M) of HCl can be calculated using the formula:
Concentration (M) = moles of solute
volume of solution (L)
Given: Moles of HCl = 0.050 mol Volume of solution = 500.0 mL = 0.500 L
Plugging in the values:
Concentration of HCl = 0.050 mol
0.500 L = 0.10 M
Step 2: Calculate the pH of the solution. Since HCl is a strong acid that fully
dissociates in water, the concentration of H+ ions is equal to the concentration
of HCl.
The pH can be calculated using the formula:
pH = −log[H+]
Given that [H+] = 0.10M: pH = −log(0.10) = 1.00
Therefore, the pH of the solution is 1.00.
Step 3: Calculate the pOH of the solution. The pOH can be calculated using
the formula:
pOH = −log[OH−]
Since the solution only contains HCl, there are no OH- ions present. There-
fore, the concentration of OH- ions is 0.
pOH = −log(0) = undefined
Therefore, the pOH of the solution is undefined.
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.6×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH =−log[OH−]
pOH =−log3.6×10−5
pOH ≈4.44
18
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.44
pH ≈9.56
Therefore, the pH of the solution with a hydroxide ion concentration of
3.6×10−5M is approximately 9.56.
Question 29
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
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 pH for-
mula:
pH = −log3.2×10−6
Step 3: Use the logarithm property log(a×b) = log a+ log bto simplify the
calculation:
pH = −(log 3.2 + log 10−6)
Step 4: Recall that log(10n) = n, then simplify further:
pH = −(log 3.2−6)
Step 5: Use a calculator to find log 3.2≈0.5051, then calculate the pH:
pH = −(0.5051 −6) = −(−5.4949) = 5.4949
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−6M is approximately 5.49.
Question 30
Question
A solution has a hydrogen ion concentration of 1.5×10−4M. Calculate the pH
and pOH of the solution.
19
Solution
Step 1: Recall that the pH is calculated using the formula: pH =−log[H+],
where [H+] is the hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log1.5×10−4
Step 3: Calculate the pH:
pH =−log1.5×10−4=−log 1.5−log 10−4=−0.1761 −(−4)
Step 4: Simplify the calculation:
pH = 3.8239
Step 5: Therefore, the pH of the solution is 3.82.
Step 6: Since pH + pOH = 14, we can calculate the pOH using the formula:
pOH = 14 −pH.
Step 7: Substitute the pH value into the formula to calculate pOH:
pOH = 14 −3.82
Step 8: Calculate the pOH:
pOH = 10.18
Step 9: Therefore, the pOH of the solution is 10.18.
Question 31
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid (HCl):
HCl →H++Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely
in water. This means that the concentration of H+ions is equal to the initial
concentration of the hydrochloric acid, which is 0.025 M.
Step 3: Calculate the pH using the formula:
pH =−log[H+]
Step 4: Substitute the given concentration of H+ions into the formula:
pH =−log(0.025)
20
Step 5: Calculate the pH:
pH =−log(0.025) = −log2.5×10−2=−(−1.602) = 1.602
Answer: The pH of a 0.025 M solution of hydrochloric acid is 1.602.
Question 32
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 and hydronium ion concentration. The pH
of a solution is defined as −log[H3O+], where [H3O+] is the concentration of
hydronium ions in the solution.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula.
pH = −log3.2×10−5
Step 3: Calculate the pH of the solution.
pH = −log3.2×10−5=−log(3.2) + log10−5=−(0.5051) −(−5) = 4.4949
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.49.
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.60×10−5
M.
Solution
Step 1: Use the relationship between pOH and the hydroxide ion concentration
to find the pOH of the solution.
pOH = −log[OH−]
pOH = −log5.60 ×10−5
pOH = −(−4.252)
pOH ≈4.25
21
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
pH + 4.25 = 14
pH = 14 −4.25
pH ≈9.75
The pH of the solution is approximately 9.75.
Question 34
Question
A solution is prepared by mixing 50.0 mL of 0.200 M hydrochloric acid (HCl)
with 75.0 mL of 0.150 M sodium hydroxide (NaOH). Calculate the pH of the
resulting solution. (Given: Kw= 1.0×10−14)
Solution
Step 1: Determine the moles of HCl and NaOH used.
Moles of HCl = Volume ×Molarity
= (0.050 L) ×(0.200 mol/L)
= 0.010 mol
Moles of NaOH = Volume ×Molarity
= (0.075 L) ×(0.150 mol/L)
= 0.01125 mol
Step 2: Calculate the limiting reactant by comparing the moles of HCl and
NaOH. Since HCl and NaOH react in a 1:1 ratio (1 mole of HCl reacts with
1 mole of NaOH), HCl is the limiting reactant as it produces fewer moles of
reactant.
Step 3: Calculate the excess moles of NaOH.
Excess moles of NaOH = Moles of NaOH −Moles of HCl
= 0.01125 mol −0.010 mol
= 0.00125 mol
Step 4: Calculate the moles of the resulting base, which is NaCl. Since 1
mole of NaOH produces 1 mole of NaCl, the moles of NaCl formed will equal
the excess moles of NaOH.
Moles of NaCl = Excess moles of NaOH
= 0.00125 mol
22
Step 5: Calculate the concentration of NaCl.
Volume of resulting solution = 50.0 mL + 75.0 mL
= 125.0 mL = 0.125 L
Molarity of NaCl = Moles of NaCl
Volume of resulting solution
=0.00125 mol
0.125 L
= 0.010 mol/L
Step 6: Calculate the pOH of the resulting solution.
pOH =−log[OH−]
=−log(0.010)
= 2
Step 7: Calculate the pH of the resulting solution. Since pH +pOH = 14,
pH = 14 −pOH
= 14 −2
= 12
Therefore, the pH of the resulting solution is 12.
Question 35
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−7
M.
Solution
Step 1: Use the formula pOH =−log[OH−] to find the pOH of the solution.
Given: [OH−]=2.5×10−7M
pOH =−log2.5×10−7
Step 2: Calculate the pOH.
pOH =−log2.5×10−7
pOH =−(log 2.5 + log 10−7)
pOH =−(0.3979 −7)
23
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that the hydrogen ion concentration is 2.5×10−10 M, we can
calculate the pH:
pH = −log2.5×10−10
pH = −log(2.5) −log10−10
pH = −(log(2.5) + (−10 log(10)))
pH = −(log(2.5) + (−10))
pH = −(0.3979 + (−10))
pH = −(−9.6021)
pH = 9.6021
Step 3: Now, we can calculate the pOH using the relationship pH + pOH =
14:
pOH = 14 −9.6021
pOH = 4.3979
Therefore, the pH of the solution is 9.6021 and the pOH of the solution is
4.3979.
Question 3
Question
Calculate the pH of a solution with a hydrogen ion concentration of 5.8×10−4
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 to
find the pH:
pH = −log5.8×10−4
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(5.8) −log10−4=−log(5.8) + 4
2
Step 4: Use a calculator to find the value of log(5.8) and then calculate the
pH:
pH ≈ −(log 5.8) + 4 ≈ −0.763 −4≈3.237
Step 5: Therefore, the pH of the solution is approximately 3.24.
Question 4
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 pOH.
pOH =−log[OH−]
Step 2: Calculate pOH using the given hydroxide ion concentration.
pOH =−log1.5×10−3
pOH =−log(1.5) + log10−3
pOH =−0.176 + 3 = 2.824
Step 3: Use the relationship between pOH and pH to find pH.
pOH +pH = 14
pH = 14 −pOH
pH = 14 −2.824 = 11.176
Therefore, the pH of a solution with a hydroxide ion concentration of 1.5×
10−3M is 11.176.
Question 5
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−4
M.
3
Solution
Step 1: Recall that the pH is related to the hydronium ion concentration by the
formula: pH = -log[H3O+]. Thus, we have:
pH = −log1.5×10−4
Step 2: Substitute the given hydronium ion concentration into the formula
and solve for the pH:
pH = −log1.5×10−4
pH = −log(1.5) + log10−4
pH = −(log(1.5) −4)
Step 3: Use a calculator to determine the numerical value of log(1.5):
pH = −(log(1.5) −4)
pH ≈ −(0.1761 −4)
pH ≈ −(−3.8239)
pH ≈3.8239
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 1.5×10−4M is approximately 3.82.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula:
pH = −log2.5×10−4
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(2.5) −log10−4
4
Step 4: Recall that log(10n) = n, so log10−4=−4:
pH = −log(2.5) −(−4)
Step 5: Calculate the pH value:
pH = −log(2.5) + 4
Step 6: Use a calculator to find the pH:
pH ≈ − log(2.5) + 4 ≈ −0.3979 + 4 ≈3.6021
Step 7: Therefore, the pH of the solution is approximately 3.60.
Question 7
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−3
M.
Solution
Given that the hydronium ion concentration is 1.5×10−3M, we can use the
formula pH =−log[H3O+] to find the pH of the solution.
Step 1: Calculate the pH using the given hydronium ion concentration.
pH = −log1.5×10−3
pH = −log(1.5) + log10−3
pH = −log(1.5) −3
Step 2: Use a calculator to find the pH.
pH ≈ −0.176 −3
pH ≈ −3.176
Therefore, the pH of the solution is approximately 3.176.
Question 8
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 1.5×
10−9M.
5
Solution
Step 1: Write the expression for the ion product of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
[OH−] = 1.5×10−9M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−9
[H+] = 6.67 ×10−6M
Step 3: Calculate the pH of the solution.
pH =−log[H+]=−log6.67 ×10−6
pH =−log(6.67) −log10−6
pH =−log(6.67) + 6
pH ≈5.18
Therefore, the pH of the solution is approximately 5.18.
Question 9
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that pH is calculated using the formula: pH = -log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
and calculate the pH.
pH = −log2.5×10−4
Step 3: Use the properties of logarithms to simplify the calculation.
pH = −log(2.5) −log10−4
Step 4: Recall that log(10n) = nfor any real number n.
pH = −log(2.5) −(−4)
Step 5: Calculate the first term using a calculator.
log(2.5) ≈0.3979
6
Step 6: Substitute the values into the equation.
pH = −0.3979 + 4
Step 7: Calculate the final value of pH.
pH = 4 −0.3979 = 3.6021
Therefore, the pH of the solution with a hydronium ion concentration of
2.5×10−4M is approximately 3.60.
Question 10
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.0×10−4
M.
Solution
Step 1: Calculate the pOH of the solution.
Given: [OH−] = 3.0×10−4M
pOH =−log[OH−]
pOH =−log3.0×10−4
pOH ≈3.52
Step 2: Use the relationship
pH +pOH = 14
to find the pH of the solution.
pH = 14 −pOH
pH = 14 −3.52
pH ≈10.48
Therefore, the pH of the solution is approximately 10.48.
Question 11
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−3
M.
7
Solution
Step 1: Write the expression for the autoionization of water and the equilibrium
expression for Kw.
Autoionization of water: 2H2O(l)⇌H3O+(aq) + OH−(aq)
Kw= [H3O+][OH−]=1.0×10−14
Step 2: Use Kwto find the [H3O+] based on the given [OH−].
Given [OH−] = 1.5×10−3M
Kw= [H3O+][OH−]=1.0×10−14
[H3O+] = Kw
[OH−]=1.0×10−14
1.5×10−3
Step 3: Calculate the concentration of [H3O+].
[H3O+] = 1.0×10−14
1.5×10−3= 6.67 ×10−12 M
Step 4: Calculate the pH of the solution.
pH = −log[H3O+] = −log6.67 ×10−12
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula
pH =−log[H+]. To find the pH from hydroxide ion concentration, we first
need to find the hydrogen ion concentration using the relation [H+][OH−] =
1.0×10−14 for a neutral solution at 25
°
C.
Step 2: Given that [OH−] = 2.5×10−4M, we can substitute this value into
the equation [H+][OH−]=1.0×10−14 and solve for [H+].
[H+]×2.5×10−4= 1.0×10−14
[H+] = 1.0×10−14
2.5×10−4
[H+] = 4.0×10−11 M
8
Step 3: Now that we have the hydrogen ion concentration, we can calculate
the pH.
pH =−log4.0×10−11
pH =−(log 4.0 + log 10−11)
pH =−(0.6021 + (−11))
pH =−(−10.3979)
pH ≈10.4
Therefore, the pH of the solution with a hydroxide ion concentration of
2.5×10−4M is approximately 10.4.
Question 13
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
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 = −log2.5×10−3
Step 3: Calculate the pH:
pH = −log2.5×10−3=−(−2.60) = 2.60
Step 4: Thus, the pH of the solution with a hydronium ion concentration of
2.5×10−3M is 2.60 .
Question 14
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.72×10−5
M. Express the answer to two decimal places.
Solution
Step 1: Recall that pH is defined as the negative base 10 logarithm of the
hydronium ion concentration ([H3O+]) in a solution:
pH = −log[H3O+]
9
Step 2: Plug in the given hydronium ion concentration:
pH = −log3.72 ×10−5
Step 3: Calculate the pH using a calculator:
pH = −log3.72 ×10−5≈ − log(3.72)+log10−5≈ −(−0.571)−5≈0.571−5≈ −4.43
Step 4: Therefore, the pH of the solution is approximately −4.43.
Question 15
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−9
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 = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9=−(−8.60) = 8.60
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 2.5×10−9M is 8.60.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Use the relationship between pOH and [OH−] to find the pOH of the
solution.
pOH =−log[OH−]
pOH =−log2.5×10−3
10
pOH =−log 2.5−log 10−3
pOH =−log 2.5+3
pOH =−0.3979 + 3
pOH = 2.6021
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH +pOH = 14
pH = 14 −pOH
pH = 14 −2.6021
pH = 11.3979
Therefore, the pH of the solution is 11.4.
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: Use the relationship between hydroxide ion concentration and pOH to
find the pOH of the solution.
pOH = −log[OH−] = −log3.2×10−5
Step 2: Calculate the pOH value.
pOH = −log3.2×10−5=−(−4.495) = 4.495
Step 3: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
Step 4: Calculate the pH value.
pH + 4.495 = 14
pH = 14 −4.495
pH ≈9.505
Therefore, the pH of the solution is approximately 9.505.
11
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−5
M.
Solution
Step 1: Recall that pH is calculated using the formula: pH =−log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula:
pH =−log2.5×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH =−log(2.5) −log10−5
Step 4: Recall that log(10−n) = −nfor any positive value of n. So:
pH =−log(2.5) −(−5)
Step 5: Calculate the values inside the logarithms:
pH =−log(2.5) + 5
Step 6: Use a calculator to find the logarithm:
pH ≈ −0.3979 + 5
Step 7: Add the values to get the final result:
pH ≈4.6021
Therefore, the pH of the solution is approximately 4.6021.
Question 19
Question
Calculate the pH of a solution that has a hydronium ion concentration of 3.5×
10−4M.
12
Solution
Step 1: Recall that pH is defined as −log[H3O+]. First, determine the hydro-
nium ion concentration from the given information.
Given: [H3O+]=3.5×10−4M.
Step 2: Substitute the hydronium ion concentration into the pH formula and
solve for pH.
pH = −log3.5×10−4
Step 3: Calculate the pH.
pH = −log3.5×10−4=−log(3.5)+log10−4=−log(3.5)−4=3.46−4 = −0.54
Step 4: Therefore, the pH of the solution is −0.54.
Question 20
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−]=1.0×10−14
Step 2: Use the hydroxide ion concentration to solve for the hydrogen ion
concentration.
[OH−] = 2.5×10−4M
[H+] = Kw
[OH−]=1.0×10−14
2.5×10−4= 4.0×10−11 M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH = −log[H+]=−log4.0×10−11≈10.398
Therefore, the pH of the solution is approximately 10.40.
Question 21
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
1.5×10−3M.
13
Solution
Step 1: Calculate the pH of the solution. Given that the hydronium ion con-
centration is 1.5×10−3M, we can use the formula:
pH = −log[H3O+]
Substitute the given hydronium ion concentration into the formula to find
the pH:
pH = −log1.5×10−3
pH = −log(1.5) + log10−3
pH = −(log(1.5) −3)
pH = −(0.176 −3)
pH = −(−2.824)
pH = 2.824
Therefore, the pH of the solution is 2.824.
Step 2: Calculate the pOH of the solution. The relation between pH and
pOH is:
pH + pOH = 14
Substitute the calculated pH into the equation to find the pOH:
2.824 + pOH = 14
pOH = 14 −2.824
pOH = 11.176
Therefore, the pOH of the solution is 11.176.
Question 22
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid, HCl.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Identify the initial concentration of HCl as 0.025 M, which also
represents the initial concentration of H+ions.
14
Step 3: Since hydrochloric acid is a strong acid, it dissociates completely in
water, so the concentration of H+ions is equal to the initial concentration of
HCl.
Step 4: Calculate the pH using the formula:
pH = −log[H+]
Step 5: Substitute the concentration of H+ions into the formula to find the
pH:
pH = −log(0.025)
Step 6: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−(−1.602) = 1.602
Therefore, the pH of a 0.025 M solution of hydrochloric acid is 1.602.
Question 23
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−9
M.
Solution
Step 1: Write the relationship between pOH and OH- concentration.
pOH = −log[OH-]
Step 2: Substitute the given hydroxide ion concentration into the equation
to find the pOH.
pOH = −log1.5×10−9
pOH = −log(1.5) −log10−9
pOH ≈8.82
Step 3: Use the relationship between pH and pOH.
pH + pOH = 14
Step 4: Calculate the pH by subtracting the pOH from 14.
pH = 14 −8.82
pH ≈5.18
Therefore, the pH of the solution is approximately 5.18.
15
Question 24
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.5×
10−5M.
Solution
Step 1: Write down the expression for calculating the pOH of the solution. The
pOH of a solution can be calculated using the formula:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration into the formula.
pOH =−log3.5×10−5
Step 3: Calculate the pOH.
pOH =−log3.5×10−5=−(log 3.5 + log 10−5) = −(log 3.5−5)
pOH ≈ −(log 3.5−5)
Step 4: Now, calculate the pH of the solution using the relationship between
pH and pOH in water. In water, pH +pOH = 14.
pH = 14 −pOH = 14 −(log 3.5−5)
Step 5: Calculate the pH of the solution.
pH ≈14 −(log 3.5−5)
Question 25
Question
Calculate the pH of a solution that has a pOH of 2.5.
Solution
Step 1: Recall that the pH and pOH of a solution are related by the equation:
pH + pOH = 14
Step 2: Given that the pOH of the solution is 2.5, we can calculate the pH
using the equation above:
pH + 2.5 = 14
16
Step 3: Subtracting 2.5 from both sides of the equation gives:
pH = 14 −2.5
Step 4: Therefore, the pH of the solution is:
pH = 11.5
Step 5: The pH of the solution with a pOH of 2.5 is 11.5.
Question 26
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−11
M.
Solution
Step 1: Write the expression for Kw, the ion product of water.
Kw= [H+][OH−]
Step 2: Since Kw= 1.0×10−14 at 25
°
C, and we have the concentration of
hydroxide ions, we can solve for the concentration of hydronium ions.
Kw= [H+]·1.5×10−11
1.0×10−14 = [H+]·1.5×10−11
[H+] = 1.0×10−14
1.5×10−11
[H+]≈6.67 ×10−4M
Step 3: Calculate the pH using the formula pH =−log [H+].
pH =−log 6.67 ×10−4
pH =−log 6.67 −log 10−4
pH ≈3.18
Therefore, the pH of the solution is approximately 3.18.
Question 27
Question
A solution is prepared by dissolving 0.050 moles of hydrochloric acid (HCl) in
enough water to make 500.0 mL of solution. Calculate the pH and pOH of the
resulting solution.
17
Solution
Step 1: Calculate the concentration of HCl in the solution. The concentration
(in M) of HCl can be calculated using the formula:
Concentration (M) = moles of solute
volume of solution (L)
Given: Moles of HCl = 0.050 mol Volume of solution = 500.0 mL = 0.500 L
Plugging in the values:
Concentration of HCl = 0.050 mol
0.500 L = 0.10 M
Step 2: Calculate the pH of the solution. Since HCl is a strong acid that fully
dissociates in water, the concentration of H+ ions is equal to the concentration
of HCl.
The pH can be calculated using the formula:
pH = −log[H+]
Given that [H+] = 0.10M: pH = −log(0.10) = 1.00
Therefore, the pH of the solution is 1.00.
Step 3: Calculate the pOH of the solution. The pOH can be calculated using
the formula:
pOH = −log[OH−]
Since the solution only contains HCl, there are no OH- ions present. There-
fore, the concentration of OH- ions is 0.
pOH = −log(0) = undefined
Therefore, the pOH of the solution is undefined.
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.6×10−5
M.
Solution
Step 1: Calculate the pOH of the solution using the hydroxide ion concentration:
pOH =−log[OH−]
pOH =−log3.6×10−5
pOH ≈4.44
18
Step 2: Use the relationship between pH and pOH to find the pH of the
solution:
pH +pOH = 14
pH = 14 −pOH
pH = 14 −4.44
pH ≈9.56
Therefore, the pH of the solution with a hydroxide ion concentration of
3.6×10−5M is approximately 9.56.
Question 29
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−6
M.
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 pH for-
mula:
pH = −log3.2×10−6
Step 3: Use the logarithm property log(a×b) = log a+ log bto simplify the
calculation:
pH = −(log 3.2 + log 10−6)
Step 4: Recall that log(10n) = n, then simplify further:
pH = −(log 3.2−6)
Step 5: Use a calculator to find log 3.2≈0.5051, then calculate the pH:
pH = −(0.5051 −6) = −(−5.4949) = 5.4949
Therefore, the pH of the solution with a hydronium ion concentration of
3.2×10−6M is approximately 5.49.
Question 30
Question
A solution has a hydrogen ion concentration of 1.5×10−4M. Calculate the pH
and pOH of the solution.
19
Solution
Step 1: Recall that the pH is calculated using the formula: pH =−log[H+],
where [H+] is the hydrogen ion concentration.
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH =−log1.5×10−4
Step 3: Calculate the pH:
pH =−log1.5×10−4=−log 1.5−log 10−4=−0.1761 −(−4)
Step 4: Simplify the calculation:
pH = 3.8239
Step 5: Therefore, the pH of the solution is 3.82.
Step 6: Since pH + pOH = 14, we can calculate the pOH using the formula:
pOH = 14 −pH.
Step 7: Substitute the pH value into the formula to calculate pOH:
pOH = 14 −3.82
Step 8: Calculate the pOH:
pOH = 10.18
Step 9: Therefore, the pOH of the solution is 10.18.
Question 31
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid.
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid (HCl):
HCl →H++Cl−
Step 2: Since hydrochloric acid is a strong acid, it dissociates completely
in water. This means that the concentration of H+ions is equal to the initial
concentration of the hydrochloric acid, which is 0.025 M.
Step 3: Calculate the pH using the formula:
pH =−log[H+]
Step 4: Substitute the given concentration of H+ions into the formula:
pH =−log(0.025)
20
Step 5: Calculate the pH:
pH =−log(0.025) = −log2.5×10−2=−(−1.602) = 1.602
Answer: The pH of a 0.025 M solution of hydrochloric acid is 1.602.
Question 32
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 and hydronium ion concentration. The pH
of a solution is defined as −log[H3O+], where [H3O+] is the concentration of
hydronium ions in the solution.
Step 2: Substitute the given hydronium ion concentration into the pH for-
mula.
pH = −log3.2×10−5
Step 3: Calculate the pH of the solution.
pH = −log3.2×10−5=−log(3.2) + log10−5=−(0.5051) −(−5) = 4.4949
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−5M is approximately 4.49.
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.60×10−5
M.
Solution
Step 1: Use the relationship between pOH and the hydroxide ion concentration
to find the pOH of the solution.
pOH = −log[OH−]
pOH = −log5.60 ×10−5
pOH = −(−4.252)
pOH ≈4.25
21
Step 2: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
pH + 4.25 = 14
pH = 14 −4.25
pH ≈9.75
The pH of the solution is approximately 9.75.
Question 34
Question
A solution is prepared by mixing 50.0 mL of 0.200 M hydrochloric acid (HCl)
with 75.0 mL of 0.150 M sodium hydroxide (NaOH). Calculate the pH of the
resulting solution. (Given: Kw= 1.0×10−14)
Solution
Step 1: Determine the moles of HCl and NaOH used.
Moles of HCl = Volume ×Molarity
= (0.050 L) ×(0.200 mol/L)
= 0.010 mol
Moles of NaOH = Volume ×Molarity
= (0.075 L) ×(0.150 mol/L)
= 0.01125 mol
Step 2: Calculate the limiting reactant by comparing the moles of HCl and
NaOH. Since HCl and NaOH react in a 1:1 ratio (1 mole of HCl reacts with
1 mole of NaOH), HCl is the limiting reactant as it produces fewer moles of
reactant.
Step 3: Calculate the excess moles of NaOH.
Excess moles of NaOH = Moles of NaOH −Moles of HCl
= 0.01125 mol −0.010 mol
= 0.00125 mol
Step 4: Calculate the moles of the resulting base, which is NaCl. Since 1
mole of NaOH produces 1 mole of NaCl, the moles of NaCl formed will equal
the excess moles of NaOH.
Moles of NaCl = Excess moles of NaOH
= 0.00125 mol
22
Step 5: Calculate the concentration of NaCl.
Volume of resulting solution = 50.0 mL + 75.0 mL
= 125.0 mL = 0.125 L
Molarity of NaCl = Moles of NaCl
Volume of resulting solution
=0.00125 mol
0.125 L
= 0.010 mol/L
Step 6: Calculate the pOH of the resulting solution.
pOH =−log[OH−]
=−log(0.010)
= 2
Step 7: Calculate the pH of the resulting solution. Since pH +pOH = 14,
pH = 14 −pOH
= 14 −2
= 12
Therefore, the pH of the resulting solution is 12.
Question 35
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−7
M.
Solution
Step 1: Use the formula pOH =−log[OH−] to find the pOH of the solution.
Given: [OH−]=2.5×10−7M
pOH =−log2.5×10−7
Step 2: Calculate the pOH.
pOH =−log2.5×10−7
pOH =−(log 2.5 + log 10−7)
pOH =−(0.3979 −7)
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pOH =−(−6.6021)
pOH = 6.6021
Step 3: Use the relationship pH +pOH = 14 to find the pH.
pOH = 6.6021 ⇒pH + 6.6021 = 14
Step 4: Calculate the pH.
pH = 14 −6.6021
pH = 7.3979
Answer: The pH of the solution is 7.3979.
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