CHEM 105 - ELEMENTS OF
GENERAL CHEMISTRY - pH and
pOH calculations
Question Bank - Set 3
Liberty University
Question 1
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−4
M.
Solution
Step 1: Recall that the pH is defined as the negative base 10 logarithm of the
hydronium ion concentration. The formula for pH is given by:
pH = −log[H3O+]
Step 2: Substituting the given hydronium ion concentration into the formula:
pH = −log2.5×10−4
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(2.5) + log10−4
Step 4: Remember that log(10x) = x, so log10−4=−4:
pH = −log(2.5) −4
Step 5: Using a calculator, compute the value of log(2.5):
log(2.5) ≈0.3979
Step 6: Substitute the value of log(2.5) back into the pH formula:
pH ≈ −(0.3979) −4
Step 7: Finally, calculate the pH of the solution:
pH ≈4.3979
Therefore, the pH of the solution with a hydronium ion concentration of
2.5×10−4M is approximately 4.40.
Question 2
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 defined as −log[H3O+]. Therefore, we can calculate
the pH using the given concentration of hydronium ions. Step 2: Substitute the
given concentration of hydronium ions into the pH formula:
pH = −log2.5×10−5
Step 3: Use a calculator to find the value of −log2.5×10−5:
pH = −log2.5×10−5≈4.60
Step 4: Therefore, the pH of the solution with a hydronium ion concentration
of 2.5×10−5M is approximately 4.60.
Question 3
Question
Calculate the pH of a solution with a pOH of 2.6.
Solution
Step 1: Recall that pH and pOH are related by the equation: pH +pOH = 14.
Step 2: Given that pOH = 2.6, we can find pH by rearranging the equation:
pH = 14 −pOH.
Step 3: Substitute the given value of pOH into the equation to solve for pH:
pH = 14 −2.6
Step 4: Calculate the pH:
pH = 11.4
Step 5: Therefore, the pH of the solution is 11.4 .
2
Question 4
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.0×10−3
M.
Solution
Step 1: Use the formula for the relationship between pH and pOH:
pH +pOH = 14
Step 2: Calculate the pOH of the solution using the hydroxide ion concen-
tration given:
pOH =−log5.0×10−3
pOH =−log(5.0) −log10−3
pOH =−(log(5.0) −3)
pOH ≈ −0.6990 −3
pOH ≈3.301
Step 3: Use the relationship between pH and pOH to find the pH:
pH = 14 −pOH
pH = 14 −3.301
pH ≈10.699
Therefore, the pH of the solution with a hydroxide ion concentration of
5.0×10−3M is approximately 10.699.
Question 5
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.8×10−5
M.
3
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.8×10−5
Step 3: Calculate the pH:
pH = −log3.8×10−5=−(log 3.8 + log 10−5)
Step 4: Simplify the expression:
pH = −(log 3.8−5)
Step 5: Use the property of logarithms to simplify further:
pH = −(0.58 −5) = −(−4.42) = 4.42
Therefore, the pH of the solution with a hydrogen ion concentration of 3.8×
10−5M is 4.42.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.5×10−9
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
for pH:
pH = −log3.5×10−9
Step 3: Calculate the pH:
pH = −log3.5×10−9=−log(3.5) −log10−9
Step 4: Simplify further:
pH = −log(3.5) −(−9)
Step 5: Using the properties of logarithms, we see that −log(3.5) = −0.5441.
Step 6: Therefore, the pH of the solution is:
pH = −(−0.5441) −9=0.5441 −9 = 8.4559
Step 7: Thus, the pH of the solution with a hydronium ion concentration of
3.5×10−9M is 8.46.
4
Question 7
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: The pH of a solution can be calculated using the formula:
pH = −log[H3O+]
where [H3O+] is the concentration of hydronium ions in the solution.
Step 2: Substituting the given concentration into the formula, we get:
pH = −log1.5×10−9
Step 3: Calculate the pH by taking the negative logarithm of the concentra-
tion:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 4: Using the property of logarithms log(ab) = log(a) + log(b), we sim-
plify the expression:
pH = −(log(1.5) + log10−9) = −(log(1.5) −9)
Step 5: Finally, calculate the pH:
pH = −(log(1.5) −9) ≈ −(0.176 −9) = −8.824
Therefore, the pH of the solution is approximately 8.824.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−4
M.
Solution
Step 1: Remember that pH is defined as −log[H3O+]. Thus, we need to de-
termine the pH given the hydronium ion concentration. Step 2: Substitute the
given hydronium ion concentration into the pH formula:
pH = −log3.2×10−4
5
Step 3: Calculate the pH:
pH = −log3.2×10−4=−log(3.2) −log10−4
Step 4: Recall that log10−4=−4:
pH = −log(3.2) −(−4) = −log(3.2) + 4
Step 5: Use a calculator to find the value of log(3.2) and then subtract that
from 4 to find the pH value. It should be around 3.5.
pH ≈ −0.5052 + 4 = 3.4948
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−4M is approximately 3.5.
Question 9
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration ([H+]) in a solution:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that [H+] = 3.2×10−9M, we can calculate the pH by plugging
this value into the formula for pH:
pH = −log3.2×10−9=−log(3.2) −log10−9
Step 3: Simplifying further, we have:
pH ≈ −0.505 −(−9) = 8.495
Step 4: Next, we can calculate the pOH using the relationship pH + pOH =
14:
pOH = 14 −pH = 14 −8.495 = 5.505
Step 5: Therefore, the pH of the solution is approximately 8.495 and the
pOH is approximately 5.505.
6
Question 10
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−4M.
Solution
Step 1: Recall that pH is defined as −log[H3O+] and pOH is defined as −log[OH−].
Step 2: Given that the hydronium ion concentration is 3.2×10−4M, we can
calculate the pH using the formula: pH = −log3.2×10−4.
Step 3: Calculate the pH:
pH = −log3.2×10−4=−(−3.49485) = 3.49485
Step 4: Now, since pH + pOH = 14, we can find the pOH:
pOH = 14 −pH = 14 −3.49485 = 10.50515
Step 5: Therefore, the pH of the solution is 3.49485 and the pOH is 10.50515.
Question 11
Question
Calculate the pH of a solution with a hydrogen ion concentration of 7.5×10−4
M.
Solution
Step 1: Recall the definition of pH: pH = −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log7.5×10−4
Step 3: Calculate the pH:
pH = −log7.5×10−4=−log(7.5)+log10−4=−(−0.875)−4=0.875−4 = −3.125
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 7.5×10−4M is pH = 3.125.
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
7
Solution
Step 1: Use the equation pOH =−log[OH−] to find the pOH of the solution.
Given: [OH−]=2.5×10−4M
pOH =−log2.5×10−4
pOH =−log(2.5) + log10−4
pOH =−(log(2.5) −4)
pOH ≈ −0.3979
Step 2: Use the relationship pH +pOH = 14 to find the pH of the solution.
pH = 14 −pOH
pH = 14 −(−0.3979)
pH ≈14.3979
Therefore, the pH of the solution is approximately 14.40.
Question 13
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall that the pH is calculated using the formula pH =−log[H+],
where [H+] is the hydrogen ion concentration. Similarly, the pOH is calculated
using the formula pOH =−log[OH−].
Step 2: Given that the hydrogen ion concentration is 3.2×10−9M, we can
calculate the pH using the formula pH =−log3.2×10−9.
Step 3: Calculate the pH:
pH =−log3.2×10−9
pH ≈ − log(3.2) + log10−9
pH ≈ −0.5052 + 9
pH ≈8.4948
Step 4: To find the pOH, we know that pH +pOH = 14. Therefore, we can
calculate the pOH as:
pOH = 14 −pH
pOH = 14 −8.4948
pOH ≈5.5052
Step 5: Therefore, the pH of the solution is approximately 8.4948 and the
pOH is approximately 5.5052.
8
Question 14
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.2×
10−10 M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H+]. To find the pH
from the hydroxide ion concentration, we first need to find the concentration of
the hydrogen ion using the relation Kw= [H+][OH−] where Kw= 1.0×10−14
at 25
°
C.
Step 2: Given that [OH−] = 3.2×10−10 M, we can substitute this into the
equation: 1.0×10−14 = [H+](3.2×10−10).
Step 3: Solve for [H+]:
[H+] = 1.0×10−14
3.2×10−10
Step 4: Calculate [H+]:
[H+]=3.125 ×10−5M
Step 5: Calculate the pH, which is −log3.125 ×10−5.
Step 6: Calculate the pH of the solution:
pH = −log3.125 ×10−5
Step 7: Using a calculator, we find:
pH ≈4.504
Therefore, the pH of a solution with a hydroxide ion concentration of 3.2×
10−10 M is approximately 4.504.
Question 15
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration. The formula for pH is given by:
pH = −log[H3O+]
9
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
pH ≈ − log(1.5) −log10−9
pH ≈ −0.1761 −(−9)
pH ≈8.8239
Step 4: Round the pH to the appropriate number of decimal places:
pH ≈8.8
Therefore, the pH of a solution with a hydronium ion concentration of 1.5×
10−9M is approximately 8.8.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.2×10−3
M.
Solution
Step 1: Determine the pOH of the solution using the hydroxide ion concentra-
tion.
pOH = −log[OH−] = −log1.2×10−3
Step 2: Calculate the pOH.
pOH ≈ − log1.2×10−3= 2.92
Step 3: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
Step 4: Calculate the pH.
pH = 14 −pOH = 14 −2.92 = 11.08
Therefore, the pH of the solution is approximately 11.08.
10
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula
pH =−log[H+], where [H+] is the concentration of hydrogen ions in the so-
lution. Since we are given the hydroxide ion concentration, we can use the
relationship [H+][OH−] = 1.0×10−14 for water at 25
°
C to find [H+].
Step 2: First, calculate the hydroxide ion concentration:
[OH−]=2.5×10−3M
Step 3: Use the relationship [H+][OH−]=1.0×10−14 to find [H+]:
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 4: Now, calculate the pH using the formula pH =−log[H+]:
pH =−log4.0×10−12=−log(4.0) −log10−12=−0.6021 −(−12) = 11.40
Step 5: Therefore, the pH of the solution with a hydroxide ion concentration
of 2.5×10−3M is 11.40.
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Write the expression for the hydronium ion concentration and pH.
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH ex-
pression.
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator.
pH = −log3.2×10−9=−(−8.494) = 8.494
Step 4: Provide the final answer. The pH of the solution with a hydronium
ion concentration of 3.2×10−9M is ≈8.494.
11
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. So, we have:
pH = −logH3O+
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3≈ − log(2.5) + 3
Step 4: Continue the calculation:
pH ≈ −0.398 + 3 = 2.602
Step 5: Therefore, the pH of the solution is 2.602 .
Question 20
Question
Calculate the pH of a solution with hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
[OH−] = 1.5×10−3M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−3M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH =−log[H+]=−log 1.0×10−14
1.5×10−3
12
Step 4: Solve for the pH.
pH =−log 1.0×10−14
1.5×10−3=−log6.67 ×10−12
Step 5: Calculate the final pH value.
pH =−log6.67 ×10−12≈11.18
Therefore, the pH of the solution is approximately 11.18.
Question 21
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall the relationship between pH, hydronium ion concentration, and
pOH:
pH = −log[H3O+]
pOH = −log[OH−]
Step 2: Given that [H3O+]=3.2×10−5M, we can calculate the pH:
pH = −log3.2×10−5
pH = −log(3.2) + log10−5
pH = −(0.505) + (−5)
pH = −5.505
Step 3: Now, we can calculate the pOH using the relationship with pH:
pH + pOH = 14
pOH = 14 −pH
pOH = 14 −(−5.505)
pOH = 19.505
Step 4: Therefore, the pH of the solution is 5.505 and the pOH is 19.505.
Question 22
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid (HCl) at 25◦C.
13
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl (aq) →H+(aq) + Cl−(aq)
Step 2: Determine the initial concentration of H+ions in the solution. Since
hydrochloric acid is a strong acid, it dissociates completely in water. Therefore,
the concentration of H+ions is equal to the initial concentration of HCl, which
is 0.025 M.
Step 3: Use the definition of pH to calculate the pH of the solution. The pH
is defined as −log[H+].
pH = −log(0.025) = −log2.5×10−2=−(−1.60) = 1.60
Therefore, the pH of a 0.025 M solution of hydrochloric acid at 25◦C is 1.60.
Question 23
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 1.5×
10−4M.
Solution
Step 1: Write the equilibrium expression for the auto-ionization of water:
H2O⇌H++ OH−
The equilibrium constant expression for this reaction is:
Kw= [H+][OH−] = 1 ×10−14
Step 2: Given that the hydroxide ion concentration is 1.5×10−4M, we can
substitute this into the equilibrium constant expression to find the concentration
of hydronium ions:
1×10−14 =x×1.5×10−4
x=1×10−14
1.5×10−4
x= 6.67 ×10−11
Step 3: Calculate the pH using the formula:
pH =−logH+
pH =−log6.67 ×10−11
14
pH =−(log(6.67) + log10−11)
pH =−(log(6.67) −11)
pH =−(≈0.8241 −11)
pH ≈10.18
Therefore, the pH of a solution with a hydroxide ion concentration of 1.5×
10−4M is approximately 10.18.
Question 24
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
plug this value into the formula to find the pH:
pH = −log3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−5
Step 4: Remember that log10−5=−5:
pH = −log(3.2) −(−5)
Step 5: Calculate −log(3.2):
pH = −log(3.2) + 5
Step 6: Using a calculator, find −log(3.2) ≈0.494:
pH ≈0.494 + 5
Step 7: Sum the values to find the pH of the solution:
pH ≈5.494
Thus, the pH of a solution with a hydronium ion concentration of 3.2×10−5
M is approximately 5.494.
15
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.2×10−8
M.
Solution
Step 1: Write the expression relating pH and [OH−]. The pH of a solution is
related to the hydroxide ion concentration ([OH−]) by the equation:
pOH = −log[OH−]
We also know that pH + pOH = 14 at 25
°
C.
Step 2: Calculate the pOH. Given that [OH−]=1.2×10−8M, we can
calculate the pOH as follows:
pOH = −log1.2×10−8
pOH = −(log 1.2 + log 10−8)
pOH = −(log 1.2−8)
pOH ≈ −(−0.0792)
pOH ≈0.0792
Step 3: Calculate the pH. Now, we can find the pH using the relationship
pH + pOH = 14:
pH = 14 −pOH
pH = 14 −0.0792
pH ≈13.9208
So, the pH of the solution is approximately 13.92.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
16
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−10
Step 3: Calculate the pH using a calculator:
pH ≈ − log2.5×10−10≈ −(log 2.5 + log 10−10)
≈ −(log 2.5−10) ≈ −(0.3979 −10) ≈ −(9.6021) ≈9.60
Step 4: Therefore, the pH of the solution is approximately 9.60.
Question 27
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm of the hydronium
ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9
pH = −(−8.60)
pH = 8.60
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 2.5×10−9M is 8.60.
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−9
M.
17
Solution
Step 1: Recall the relationship between pOH and [OH−]:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration to find pOH:
pOH =−log3.2×10−9
pOH =−(−8.50)
pOH = 8.50
Step 3: Use the fact that pH +pOH = 14 to find pH:
pH = 14 −pOH
pH = 14 −8.50
pH = 5.50
Answer: The pH of the solution is 5.50.
Question 29
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.0×
10−8M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Given the hydroxide ion concentration, calculate the hydrogen ion
concentration.
[OH−] = 3.0×10−8M
[H+] = Kw
[OH−]=1.0×10−14
3.0×10−8= 3.33 ×10−7M
Step 3: Calculate the pH of the solution.
pH =−log[H+] = −log3.33 ×10−7=−(log 3 + log 33 + log 10−7)
pH =−(log 3 + log 33 −7) ≈ −0.48 −1.52 = 2.00
Therefore, the pH of the solution is 2.00.
18
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Write the expression for the ion product constant of water. Step 2: Use
the ion product constant of water to find the concentration of hydrogen ions.
Step 3: Calculate the pH of the solution by taking the negative logarithm of the
hydrogen ion concentration.
Step 1: Write the expression for the ion product constant of water. The
ion product constant of water, Kw, is equal to 1.0×10−14 at 25
°
C.
Kw= [H+][OH−]
Step 2: Use the ion product constant of water to find the concentration
of hydrogen ions. Given that the concentration of hydroxide ions is 3.2×10−4
M, we can use the ion product constant of water to find the concentration of
hydrogen ions.
Kw= [H+][OH−]
1.0×10−14 = [H+](3.2×10−4)
[H+] = 1.0×10−14
3.2×10−4
[H+]=3.125 ×10−11 M
Step 3: Calculate the pH of the solution by taking the negative logarithm
of the hydrogen ion concentration.
pH = −log[H+]
pH = −log3.125 ×10−11
pH = −(log(3.125) + log10−11)
pH ≈ −(−0.504 + 11)
pH ≈10.504
Therefore, the pH of the solution is approximately 10.504.
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−6
M.
19
Solution
Step 1: Recall that the pH of a solution is calculated using the formula: pH =
−log[H3O+]. Given that the hydronium ion concentration is 1.5×10−6M, we
can substitute this value into the formula to find the pH.
pH =−log1.5×10−6
Step 2: Use the property of logarithms log(ab) = log(a) + log(b) to simplify
the calculation.
pH =−log(1.5) −log10−6
Step 3: Recall the properties of logarithms logab=blog(a) and log(10) =
1.
pH =−(log(1.5) −6)
Step 4: Calculate the logarithm of 1.5 using a calculator.
pH =−(0.1761 −6)
Step 5: Subtract 0.1761 from 6.
pH =−5.8239
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−6M is 5.8239 .
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: First, we need to calculate the pOH of the solution using the hydroxide
ion concentration:
pOH =−log[OH−] = −log3.2×10−5
Step 2: Calculate pOH:
pOH =−log3.2×10−5≈ −(−4.495) ≈4.495
Step 3: Since pH +pOH = 14, we can find the pH of the solution:
pH = 14 −pOH = 14 −4.495 ≈9.505
Step 4: Therefore, the pH of the solution is approximately 9.505.
20
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Calculate the concentration of H+ions in the solution using the ion
product of water (Kw= 1.0×10−14 at 25◦C):
[H+]×[OH−] = Kw
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
1.5×10−4
[H+] = 6.67 ×10−11 M
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log6.67 ×10−11
pH = −(log(6.67) + log10−11)
pH = −(0.825 + (−11))
pH = −(−10.175)
pH = 10.175
Therefore, the pH of the solution is 10.175.
Question 34
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−4
M.
21
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we need to find
the negative logarithm of the hydronium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the formula
for pH:
pH = −log1.5×10−4
Step 3: Calculate the pH:
pH = −log1.5×10−4=−log(1.5)−log10−4=−log(1.5)−(−4) = −log(1.5)+4
Step 4: Use a calculator to find the value of −log(1.5), which is approxi-
mately 0.1761.
Step 5: Finally, calculate the pH:
pH = 0.1761 + 4 = 4.1761
Therefore, the pH of the solution is approximately 4.1761.
Question 35
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 in water:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Since HCl is a strong acid, it dissociates completely in water. There-
fore, the concentration of H+ions is equal to the initial concentration of HCl,
which is 0.025 M.
Step 3: Calculate the pH using the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
Step 5: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−log(2.5) + log10−2= 2 −2=0
Therefore, the pH of a 0.025 M solution of hydrochloric acid is 0.
22
Question 4
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.0×10−3
M.
Solution
Step 1: Use the formula for the relationship between pH and pOH:
pH +pOH = 14
Step 2: Calculate the pOH of the solution using the hydroxide ion concen-
tration given:
pOH =−log5.0×10−3
pOH =−log(5.0) −log10−3
pOH =−(log(5.0) −3)
pOH ≈ −0.6990 −3
pOH ≈3.301
Step 3: Use the relationship between pH and pOH to find the pH:
pH = 14 −pOH
pH = 14 −3.301
pH ≈10.699
Therefore, the pH of the solution with a hydroxide ion concentration of
5.0×10−3M is approximately 10.699.
Question 5
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.8×10−5
M.
3
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.8×10−5
Step 3: Calculate the pH:
pH = −log3.8×10−5=−(log 3.8 + log 10−5)
Step 4: Simplify the expression:
pH = −(log 3.8−5)
Step 5: Use the property of logarithms to simplify further:
pH = −(0.58 −5) = −(−4.42) = 4.42
Therefore, the pH of the solution with a hydrogen ion concentration of 3.8×
10−5M is 4.42.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.5×10−9
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
for pH:
pH = −log3.5×10−9
Step 3: Calculate the pH:
pH = −log3.5×10−9=−log(3.5) −log10−9
Step 4: Simplify further:
pH = −log(3.5) −(−9)
Step 5: Using the properties of logarithms, we see that −log(3.5) = −0.5441.
Step 6: Therefore, the pH of the solution is:
pH = −(−0.5441) −9=0.5441 −9 = 8.4559
Step 7: Thus, the pH of the solution with a hydronium ion concentration of
3.5×10−9M is 8.46.
4
Question 7
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: The pH of a solution can be calculated using the formula:
pH = −log[H3O+]
where [H3O+] is the concentration of hydronium ions in the solution.
Step 2: Substituting the given concentration into the formula, we get:
pH = −log1.5×10−9
Step 3: Calculate the pH by taking the negative logarithm of the concentra-
tion:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 4: Using the property of logarithms log(ab) = log(a) + log(b), we sim-
plify the expression:
pH = −(log(1.5) + log10−9) = −(log(1.5) −9)
Step 5: Finally, calculate the pH:
pH = −(log(1.5) −9) ≈ −(0.176 −9) = −8.824
Therefore, the pH of the solution is approximately 8.824.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−4
M.
Solution
Step 1: Remember that pH is defined as −log[H3O+]. Thus, we need to de-
termine the pH given the hydronium ion concentration. Step 2: Substitute the
given hydronium ion concentration into the pH formula:
pH = −log3.2×10−4
5
Step 3: Calculate the pH:
pH = −log3.2×10−4=−log(3.2) −log10−4
Step 4: Recall that log10−4=−4:
pH = −log(3.2) −(−4) = −log(3.2) + 4
Step 5: Use a calculator to find the value of log(3.2) and then subtract that
from 4 to find the pH value. It should be around 3.5.
pH ≈ −0.5052 + 4 = 3.4948
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−4M is approximately 3.5.
Question 9
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration ([H+]) in a solution:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that [H+] = 3.2×10−9M, we can calculate the pH by plugging
this value into the formula for pH:
pH = −log3.2×10−9=−log(3.2) −log10−9
Step 3: Simplifying further, we have:
pH ≈ −0.505 −(−9) = 8.495
Step 4: Next, we can calculate the pOH using the relationship pH + pOH =
14:
pOH = 14 −pH = 14 −8.495 = 5.505
Step 5: Therefore, the pH of the solution is approximately 8.495 and the
pOH is approximately 5.505.
6
Question 10
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−4M.
Solution
Step 1: Recall that pH is defined as −log[H3O+] and pOH is defined as −log[OH−].
Step 2: Given that the hydronium ion concentration is 3.2×10−4M, we can
calculate the pH using the formula: pH = −log3.2×10−4.
Step 3: Calculate the pH:
pH = −log3.2×10−4=−(−3.49485) = 3.49485
Step 4: Now, since pH + pOH = 14, we can find the pOH:
pOH = 14 −pH = 14 −3.49485 = 10.50515
Step 5: Therefore, the pH of the solution is 3.49485 and the pOH is 10.50515.
Question 11
Question
Calculate the pH of a solution with a hydrogen ion concentration of 7.5×10−4
M.
Solution
Step 1: Recall the definition of pH: pH = −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log7.5×10−4
Step 3: Calculate the pH:
pH = −log7.5×10−4=−log(7.5)+log10−4=−(−0.875)−4=0.875−4 = −3.125
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 7.5×10−4M is pH = 3.125.
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
7
Solution
Step 1: Use the equation pOH =−log[OH−] to find the pOH of the solution.
Given: [OH−]=2.5×10−4M
pOH =−log2.5×10−4
pOH =−log(2.5) + log10−4
pOH =−(log(2.5) −4)
pOH ≈ −0.3979
Step 2: Use the relationship pH +pOH = 14 to find the pH of the solution.
pH = 14 −pOH
pH = 14 −(−0.3979)
pH ≈14.3979
Therefore, the pH of the solution is approximately 14.40.
Question 13
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall that the pH is calculated using the formula pH =−log[H+],
where [H+] is the hydrogen ion concentration. Similarly, the pOH is calculated
using the formula pOH =−log[OH−].
Step 2: Given that the hydrogen ion concentration is 3.2×10−9M, we can
calculate the pH using the formula pH =−log3.2×10−9.
Step 3: Calculate the pH:
pH =−log3.2×10−9
pH ≈ − log(3.2) + log10−9
pH ≈ −0.5052 + 9
pH ≈8.4948
Step 4: To find the pOH, we know that pH +pOH = 14. Therefore, we can
calculate the pOH as:
pOH = 14 −pH
pOH = 14 −8.4948
pOH ≈5.5052
Step 5: Therefore, the pH of the solution is approximately 8.4948 and the
pOH is approximately 5.5052.
8
Question 14
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.2×
10−10 M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H+]. To find the pH
from the hydroxide ion concentration, we first need to find the concentration of
the hydrogen ion using the relation Kw= [H+][OH−] where Kw= 1.0×10−14
at 25
°
C.
Step 2: Given that [OH−] = 3.2×10−10 M, we can substitute this into the
equation: 1.0×10−14 = [H+](3.2×10−10).
Step 3: Solve for [H+]:
[H+] = 1.0×10−14
3.2×10−10
Step 4: Calculate [H+]:
[H+]=3.125 ×10−5M
Step 5: Calculate the pH, which is −log3.125 ×10−5.
Step 6: Calculate the pH of the solution:
pH = −log3.125 ×10−5
Step 7: Using a calculator, we find:
pH ≈4.504
Therefore, the pH of a solution with a hydroxide ion concentration of 3.2×
10−10 M is approximately 4.504.
Question 15
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration. The formula for pH is given by:
pH = −log[H3O+]
9
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
pH ≈ − log(1.5) −log10−9
pH ≈ −0.1761 −(−9)
pH ≈8.8239
Step 4: Round the pH to the appropriate number of decimal places:
pH ≈8.8
Therefore, the pH of a solution with a hydronium ion concentration of 1.5×
10−9M is approximately 8.8.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.2×10−3
M.
Solution
Step 1: Determine the pOH of the solution using the hydroxide ion concentra-
tion.
pOH = −log[OH−] = −log1.2×10−3
Step 2: Calculate the pOH.
pOH ≈ − log1.2×10−3= 2.92
Step 3: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
Step 4: Calculate the pH.
pH = 14 −pOH = 14 −2.92 = 11.08
Therefore, the pH of the solution is approximately 11.08.
10
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula
pH =−log[H+], where [H+] is the concentration of hydrogen ions in the so-
lution. Since we are given the hydroxide ion concentration, we can use the
relationship [H+][OH−] = 1.0×10−14 for water at 25
°
C to find [H+].
Step 2: First, calculate the hydroxide ion concentration:
[OH−]=2.5×10−3M
Step 3: Use the relationship [H+][OH−]=1.0×10−14 to find [H+]:
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 4: Now, calculate the pH using the formula pH =−log[H+]:
pH =−log4.0×10−12=−log(4.0) −log10−12=−0.6021 −(−12) = 11.40
Step 5: Therefore, the pH of the solution with a hydroxide ion concentration
of 2.5×10−3M is 11.40.
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Write the expression for the hydronium ion concentration and pH.
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH ex-
pression.
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator.
pH = −log3.2×10−9=−(−8.494) = 8.494
Step 4: Provide the final answer. The pH of the solution with a hydronium
ion concentration of 3.2×10−9M is ≈8.494.
11
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. So, we have:
pH = −logH3O+
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3≈ − log(2.5) + 3
Step 4: Continue the calculation:
pH ≈ −0.398 + 3 = 2.602
Step 5: Therefore, the pH of the solution is 2.602 .
Question 20
Question
Calculate the pH of a solution with hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
[OH−] = 1.5×10−3M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−3M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH =−log[H+]=−log 1.0×10−14
1.5×10−3
12
Step 4: Solve for the pH.
pH =−log 1.0×10−14
1.5×10−3=−log6.67 ×10−12
Step 5: Calculate the final pH value.
pH =−log6.67 ×10−12≈11.18
Therefore, the pH of the solution is approximately 11.18.
Question 21
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall the relationship between pH, hydronium ion concentration, and
pOH:
pH = −log[H3O+]
pOH = −log[OH−]
Step 2: Given that [H3O+]=3.2×10−5M, we can calculate the pH:
pH = −log3.2×10−5
pH = −log(3.2) + log10−5
pH = −(0.505) + (−5)
pH = −5.505
Step 3: Now, we can calculate the pOH using the relationship with pH:
pH + pOH = 14
pOH = 14 −pH
pOH = 14 −(−5.505)
pOH = 19.505
Step 4: Therefore, the pH of the solution is 5.505 and the pOH is 19.505.
Question 22
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid (HCl) at 25◦C.
13
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl (aq) →H+(aq) + Cl−(aq)
Step 2: Determine the initial concentration of H+ions in the solution. Since
hydrochloric acid is a strong acid, it dissociates completely in water. Therefore,
the concentration of H+ions is equal to the initial concentration of HCl, which
is 0.025 M.
Step 3: Use the definition of pH to calculate the pH of the solution. The pH
is defined as −log[H+].
pH = −log(0.025) = −log2.5×10−2=−(−1.60) = 1.60
Therefore, the pH of a 0.025 M solution of hydrochloric acid at 25◦C is 1.60.
Question 23
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 1.5×
10−4M.
Solution
Step 1: Write the equilibrium expression for the auto-ionization of water:
H2O⇌H++ OH−
The equilibrium constant expression for this reaction is:
Kw= [H+][OH−] = 1 ×10−14
Step 2: Given that the hydroxide ion concentration is 1.5×10−4M, we can
substitute this into the equilibrium constant expression to find the concentration
of hydronium ions:
1×10−14 =x×1.5×10−4
x=1×10−14
1.5×10−4
x= 6.67 ×10−11
Step 3: Calculate the pH using the formula:
pH =−logH+
pH =−log6.67 ×10−11
14
pH =−(log(6.67) + log10−11)
pH =−(log(6.67) −11)
pH =−(≈0.8241 −11)
pH ≈10.18
Therefore, the pH of a solution with a hydroxide ion concentration of 1.5×
10−4M is approximately 10.18.
Question 24
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
plug this value into the formula to find the pH:
pH = −log3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−5
Step 4: Remember that log10−5=−5:
pH = −log(3.2) −(−5)
Step 5: Calculate −log(3.2):
pH = −log(3.2) + 5
Step 6: Using a calculator, find −log(3.2) ≈0.494:
pH ≈0.494 + 5
Step 7: Sum the values to find the pH of the solution:
pH ≈5.494
Thus, the pH of a solution with a hydronium ion concentration of 3.2×10−5
M is approximately 5.494.
15
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.2×10−8
M.
Solution
Step 1: Write the expression relating pH and [OH−]. The pH of a solution is
related to the hydroxide ion concentration ([OH−]) by the equation:
pOH = −log[OH−]
We also know that pH + pOH = 14 at 25
°
C.
Step 2: Calculate the pOH. Given that [OH−]=1.2×10−8M, we can
calculate the pOH as follows:
pOH = −log1.2×10−8
pOH = −(log 1.2 + log 10−8)
pOH = −(log 1.2−8)
pOH ≈ −(−0.0792)
pOH ≈0.0792
Step 3: Calculate the pH. Now, we can find the pH using the relationship
pH + pOH = 14:
pH = 14 −pOH
pH = 14 −0.0792
pH ≈13.9208
So, the pH of the solution is approximately 13.92.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
16
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−10
Step 3: Calculate the pH using a calculator:
pH ≈ − log2.5×10−10≈ −(log 2.5 + log 10−10)
≈ −(log 2.5−10) ≈ −(0.3979 −10) ≈ −(9.6021) ≈9.60
Step 4: Therefore, the pH of the solution is approximately 9.60.
Question 27
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm of the hydronium
ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9
pH = −(−8.60)
pH = 8.60
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 2.5×10−9M is 8.60.
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−9
M.
17
Solution
Step 1: Recall the relationship between pOH and [OH−]:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration to find pOH:
pOH =−log3.2×10−9
pOH =−(−8.50)
pOH = 8.50
Step 3: Use the fact that pH +pOH = 14 to find pH:
pH = 14 −pOH
pH = 14 −8.50
pH = 5.50
Answer: The pH of the solution is 5.50.
Question 29
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.0×
10−8M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Given the hydroxide ion concentration, calculate the hydrogen ion
concentration.
[OH−] = 3.0×10−8M
[H+] = Kw
[OH−]=1.0×10−14
3.0×10−8= 3.33 ×10−7M
Step 3: Calculate the pH of the solution.
pH =−log[H+] = −log3.33 ×10−7=−(log 3 + log 33 + log 10−7)
pH =−(log 3 + log 33 −7) ≈ −0.48 −1.52 = 2.00
Therefore, the pH of the solution is 2.00.
18
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Write the expression for the ion product constant of water. Step 2: Use
the ion product constant of water to find the concentration of hydrogen ions.
Step 3: Calculate the pH of the solution by taking the negative logarithm of the
hydrogen ion concentration.
Step 1: Write the expression for the ion product constant of water. The
ion product constant of water, Kw, is equal to 1.0×10−14 at 25
°
C.
Kw= [H+][OH−]
Step 2: Use the ion product constant of water to find the concentration
of hydrogen ions. Given that the concentration of hydroxide ions is 3.2×10−4
M, we can use the ion product constant of water to find the concentration of
hydrogen ions.
Kw= [H+][OH−]
1.0×10−14 = [H+](3.2×10−4)
[H+] = 1.0×10−14
3.2×10−4
[H+]=3.125 ×10−11 M
Step 3: Calculate the pH of the solution by taking the negative logarithm
of the hydrogen ion concentration.
pH = −log[H+]
pH = −log3.125 ×10−11
pH = −(log(3.125) + log10−11)
pH ≈ −(−0.504 + 11)
pH ≈10.504
Therefore, the pH of the solution is approximately 10.504.
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−6
M.
19
Solution
Step 1: Recall that the pH of a solution is calculated using the formula: pH =
−log[H3O+]. Given that the hydronium ion concentration is 1.5×10−6M, we
can substitute this value into the formula to find the pH.
pH =−log1.5×10−6
Step 2: Use the property of logarithms log(ab) = log(a) + log(b) to simplify
the calculation.
pH =−log(1.5) −log10−6
Step 3: Recall the properties of logarithms logab=blog(a) and log(10) =
1.
pH =−(log(1.5) −6)
Step 4: Calculate the logarithm of 1.5 using a calculator.
pH =−(0.1761 −6)
Step 5: Subtract 0.1761 from 6.
pH =−5.8239
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−6M is 5.8239 .
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: First, we need to calculate the pOH of the solution using the hydroxide
ion concentration:
pOH =−log[OH−] = −log3.2×10−5
Step 2: Calculate pOH:
pOH =−log3.2×10−5≈ −(−4.495) ≈4.495
Step 3: Since pH +pOH = 14, we can find the pH of the solution:
pH = 14 −pOH = 14 −4.495 ≈9.505
Step 4: Therefore, the pH of the solution is approximately 9.505.
20
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Calculate the concentration of H+ions in the solution using the ion
product of water (Kw= 1.0×10−14 at 25◦C):
[H+]×[OH−] = Kw
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
1.5×10−4
[H+] = 6.67 ×10−11 M
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log6.67 ×10−11
pH = −(log(6.67) + log10−11)
pH = −(0.825 + (−11))
pH = −(−10.175)
pH = 10.175
Therefore, the pH of the solution is 10.175.
Question 34
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−4
M.
21
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we need to find
the negative logarithm of the hydronium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the formula
for pH:
pH = −log1.5×10−4
Step 3: Calculate the pH:
pH = −log1.5×10−4=−log(1.5)−log10−4=−log(1.5)−(−4) = −log(1.5)+4
Step 4: Use a calculator to find the value of −log(1.5), which is approxi-
mately 0.1761.
Step 5: Finally, calculate the pH:
pH = 0.1761 + 4 = 4.1761
Therefore, the pH of the solution is approximately 4.1761.
Question 35
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 in water:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Since HCl is a strong acid, it dissociates completely in water. There-
fore, the concentration of H+ions is equal to the initial concentration of HCl,
which is 0.025 M.
Step 3: Calculate the pH using the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
Step 5: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−log(2.5) + log10−2= 2 −2=0
Therefore, the pH of a 0.025 M solution of hydrochloric acid is 0.
22
Question 4
Question
Calculate the pH of a solution with a hydroxide ion concentration of 5.0×10−3
M.
Solution
Step 1: Use the formula for the relationship between pH and pOH:
pH +pOH = 14
Step 2: Calculate the pOH of the solution using the hydroxide ion concen-
tration given:
pOH =−log5.0×10−3
pOH =−log(5.0) −log10−3
pOH =−(log(5.0) −3)
pOH ≈ −0.6990 −3
pOH ≈3.301
Step 3: Use the relationship between pH and pOH to find the pH:
pH = 14 −pOH
pH = 14 −3.301
pH ≈10.699
Therefore, the pH of the solution with a hydroxide ion concentration of
5.0×10−3M is approximately 10.699.
Question 5
Question
Calculate the pH of a solution with a hydrogen ion concentration of 3.8×10−5
M.
3
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula:
pH = −log[H+]
Step 2: Substitute the given hydrogen ion concentration into the formula:
pH = −log3.8×10−5
Step 3: Calculate the pH:
pH = −log3.8×10−5=−(log 3.8 + log 10−5)
Step 4: Simplify the expression:
pH = −(log 3.8−5)
Step 5: Use the property of logarithms to simplify further:
pH = −(0.58 −5) = −(−4.42) = 4.42
Therefore, the pH of the solution with a hydrogen ion concentration of 3.8×
10−5M is 4.42.
Question 6
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.5×10−9
M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H3O+].
Step 2: Substitute the given hydronium ion concentration into the formula
for pH:
pH = −log3.5×10−9
Step 3: Calculate the pH:
pH = −log3.5×10−9=−log(3.5) −log10−9
Step 4: Simplify further:
pH = −log(3.5) −(−9)
Step 5: Using the properties of logarithms, we see that −log(3.5) = −0.5441.
Step 6: Therefore, the pH of the solution is:
pH = −(−0.5441) −9=0.5441 −9 = 8.4559
Step 7: Thus, the pH of the solution with a hydronium ion concentration of
3.5×10−9M is 8.46.
4
Question 7
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: The pH of a solution can be calculated using the formula:
pH = −log[H3O+]
where [H3O+] is the concentration of hydronium ions in the solution.
Step 2: Substituting the given concentration into the formula, we get:
pH = −log1.5×10−9
Step 3: Calculate the pH by taking the negative logarithm of the concentra-
tion:
pH = −log1.5×10−9=−log(1.5) −log10−9
Step 4: Using the property of logarithms log(ab) = log(a) + log(b), we sim-
plify the expression:
pH = −(log(1.5) + log10−9) = −(log(1.5) −9)
Step 5: Finally, calculate the pH:
pH = −(log(1.5) −9) ≈ −(0.176 −9) = −8.824
Therefore, the pH of the solution is approximately 8.824.
Question 8
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−4
M.
Solution
Step 1: Remember that pH is defined as −log[H3O+]. Thus, we need to de-
termine the pH given the hydronium ion concentration. Step 2: Substitute the
given hydronium ion concentration into the pH formula:
pH = −log3.2×10−4
5
Step 3: Calculate the pH:
pH = −log3.2×10−4=−log(3.2) −log10−4
Step 4: Recall that log10−4=−4:
pH = −log(3.2) −(−4) = −log(3.2) + 4
Step 5: Use a calculator to find the value of log(3.2) and then subtract that
from 4 to find the pH value. It should be around 3.5.
pH ≈ −0.5052 + 4 = 3.4948
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 3.2×10−4M is approximately 3.5.
Question 9
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall the relationship between pH, pOH, and the hydrogen ion con-
centration ([H+]) in a solution:
pH = −log[H+]
pOH = −log[OH−]
pH + pOH = 14
Step 2: Given that [H+] = 3.2×10−9M, we can calculate the pH by plugging
this value into the formula for pH:
pH = −log3.2×10−9=−log(3.2) −log10−9
Step 3: Simplifying further, we have:
pH ≈ −0.505 −(−9) = 8.495
Step 4: Next, we can calculate the pOH using the relationship pH + pOH =
14:
pOH = 14 −pH = 14 −8.495 = 5.505
Step 5: Therefore, the pH of the solution is approximately 8.495 and the
pOH is approximately 5.505.
6
Question 10
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−4M.
Solution
Step 1: Recall that pH is defined as −log[H3O+] and pOH is defined as −log[OH−].
Step 2: Given that the hydronium ion concentration is 3.2×10−4M, we can
calculate the pH using the formula: pH = −log3.2×10−4.
Step 3: Calculate the pH:
pH = −log3.2×10−4=−(−3.49485) = 3.49485
Step 4: Now, since pH + pOH = 14, we can find the pOH:
pOH = 14 −pH = 14 −3.49485 = 10.50515
Step 5: Therefore, the pH of the solution is 3.49485 and the pOH is 10.50515.
Question 11
Question
Calculate the pH of a solution with a hydrogen ion concentration of 7.5×10−4
M.
Solution
Step 1: Recall the definition of pH: pH = −log[H+].
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log7.5×10−4
Step 3: Calculate the pH:
pH = −log7.5×10−4=−log(7.5)+log10−4=−(−0.875)−4=0.875−4 = −3.125
Step 4: Therefore, the pH of the solution with a hydrogen ion concentration
of 7.5×10−4M is pH = 3.125.
Question 12
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−4
M.
7
Solution
Step 1: Use the equation pOH =−log[OH−] to find the pOH of the solution.
Given: [OH−]=2.5×10−4M
pOH =−log2.5×10−4
pOH =−log(2.5) + log10−4
pOH =−(log(2.5) −4)
pOH ≈ −0.3979
Step 2: Use the relationship pH +pOH = 14 to find the pH of the solution.
pH = 14 −pOH
pH = 14 −(−0.3979)
pH ≈14.3979
Therefore, the pH of the solution is approximately 14.40.
Question 13
Question
Calculate the pH and pOH of a solution with a hydrogen ion concentration of
3.2×10−9M.
Solution
Step 1: Recall that the pH is calculated using the formula pH =−log[H+],
where [H+] is the hydrogen ion concentration. Similarly, the pOH is calculated
using the formula pOH =−log[OH−].
Step 2: Given that the hydrogen ion concentration is 3.2×10−9M, we can
calculate the pH using the formula pH =−log3.2×10−9.
Step 3: Calculate the pH:
pH =−log3.2×10−9
pH ≈ − log(3.2) + log10−9
pH ≈ −0.5052 + 9
pH ≈8.4948
Step 4: To find the pOH, we know that pH +pOH = 14. Therefore, we can
calculate the pOH as:
pOH = 14 −pH
pOH = 14 −8.4948
pOH ≈5.5052
Step 5: Therefore, the pH of the solution is approximately 8.4948 and the
pOH is approximately 5.5052.
8
Question 14
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.2×
10−10 M.
Solution
Step 1: Recall that the pH of a solution is defined as −log[H+]. To find the pH
from the hydroxide ion concentration, we first need to find the concentration of
the hydrogen ion using the relation Kw= [H+][OH−] where Kw= 1.0×10−14
at 25
°
C.
Step 2: Given that [OH−] = 3.2×10−10 M, we can substitute this into the
equation: 1.0×10−14 = [H+](3.2×10−10).
Step 3: Solve for [H+]:
[H+] = 1.0×10−14
3.2×10−10
Step 4: Calculate [H+]:
[H+]=3.125 ×10−5M
Step 5: Calculate the pH, which is −log3.125 ×10−5.
Step 6: Calculate the pH of the solution:
pH = −log3.125 ×10−5
Step 7: Using a calculator, we find:
pH ≈4.504
Therefore, the pH of a solution with a hydroxide ion concentration of 3.2×
10−10 M is approximately 4.504.
Question 15
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−9
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm (base 10) of the
hydronium ion concentration. The formula for pH is given by:
pH = −log[H3O+]
9
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
pH ≈ − log(1.5) −log10−9
pH ≈ −0.1761 −(−9)
pH ≈8.8239
Step 4: Round the pH to the appropriate number of decimal places:
pH ≈8.8
Therefore, the pH of a solution with a hydronium ion concentration of 1.5×
10−9M is approximately 8.8.
Question 16
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.2×10−3
M.
Solution
Step 1: Determine the pOH of the solution using the hydroxide ion concentra-
tion.
pOH = −log[OH−] = −log1.2×10−3
Step 2: Calculate the pOH.
pOH ≈ − log1.2×10−3= 2.92
Step 3: Use the relationship between pH and pOH to find the pH of the
solution.
pH + pOH = 14
Step 4: Calculate the pH.
pH = 14 −pOH = 14 −2.92 = 11.08
Therefore, the pH of the solution is approximately 11.08.
10
Question 17
Question
Calculate the pH of a solution with a hydroxide ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that the pH of a solution can be calculated using the formula
pH =−log[H+], where [H+] is the concentration of hydrogen ions in the so-
lution. Since we are given the hydroxide ion concentration, we can use the
relationship [H+][OH−] = 1.0×10−14 for water at 25
°
C to find [H+].
Step 2: First, calculate the hydroxide ion concentration:
[OH−]=2.5×10−3M
Step 3: Use the relationship [H+][OH−]=1.0×10−14 to find [H+]:
[H+] = 1.0×10−14
2.5×10−3= 4.0×10−12 M
Step 4: Now, calculate the pH using the formula pH =−log[H+]:
pH =−log4.0×10−12=−log(4.0) −log10−12=−0.6021 −(−12) = 11.40
Step 5: Therefore, the pH of the solution with a hydroxide ion concentration
of 2.5×10−3M is 11.40.
Question 18
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−9
M.
Solution
Step 1: Write the expression for the hydronium ion concentration and pH.
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the pH ex-
pression.
pH = −log3.2×10−9
Step 3: Calculate the pH using a calculator.
pH = −log3.2×10−9=−(−8.494) = 8.494
Step 4: Provide the final answer. The pH of the solution with a hydronium
ion concentration of 3.2×10−9M is ≈8.494.
11
Question 19
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−3
M.
Solution
Step 1: Recall that pH is defined as −log[H3O+]. So, we have:
pH = −logH3O+
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−3
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−3≈ − log(2.5) + 3
Step 4: Continue the calculation:
pH ≈ −0.398 + 3 = 2.602
Step 5: Therefore, the pH of the solution is 2.602 .
Question 20
Question
Calculate the pH of a solution with hydroxide ion concentration of 1.5×10−3
M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Use the given hydroxide ion concentration to find the hydrogen ion
concentration.
[OH−] = 1.5×10−3M
[H+] = Kw
[OH−]=1.0×10−14
1.5×10−3M
Step 3: Calculate the pH of the solution using the hydrogen ion concentra-
tion.
pH =−log[H+]=−log 1.0×10−14
1.5×10−3
12
Step 4: Solve for the pH.
pH =−log 1.0×10−14
1.5×10−3=−log6.67 ×10−12
Step 5: Calculate the final pH value.
pH =−log6.67 ×10−12≈11.18
Therefore, the pH of the solution is approximately 11.18.
Question 21
Question
Calculate the pH and pOH of a solution with a hydronium ion concentration of
3.2×10−5M.
Solution
Step 1: Recall the relationship between pH, hydronium ion concentration, and
pOH:
pH = −log[H3O+]
pOH = −log[OH−]
Step 2: Given that [H3O+]=3.2×10−5M, we can calculate the pH:
pH = −log3.2×10−5
pH = −log(3.2) + log10−5
pH = −(0.505) + (−5)
pH = −5.505
Step 3: Now, we can calculate the pOH using the relationship with pH:
pH + pOH = 14
pOH = 14 −pH
pOH = 14 −(−5.505)
pOH = 19.505
Step 4: Therefore, the pH of the solution is 5.505 and the pOH is 19.505.
Question 22
Question
Calculate the pH of a 0.025 M solution of hydrochloric acid (HCl) at 25◦C.
13
Solution
Step 1: Write the balanced chemical equation for the dissociation of hydrochloric
acid:
HCl (aq) →H+(aq) + Cl−(aq)
Step 2: Determine the initial concentration of H+ions in the solution. Since
hydrochloric acid is a strong acid, it dissociates completely in water. Therefore,
the concentration of H+ions is equal to the initial concentration of HCl, which
is 0.025 M.
Step 3: Use the definition of pH to calculate the pH of the solution. The pH
is defined as −log[H+].
pH = −log(0.025) = −log2.5×10−2=−(−1.60) = 1.60
Therefore, the pH of a 0.025 M solution of hydrochloric acid at 25◦C is 1.60.
Question 23
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 1.5×
10−4M.
Solution
Step 1: Write the equilibrium expression for the auto-ionization of water:
H2O⇌H++ OH−
The equilibrium constant expression for this reaction is:
Kw= [H+][OH−] = 1 ×10−14
Step 2: Given that the hydroxide ion concentration is 1.5×10−4M, we can
substitute this into the equilibrium constant expression to find the concentration
of hydronium ions:
1×10−14 =x×1.5×10−4
x=1×10−14
1.5×10−4
x= 6.67 ×10−11
Step 3: Calculate the pH using the formula:
pH =−logH+
pH =−log6.67 ×10−11
14
pH =−(log(6.67) + log10−11)
pH =−(log(6.67) −11)
pH =−(≈0.8241 −11)
pH ≈10.18
Therefore, the pH of a solution with a hydroxide ion concentration of 1.5×
10−4M is approximately 10.18.
Question 24
Question
Calculate the pH of a solution with a hydronium ion concentration of 3.2×10−5
M.
Solution
Step 1: Recall that the pH of a solution is calculated using the formula:
pH = −log[H+]
Step 2: Given that the hydronium ion concentration is 3.2×10−5M, we can
plug this value into the formula to find the pH:
pH = −log3.2×10−5
Step 3: Use the properties of logarithms to simplify the expression:
pH = −log(3.2) −log10−5
Step 4: Remember that log10−5=−5:
pH = −log(3.2) −(−5)
Step 5: Calculate −log(3.2):
pH = −log(3.2) + 5
Step 6: Using a calculator, find −log(3.2) ≈0.494:
pH ≈0.494 + 5
Step 7: Sum the values to find the pH of the solution:
pH ≈5.494
Thus, the pH of a solution with a hydronium ion concentration of 3.2×10−5
M is approximately 5.494.
15
Question 25
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.2×10−8
M.
Solution
Step 1: Write the expression relating pH and [OH−]. The pH of a solution is
related to the hydroxide ion concentration ([OH−]) by the equation:
pOH = −log[OH−]
We also know that pH + pOH = 14 at 25
°
C.
Step 2: Calculate the pOH. Given that [OH−]=1.2×10−8M, we can
calculate the pOH as follows:
pOH = −log1.2×10−8
pOH = −(log 1.2 + log 10−8)
pOH = −(log 1.2−8)
pOH ≈ −(−0.0792)
pOH ≈0.0792
Step 3: Calculate the pH. Now, we can find the pH using the relationship
pH + pOH = 14:
pH = 14 −pOH
pH = 14 −0.0792
pH ≈13.9208
So, the pH of the solution is approximately 13.92.
Question 26
Question
Calculate the pH of a solution with a hydrogen ion concentration of 2.5×10−10
M.
16
Solution
Step 1: Recall that pH is defined as −log[H+], where [H+] is the concentration
of hydrogen ions in the solution.
Step 2: Substitute the given hydrogen ion concentration into the pH formula:
pH = −log2.5×10−10
Step 3: Calculate the pH using a calculator:
pH ≈ − log2.5×10−10≈ −(log 2.5 + log 10−10)
≈ −(log 2.5−10) ≈ −(0.3979 −10) ≈ −(9.6021) ≈9.60
Step 4: Therefore, the pH of the solution is approximately 9.60.
Question 27
Question
Calculate the pH of a solution with a hydronium ion concentration of 2.5×10−9
M.
Solution
Step 1: Recall that the pH is defined as the negative logarithm of the hydronium
ion concentration:
pH = −log[H3O+]
Step 2: Substitute the given hydronium ion concentration into the formula:
pH = −log2.5×10−9
Step 3: Calculate the pH using a calculator:
pH = −log2.5×10−9
pH = −(−8.60)
pH = 8.60
Step 4: Therefore, the pH of a solution with a hydronium ion concentration
of 2.5×10−9M is 8.60.
Question 28
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−9
M.
17
Solution
Step 1: Recall the relationship between pOH and [OH−]:
pOH =−log[OH−]
Step 2: Substitute the given hydroxide ion concentration to find pOH:
pOH =−log3.2×10−9
pOH =−(−8.50)
pOH = 8.50
Step 3: Use the fact that pH +pOH = 14 to find pH:
pH = 14 −pOH
pH = 14 −8.50
pH = 5.50
Answer: The pH of the solution is 5.50.
Question 29
Question
Calculate the pH of a solution that has a hydroxide ion concentration of 3.0×
10−8M.
Solution
Step 1: Write the expression for the ion product constant of water.
Kw= [H+][OH−] = 1.0×10−14
Step 2: Given the hydroxide ion concentration, calculate the hydrogen ion
concentration.
[OH−] = 3.0×10−8M
[H+] = Kw
[OH−]=1.0×10−14
3.0×10−8= 3.33 ×10−7M
Step 3: Calculate the pH of the solution.
pH =−log[H+] = −log3.33 ×10−7=−(log 3 + log 33 + log 10−7)
pH =−(log 3 + log 33 −7) ≈ −0.48 −1.52 = 2.00
Therefore, the pH of the solution is 2.00.
18
Question 30
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−4
M.
Solution
Step 1: Write the expression for the ion product constant of water. Step 2: Use
the ion product constant of water to find the concentration of hydrogen ions.
Step 3: Calculate the pH of the solution by taking the negative logarithm of the
hydrogen ion concentration.
Step 1: Write the expression for the ion product constant of water. The
ion product constant of water, Kw, is equal to 1.0×10−14 at 25
°
C.
Kw= [H+][OH−]
Step 2: Use the ion product constant of water to find the concentration
of hydrogen ions. Given that the concentration of hydroxide ions is 3.2×10−4
M, we can use the ion product constant of water to find the concentration of
hydrogen ions.
Kw= [H+][OH−]
1.0×10−14 = [H+](3.2×10−4)
[H+] = 1.0×10−14
3.2×10−4
[H+]=3.125 ×10−11 M
Step 3: Calculate the pH of the solution by taking the negative logarithm
of the hydrogen ion concentration.
pH = −log[H+]
pH = −log3.125 ×10−11
pH = −(log(3.125) + log10−11)
pH ≈ −(−0.504 + 11)
pH ≈10.504
Therefore, the pH of the solution is approximately 10.504.
Question 31
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−6
M.
19
Solution
Step 1: Recall that the pH of a solution is calculated using the formula: pH =
−log[H3O+]. Given that the hydronium ion concentration is 1.5×10−6M, we
can substitute this value into the formula to find the pH.
pH =−log1.5×10−6
Step 2: Use the property of logarithms log(ab) = log(a) + log(b) to simplify
the calculation.
pH =−log(1.5) −log10−6
Step 3: Recall the properties of logarithms logab=blog(a) and log(10) =
1.
pH =−(log(1.5) −6)
Step 4: Calculate the logarithm of 1.5 using a calculator.
pH =−(0.1761 −6)
Step 5: Subtract 0.1761 from 6.
pH =−5.8239
Step 6: Therefore, the pH of the solution with a hydronium ion concentration
of 1.5×10−6M is 5.8239 .
Question 32
Question
Calculate the pH of a solution with a hydroxide ion concentration of 3.2×10−5
M.
Solution
Step 1: First, we need to calculate the pOH of the solution using the hydroxide
ion concentration:
pOH =−log[OH−] = −log3.2×10−5
Step 2: Calculate pOH:
pOH =−log3.2×10−5≈ −(−4.495) ≈4.495
Step 3: Since pH +pOH = 14, we can find the pH of the solution:
pH = 14 −pOH = 14 −4.495 ≈9.505
Step 4: Therefore, the pH of the solution is approximately 9.505.
20
Question 33
Question
Calculate the pH of a solution with a hydroxide ion concentration of 1.5×10−4
M.
Solution
Step 1: Write the equation for the ionization of water:
H2O⇌H++ OH−
Step 2: Calculate the concentration of H+ions in the solution using the ion
product of water (Kw= 1.0×10−14 at 25◦C):
[H+]×[OH−] = Kw
[H+] = Kw
[OH−]
[H+] = 1.0×10−14
1.5×10−4
[H+] = 6.67 ×10−11 M
Step 3: Calculate the pH of the solution using the formula:
pH = −log[H+]
pH = −log6.67 ×10−11
pH = −(log(6.67) + log10−11)
pH = −(0.825 + (−11))
pH = −(−10.175)
pH = 10.175
Therefore, the pH of the solution is 10.175.
Question 34
Question
Calculate the pH of a solution with a hydronium ion concentration of 1.5×10−4
M.
21
Solution
Step 1: Recall that pH is defined as −log[H3O+]. Therefore, we need to find
the negative logarithm of the hydronium ion concentration.
Step 2: Substitute the given hydronium ion concentration into the formula
for pH:
pH = −log1.5×10−4
Step 3: Calculate the pH:
pH = −log1.5×10−4=−log(1.5)−log10−4=−log(1.5)−(−4) = −log(1.5)+4
Step 4: Use a calculator to find the value of −log(1.5), which is approxi-
mately 0.1761.
Step 5: Finally, calculate the pH:
pH = 0.1761 + 4 = 4.1761
Therefore, the pH of the solution is approximately 4.1761.
Question 35
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 in water:
HCl(aq)→H+(aq) + Cl−(aq)
Step 2: Since HCl is a strong acid, it dissociates completely in water. There-
fore, the concentration of H+ions is equal to the initial concentration of HCl,
which is 0.025 M.
Step 3: Calculate the pH using the formula for pH:
pH = −log[H+]
Step 4: Substitute the concentration of H+ions into the formula:
pH = −log(0.025)
Step 5: Calculate the pH:
pH = −log(0.025) = −log2.5×10−2=−log(2.5) + log10−2= 2 −2=0
Therefore, the pH of a 0.025 M solution of hydrochloric acid is 0.
22
