(a) The measured pH of a 0.200 M HBr solution at 25°C is 0.806. Calculate the activity coefficient for H .
(b) The measured pH of a 0.200 M HNO3 solution at the same temperature is 0.822. Calculate the activity coefficient for H in this solution.
(a) The activity coefficient for H in the 0.200 M HBr solution at 25°C can be calculated using the following equation:
γH = 10^(-pH) / [H+] = 10^(-0.806) / 0.200 = 0.25
(b) The activity coefficient for H in the 0.200 M HNO3 solution at 25°C can be calculated using the following equation:
γH = 10^(-pH) / [H+] = 10^(-0.822) / 0.200 = 0.22
To calculate the activity coefficient for H in each solution, we can use the equation:
pH = -log10[H+]
(a) For the HBr solution:
Given:
pH = 0.806
[H+] = 10^(-pH)
Calculating:
[H+] = 10^(-0.806)
[H+] = 0.122 M
Now, we can calculate the activity coefficient for H. The activity coefficient (γ) can be related to the concentration using the equation:
[H+] = γ × [H] × [(molality) / (standard-state molality)]
The molality (m) can be approximated as the concentration (M) due to dilute solutions.
Plugging in the knowns:
0.122 M = γ × 0.200 M × (1 / 0.200 M)
Simplifying:
0.122 = γ × 1
Therefore, the activity coefficient for H in the HBr solution is 0.122.
(b) For the HNO3 solution:
Given:
pH = 0.822
[H+] = 10^(-pH)
Calculating:
[H+] = 10^(-0.822)
[H+] = 0.133 M
Now, we can calculate the activity coefficient for H.
Plugging in the knowns:
0.133 M = γ × 0.200 M × (1 / 0.200 M)
Simplifying:
0.133 = γ × 1
Therefore, the activity coefficient for H in the HNO3 solution is 0.133.
To calculate the activity coefficient for H in both solutions, we can use the equation for the pH of a strong acid solution, which relates the concentration of H+ ions to the activity coefficient and the activity of H+ ions:
pH = -log[H+] = -log (γ * [H])
Where:
- [H+] is the concentration of H+ ions
- γ is the activity coefficient for H
- [H] is the activity of H+ ions, which is equal to the concentration, [H+]
Rearranging the equation, we can solve for the activity coefficient:
γ = 10^(-pH) / [H]
Now let's calculate the activity coefficient for H in both solutions.
For part (a):
Given:
- pH = 0.806
- [H] = 0.200 M
Plug in the values:
γ = 10^(-0.806) / 0.200
Use a calculator to evaluate this expression:
γ ≈ 0.129
Therefore, the activity coefficient for H in the 0.200 M HBr solution is approximately 0.129.
For part (b):
Given:
- pH = 0.822
- [H] = 0.200 M
Using the same equation:
γ = 10^(-0.822) / 0.200
Again, use a calculator to evaluate this expression:
γ ≈ 0.121
Therefore, the activity coefficient for H in the 0.200 M HNO3 solution is approximately 0.121.