The mean activity coefficients of HBrin 5.0 and 20.0 mmol kg
–1 are 0.930 and 0.879,
respectively. Consider a hydrogen electrode in HBr(aq) solution at 25 °C operating at
1.15 atm.
Calculate the change in the electrode potential when the molality of the acid solution
is changed from 5.0 and 20.0 mmol kg
–1
.
To calculate the change in electrode potential when the molality of the acid solution is changed from 5.0 to 20.0 mmol kg⁻¹, we need to use the Nernst equation.
The Nernst equation is given by:
E = Eº - (RT / nF) * ln(Q)
Where:
E = electrode potential
Eº = standard electrode potential
R = gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
n = number of moles of electrons transferred in the balanced redox equation
F = Faraday's constant (96,485 C/mol)
ln = natural logarithm
Q = reaction quotient
In this case, we are given the mean activity coefficients of HBr in the two different molalities.
The formula to calculate mean activity coefficient is given by:
γ = φ / X
Where:
γ = mean activity coefficient
φ = fugacity coefficient
X = mole fraction
Using the given data, we can find the activity of HBr in the two different molalities.
For 5.0 mmol kg⁻¹:
γ₁ = 0.930
For 20.0 mmol kg⁻¹:
γ₂ = 0.879
Now, let's assume the balanced redox equation for the hydrogen electrode reaction in HBr solution is:
H₂(g) → 2H⁺(aq) + 2e⁻
Since the reaction involves the transfer of 2 moles of electrons, we can substitute the values into the Nernst equation:
E = Eº - (RT / (2F)) * ln(Q)
The reaction quotient Q can be written as:
Q = [H⁺]² / P(H₂)
Where [H⁺] is the concentration of H⁺ ions, and P(H₂) is the partial pressure of H₂ gas.
For 5.0 mmol kg⁻¹:
[H⁺]₁ = 5.0 mmol kg⁻¹ * γ₁
P(H₂) = 1.15 atm
For 20.0 mmol kg⁻¹:
[H⁺]₂ = 20.0 mmol kg⁻¹ * γ₂
P(H₂) = 1.15 atm
Now, substitute the values into the Nernst equation and calculate the change in electrode potential.