The pH in the anode compartment is -1.459.
Given the cell:
Pt(s) | H₂(1.00 atm) | H+(aq) || Ag⁺(0.100M) | Ag(s)
And the following information:
E_cell = 0.945 V
P_H2 = 1.00 atm
M_Ag = 0.100 M
The pH in the anode compartment can be calculated using the Nernst equation and the following steps:
Calculate the standard cell potential (E°).
Calculate the reaction quotient (Q).
Calculate the pH.
The Nernst equation is:
E = E° - (RT ln(Q)) / (nF)
Where:
E is the cell potential (V)
E° is the standard cell potential (V)
R is the gas constant (J/mol·K)
T is the temperature (K)
ln is the natural logarithm
Q is the reaction quotient
n is the number of electrons transferred
F is Faraday's constant (C/mol)
The reaction quotient is:
Q = [Ag⁺] / (P_H2)^(1/2)
The number of electrons transferred is 1.
Plugging in the values, we get:
0.945 = 0.7996 - (8.314 * 298 * ln(Q)) / (96485 * 1)
Solving for Q, we get:
Q = 1.729 x 10^(-3)
The pH is:
pH = -log10(Q * M_Ag / P_H2^(1/2))
Plugging in the values, we get:
pH = -1.459
Therefore, the pH in the anode compartment is -1.459.