Question #44789

Consider the following electrochemical cell with transference operating at $298\text{ K}$:

$Pt | H_2 (1\text{ bar}) | \text{Sol L} \,\vdots\, \text{Sol R} | H_2 (1\text{ bar}) | Pt$

$\text{Sol L}$ is an ideal dilute aqueous buffer containing $0.1\text{ M } RNH_2$ and $0.1\text{ M } RNH_3^+Cl^-$. Assume the activity coefficients for all species in $\text{Sol L}$ are unity ($\gamma = 1$).

$\text{Sol R}$ is a concentrated aqueous buffer containing $1.0\text{ M } RNH_2$ and $1.0\text{ M } RNH_3^+Cl^-$. Due to the high concentration of the organic amine, the dielectric constant of the medium is significantly lowered, altering the solvation dynamics. The activity coefficients in $\text{Sol R}$ are determined to be: $\gamma_{RNH_3^+} = 0.5$, $\gamma_{Cl^-} = 0.5$, and $\gamma_{RNH_2} = 2.0$ (due to the salting-out effect).

The thermodynamic acid dissociation constant of $RNH_3^+$ is $K_a = 10^{-9}$. The transport numbers of the ions across the liquid junction are $t_{Cl^-} = 0.75$ and $t_{RNH_3^+} = 0.25$.

Given: $\frac{2.303 RT}{F} = 0.06\text{ V}$, $\log 2 = 0.30$, and $\log 5 = 0.70$.

Calculate the total electromotive force ($E_{cell}$) of the cell.