Electrochemical Cell Potentials and Nernst Equation

Vocabulary terms and definitions covering the half-reactions, Nernst equation calculations, and chemical behavior of the provided electrochemical cell.

Electrochemical Cell Setup

A galvanic cell apparatus consisting of compartment A ($1\,\text{L}$ of $0.05\,\text{M}\ H_2SO_4$ with a $\text{Pt}$ electrode and $1\,\text{atm}\ H_2$ gas) and compartment B ($1\,\text{L}$ of $0.01\,\text{M}\ AgNO_3$ with a $\text{Pd}$ electrode) connected via a salt bridge and voltmeter.

Anode Half-Reaction (Compartment A)

The oxidation process occurring at the $\text{Pt}$ electrode: $H_2(g) \rightarrow 2H^+(aq) + 2e^-$, with a standard reduction potential of $E^\circ = 0.00\,\text{V}$.

Cathode Half-Reaction (Compartment B)

The reduction process occurring in compartment B: $Ag^+(aq) + e^- \rightarrow Ag(s)$, with a standard reduction potential of $E^\circ = +0.80\,\text{V}$.

Overall Cell Reaction

The complete balanced redox reaction: $H_2(g) + 2Ag^+(aq) \rightarrow 2H^+(aq) + 2Ag(s)$, transferring $n = 2$ moles of electrons.

Standard Cell Potential ($E^\circ_{\text{cell}}$)

The standard electromotive force calculated as $E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = +0.80\,\text{V} - 0.00\,\text{V} = +0.80\,\text{V}$.

Reaction Quotient ($Q$)

The ratio of concentrations and partial pressures defined by $Q = \frac{[H^+]^2}{[Ag^+]^2 \cdot P_{H_2}} = \frac{(0.10\,\text{M})^2}{(0.01\,\text{M})^2 \cdot 1\,\text{atm}} = 10^2$.

Nernst Equation (Specified Form)

The non-standard potential formula given as $E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.06}{n} \log(Q)$.

Initial Cell Potential ($E_{\text{cell}}$)

The non-standard voltage of the cell under the specified initial conditions, calculated as $0.80\,\text{V} - \frac{0.06}{2} \log(10^2) = 0.74\,\text{V}$.

Compartment A pH Trend

The pH of the solution in compartment A decreases over time because the continuous oxidation of $H_2(g)$ generates $H^+(aq)$ ions, increasing their concentration.

Effect of Adding $Pd(NO_3)_2$ to Compartment B

Dissolving $Pd(NO_3)_2$ introduces $Pd^{2+}(aq)$, which has a higher reduction potential ($E^\circ = +0.95\,\text{V}$) than $Ag^+$ ($E^\circ = +0.80\,\text{V}$), altering the reduction half-reaction and changing the initial cell potential.