A galvanic cell is assembled at 298 K using the half-reactions listed below

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

A galvanic cell is assembled at 298 K using the half-reactions listed below. All aqueous species behave ideally.

\mathrm{Cl_2(g)}+2e^-\longrightarrow 2\mathrm{Cl^-}(aq)\;(E^{\circ}=+1.36\,\text{V})

2\mathrm{H^+}(aq)+2e^-\longrightarrow \mathrm{H_2(g)}\;(E^{\circ}=0.00\,\text{V})

The left-hand electrode involves hydrogen gas and aqueous acid, and the right-hand electrode involves chlorine gas and chloride ion. • Cell M

P_{\mathrm{H_2}}=1.00\,\text{atm}

[\mathrm{H^+}]=0.010\,\text{M}

P_{\mathrm{Cl_2}}=1.00\,\text{atm}

[\mathrm{Cl^-}]=1.0\,\text{M}

• Cell N

P_{\mathrm{H_2}}=0.20\,\text{atm}

[\mathrm{H^+}]=0.010\,\text{M}

P_{\mathrm{Cl_2}}=2.0\,\text{atm}

[\mathrm{Cl^-}]=1.0\,\text{M}

Assume that gases behave ideally and that temperature remains at 298 K for both cells. (a) Write the balanced overall cell reaction that occurs spontaneously under standard conditions using the given half-reactions. (b) For Cell M, calculate the reaction quotient

Q_{\text{M}}

using the stated pressures and concentrations. (c) Determine the cell potential

E_{\text{M}}

for Cell M at 298 K. Report the answer in volts to three significant figures. (d) Repeat parts (b) and (c) for Cell N to obtain

Q_{\text{N}}

and

E_{\text{N}}

. (e) Identify which cell produces the larger magnitude potential. Explain how the relative sizes of

Q_{\text{M}}

and

Q_{\text{N}}

account for the difference, and state the spontaneous direction of the cell reaction in Cell N.

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