AdvancedChemistryHigh School (11–12)Electrochemistry › Galvanic Cells, Electrode Potential and the Nernst EquationNumericalJEE Advanced Olympiad

A cell is built from a hydrogen electrode and a silver chloride electrode, both dipping into the…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A cell is built from a hydrogen electrode and a silver chloride electrode, both dipping into the same hydrochloric acid:

\displaystyle \text{Pt}\,|\,\text{H}_2(g,\ 1\ \text{bar})\,|\,\text{HCl}(aq)\,|\,\text{AgCl}(s)\,|\,\text{Ag}(s)

The cell reaction is $\text{H}_2(g) + 2\text{AgCl}(s) \rightarrow 2\text{Ag}(s) + 2\text{H}^+(aq) + 2\text{Cl}^-(aq)$ . A chemist measures the standard emf at several temperatures, and the figure shows that the points lie on a straight line. Two marked points are $0.2320\ \text{V}$ at $283\ \text{K}$ and $0.2126\ \text{V}$ at $313\ \text{K}$ . Over this small range, take $\Delta_r H^\circ$ and $\Delta_r S^\circ$ as constant, so that $\Delta_r G^\circ = \Delta_r H^\circ - T\Delta_r S^\circ$ at each temperature, and $\Delta_r G^\circ = -nFE^\circ$ . Take $F = 96487\ \text{C mol}^{-1}$ and $\dfrac{2.303RT}{F} = 0.059\ \text{V}$ at $298\ \text{K}$ . Treat the acid as an ideal solution. This cell is a favourite for such work, because both electrodes dip into the same acid: there is no salt bridge and no liquid junction to upset the reading. Its emf is measured with a potentiometer, which draws no current.

A graph of the standard emf of the cell, in volts, against temperature, in kelvin, from 280 K to 316 K. Measured points lie on a straight line that falls gently as the temperature rises. Two points are labelled: 0.2320 V at 283 K and 0.2126 V at 313 K.

What is $E^\circ$ at $298\ \text{K}$ ?
What is $\Delta_r G^\circ$ at $298\ \text{K}$ ?
What is $\Delta_r S^\circ$ ?
What is $\Delta_r H^\circ$ ?
The cell works reversibly at $298\ \text{K}$ . How much heat does it give out to the surroundings for each mole of hydrogen used?
What is the emf at $298\ \text{K}$ when the acid is $0.0100\ \text{mol L}^{-1}$ HCl?

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Plan. The slope of the line gives $\Delta_r S^\circ$ , the emf gives $\Delta_r G^\circ$ , and the two together give $\Delta_r H^\circ$ .

(a) Slope and $E^\circ$ . Slope $= \dfrac{-0.0194\ \text{V}}{30\ \text{K}} = -6.467 \times 10^{-4}\ \text{V K}^{-1}$ (about $-0.647\ \text{mV}$ per kelvin). At $298\ \text{K}$ , $E^\circ = 0.2320 + (-6.467 \times 10^{-4})(298 - 283)\ \text{V} = 0.2223\ \text{V}$ .

(b) Gibbs energy. $\Delta_r G^\circ = -2 \times 96487 \times 0.2223\ \text{J mol}^{-1} = -42.9\ \text{kJ mol}^{-1}$ .

(c) Entropy. $\Delta_r S^\circ = nF \times \text{slope} = 2 \times 96487 \times (-6.467 \times 10^{-4})\ \text{J K}^{-1}\ \text{mol}^{-1} = -124.8\ \text{J K}^{-1}\ \text{mol}^{-1}$ . It is negative because a gas is used up.

(d) Enthalpy. $\Delta_r H^\circ = \Delta_r G^\circ + T\Delta_r S^\circ = -42.9 + 298 \times (-124.8) \times 10^{-3}\ \text{kJ mol}^{-1} = -80.1\ \text{kJ mol}^{-1}$ .

(e) Heat. $q = T\Delta_r S^\circ = -37.2\ \text{kJ}$ per mole of hydrogen, so the cell gives out $37.2\ \text{kJ}$ of heat. Of the $80.1\ \text{kJ}$ that the reaction releases, $42.9\ \text{kJ}$ leaves as electrical work and only the rest as heat.

(f) In $0.0100\ \text{mol L}^{-1}$ HCl. $Q = (0.0100)^2(0.0100)^2 = 10^{-8}$ , so $E = 0.2223 - \dfrac{0.059}{2}\log 10^{-8}\ \text{V} = (0.2223 + 0.236)\ \text{V} = 0.458\ \text{V}$ .

Watch out. Writing $Q$ as $[\text{H}^+][\text{Cl}^-]$ , as if one electron were moving, gives $0.340\ \text{V}$ in (f). And the heat in (e) is not $\Delta_r H^\circ$ : that would be the heat only if the reaction ran with no electrical work, as in a beaker.

← All Problems

← Silver chloride is far too insoluble for its solubility to be weighed easily, but a cell measures…A 25.0 mL sample contains both hydrochloric acid and acetic acid… →

More onElectrochemistry › Galvanic Cells, Electrode Potential and the Nernst Equation

Discussion (0)

Loading…