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Chapter 19: Problem 31

Calculate the standard potential of the cell consisting of the \(\mathrm{Zn} / \mathrm{Zn}^{2+}\) half-cell and the SHE. What will the emf of the cell be if \(\left[\mathrm{Zn}^{2+}\right]=0.45 \mathrm{M}, \mathrm{P}_{\mathrm{H}_{2}}=2.0 \mathrm{~atm}\), and \(\left[\mathrm{H}^{+}\right]=1.8 \mathrm{M} ?\)

Short Answer

Expert verified
So, the standard potential of the cell is \(0.76 V\) while the emf of the cell under the given conditions is \(0.705 V\).

Step by step solution

01

Calculate the Standard Cell Potential

Firstly, locate the standard reduction potential for the Zinc electrode. It's given that Zn/Zn2+ half-cell is part of the galvanic cell. The standard reduction potential for Zn/Zn2+ half-cell is -0.76 V and for SHE (Standard Hydrogen Electrode which has Hydrogen gas and H+ ions in solution) it's 0 V. \n\nThe standard potential of the cell E°cell can be calculated by the equation: \n\nE°cell = E°cathode - E°anode\n\nZn2+ has a negative potential so Zinc will be the anode (site of oxidation) and Hydrogen electrode will be the cathode (site of reduction).\n\nSo, E°cell = E°cathode - E°anode = 0 - (-0.76 V) = 0.76 V
02

Apply Nernst Equation

The Nernst equation, which defines the electromotive force (emf) of a cell under non-standard conditions, will be used for the second part of the problem. It's given as follows:\n\nEcell = E°cell - (RT/nF) lnQ\n\nIn the above equation, R is the gas constant (8.314 J/K·mol), T is the temperature in Kelvin (Assume room temperature 298 K), n is the number of electrons shared during the reaction (for both Zn and H, n=2), F is Faraday's constant (96485 C/mol), and Q is the reaction quotient.\n\nFor this cell, the formula for Q is [H+]^2 / [Zn2+].\n\nNow, we can put all the values into the Nernst equation to calculate emf Ecell.
03

Calculate EMF of the Cell

For the given values of: \n\n[H+] =1.8M,\n[Zn2+] =0.45M, and\nPH2 = 2.0 atm,\n\nwe can calculate Q as follows:\n\nQ = (1.8)^2 / 0.45 = 7.2.\n\nNow introducing all these values into the Nernst equation and simplifying, we get:\n\nEcell = E°cell - (RT/nF) lnQ\n= 0.76 V - ((8.314 J/K·mol * 298 K) / (2 * 96485 C/mol) * ln (7.2))\n= 0.76 V - 0.061 V * log10(7.2)\n= 0.76 V - 0.055 V\n= 0.705 V

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Most popular questions from this chapter

Steel hardware, including nuts and bolts, is often coated with a thin plating of cadmium. Explain the function of the cadmium layer.

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Write the Nernst equation for the following processes at some temperature \(T\) : (a) \(\mathrm{Mg}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\operatorname{Sn}(s)\) (b) \(2 \mathrm{Cr}(s)+3 \mathrm{~Pb}^{2+}(a q) \longrightarrow 2 \mathrm{Cr}^{3+}(a q)+3 \mathrm{~Pb}(s)\)

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