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Chapter 18: Problem 79

Calculate the emf of the following concentration cell at \(25^{\circ} \mathrm{C}\) : $$\mathrm{Cu}(s)\left|\mathrm{Cu}^{2+}(0.080 M) \| \mathrm{Cu}^{2+}(1.2 M)\right| \mathrm{Cu}(s)$$

Short Answer

Expert verified
The electromotive force (emf) of the cell is \(0.0295 volts\).

Step by step solution

01

Identify the Known Quantities

From the problem, the concentrations of \(Cu^{2+}\) ions on the left-hand side (0.80 M) and on the right-hand side (1.2 M) of the cell are known. The temperature is given as \(25^{\circ}C\), which is equivalent to \(298 K\) in standard SI units. Also, the values for the gas constant \(R\) and the Faraday constant \(F\) are known and are equal to \(8.314 JK^{-1}mol^{-1}\) and \(96485 Cmol^{-1}\) respectively.
02

Calculate Q, the Reaction Quotient

The quotient \(Q\) is given by the ratio of the concentration of \(Cu^{2+}\) ions on the right-hand side to the concentration of \(Cu^{2+}\) ions on the left-hand side. So, \(Q = [Cu^{2+} right-hand side]/[Cu^{2+}left-hand side] = 1.2/0.080 = 15.\)
03

Plug the Values in the Nernst Equation

Substitute the known quantities into the Nernst Equation. Note that for a concentration cell, \(E° = 0\), \(n = 2\), and using the natural logarithm ln,\(E = E° – (RT/nF) lnQ\) = 0 - \((8.314 JK^{-1}mol^{-1} * 298K) / (2 * 96485 Cmol^{-1})\) * ln(15) = -0.0295 volts
04

Convert the emf to Normal Conditions

The emf calculated in step 3 is negative because the concentration of \(Cu^{2+}\) ions is greater on the right-hand side of the cell, but emf is usually specified as a positive number. Therefore, the emf of the cell is \(0.0295 volts\).

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Most popular questions from this chapter

A quantity of \(0.300 \mathrm{~g}\) of copper was deposited from a CuSO solution by passing a current of 3.00 A through the solution for 304 s. Calculate the value of the Faraday constant.

What is the difference between a galvanic cell (such as a Daniell cell) and an electrolytic cell?

A constant electric current flows for \(3.75 \mathrm{~h}\) through two electrolytic cells connected in series. One contains a solution of \(\mathrm{AgNO}_{3}\) and the second a solution of \(\mathrm{CuCl}_{2}\). During this time \(2.00 \mathrm{~g}\) of silver are deposited in the first cell. (a) How many grams of copper are deposited in the second cell? (b) What is the current flowing, in amperes?

The \(E^{\circ}\) value of one cell reaction is positive and that of another cell reaction is negative. Which cell reaction will proceed toward the formation of more products at equilibrium?

In a certain electrolysis experiment, \(1.44 \mathrm{~g}\) of \(\mathrm{Ag}\) were deposited in one cell (containing an aqueous AgNO solution), while \(0.120 \mathrm{~g}\) of an unknown metal X was deposited in another cell (containing an aqueous \(\mathrm{XCl}_{3}\) solution in series with the \(\mathrm{AgNO}_{3}\) cell. Calculate the molar mass of X.
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