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Chapter 20: Problem 7

Consider a redox reaction for which \(E^{\circ}\) is a negative number. (a) What is the sign of \(\Delta G^{\circ}\) for the reaction? (b) Will the equilibrium constant for the reaction be larger or smaller than \(1 ?\) (c) Can an electrochemical cell based on this reaction accomplish work on its surroundings? [Section 20.5\(]\)

Short Answer

Expert verified
(a) The sign of \(\Delta G^{\circ}\) is positive since \(E^{\circ}\) is negative. (b) The equilibrium constant, K, is smaller than 1. (c) An electrochemical cell based on this reaction cannot accomplish work on its surroundings.

Step by step solution

01

Calculating the sign of ΔG°

Using the equation: \(\Delta G^\circ = -nFE^\circ\) Since \(E^\circ\) is a negative number, and both n (number of moles of electrons transferred) and F (Faraday's constant) are positive numbers, the product of -nF and the negative \(E^\circ\) will be a positive number. Thus, the sign of \(\Delta G^\circ\) is positive.
02

Determining the equilibrium constant comparison to 1

Next, we will use the equation: \(\Delta G^\circ = -RT\ln K\) Since \(\Delta G^\circ\) is positive, then the \(\ln K\) must be a negative number, because R (Ideal Gas Constant) and T (Temperature in Kelvin) are both positive numbers. Recall that the natural logarithm of a number between 0 and 1 is negative. Hence, the equilibrium constant K is smaller than 1.
03

Evaluating if the electrochemical cell can perform work on its surroundings

In an electrochemical cell, if the cell potential, \(E^\circ\), is negative, it indicates the reaction occurring is a non-spontaneous process. A non-spontaneous redox reaction will not be able to accomplish work on its surroundings under standard conditions. Therefore, an electrochemical cell based on this reaction cannot accomplish work on its surroundings.

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