Calculate the Equilibrium Constant, using the Standard Cell Voltage The graphing calculator can run a program that calculates the equilibrium constant for an electrochemical cell using an equation called the Nernst equation, given the standard potential and the number of electrons transferred. Given that the standard potential is 2.041 V and that two electrons are transferred, you will calculate the equilibrium constant. The program will be used to make the calculations. Go to Appendix c. If you are using a TI-83 Plus, you can download the program NERNST and data and run the application as directed. If you are using another calculator, your teacher will provide you with key- strokes and data sets to use. After you have run the program, answer the following questions. \begin{equation} \begin{array}{l}{\text { a. What is the equilibrium constant when }} \\\ {\text { the standard potential is } 0.099 ?} \\ {\text { b. What is the equilibrium constant when }} \\ {\text { the standard potential is } 1.125 ?} \\\ {\text { c. What is the equilibrium constant when }} \\ {\text { the standard potential is } 2.500 ?}\end{array} \end{equation}

Step by step solution

01

Understand the Nernst Equation

The Nernst Equation is: \\[ E = E_0 - \frac{RT}{nF} lnQ \\] where: \\ E is the cell potential (or voltage) \\ E_0 is the standard cell potential (or standard voltage)\\ R is the universal gas constant (8.314 J/mol·K for this problem) \\ T is the absolute temperature in Kelvin (298.15 K if we assume the temperature is 25°C) \\ n is the number of electrons transferred (given as 2 in this case) \\ F is the Faraday's Constant (96485 C/mol is the commonly accepted value) and \\ lnQ refers to the natural logarithm of the reaction quotient Q.

02

Rearrange the Equation

To find the equilibrium constant \( K \), we need to know that at equilibrium, \( E = 0 \) and \( Q = K \). Therefore, the Nernst equation becomes: \\[0 = E_0 - \frac{RT}{nF} lnK \\] Rearranging this to solve for \( K \) gives: \\[K = e^\frac{nFE_0}{RT}\\]

03

Substitute and Calculate for each value

Here, substitute the known or given values into the equation: \( n = 2 \), \( R = 8.314 J/mol·K \), \( T = 298.15 K \), and \( F = 96485 C/mol \). For each of the given standard potentials, \( E_0 \), substitute it into the equation to find the corresponding equilibrium constant \( K \). (a) For \( E_0 = 0.099 V \) \\[K = e^\frac{(2)(96485)(0.099)}{(8.314)(298.15)}\\] (b) For \( E_0 = 1.125 V \) \\[K = e^\frac{(2)(96485)(1.125)}{(8.314)(298.15)}\\] (c) For \( E_0 = 2.500 V \) \\[K = e^\frac{(2)(96485)(2.500)}{(8.314)(298.15)}\\]

04

Calculate the Equilibrium Constants

Calculate the values for each \( K \). Round off your answers to a reasonable number of significant figures.

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