A cell has a standard cell potential of +0.177 V at 298 K. What is the value of the equilibrium constant for the reaction (b) if n = 2? (c) if n = 3?
Ch.20 - Electrochemistry
Chapter 20, Problem 61
(a) In the Nernst equation, what is the numerical value of the reaction quotient, Q, under standard conditions? (b) Can the Nernst equation be used at temperatures other than room temperature?

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Step 1: Understand the Nernst equation, which is given by: E = E^0 - (RT/nF) * ln(Q), where E is the cell potential, E^0 is the standard cell potential, R is the universal gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.
Step 2: For part (a), recognize that under standard conditions, the reaction quotient Q is equal to 1. This is because standard conditions imply that all reactants and products are in their standard states, typically 1 M concentration for solutions or 1 atm pressure for gases.
Step 3: Substitute Q = 1 into the Nernst equation. Since ln(1) = 0, the term (RT/nF) * ln(Q) becomes zero, simplifying the equation to E = E^0 under standard conditions.
Step 4: For part (b), consider the applicability of the Nernst equation at different temperatures. The Nernst equation can indeed be used at temperatures other than room temperature, but the temperature T in the equation must be adjusted to reflect the actual temperature in Kelvin.
Step 5: To use the Nernst equation at a temperature other than room temperature, ensure that the value of T is correctly converted to Kelvin by adding 273.15 to the Celsius temperature, and adjust the equation accordingly.
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At 298 K a cell reaction has a standard cell potential of +0.17 V. The equilibrium constant for the reaction is 5.5 × 105. What is the value of n for the reaction?
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