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Question:

If the Eocell for a given reaction has a negative value, then which of the following gives the correct relationships for the values of ΔGo and Keq?

ΔGo>0;Keq>1

ΔGo<0;Keq>1

ΔGo<0;Keq<1

ΔGo>0;Keq<1

Solution:

We have Eocell negative. The relationship between the standard cell potential (Eocell), the standard Gibbs free energy change (ΔGo), and the equilibrium constant (Keq) is given by the following equations:

ΔGo = -nFEocell

ΔGo = -RTlnKeq

where:

  • n is the number of moles of electrons transferred in the balanced redox reaction.
  • F is Faraday's constant (96485 C/mol).
  • R is the ideal gas constant (8.314 J/mol·K).
  • T is the temperature in Kelvin.

Since Eocell is negative, ΔGo = -nFEocell will be positive (a negative multiplied by a negative is positive). A positive ΔGo indicates a non-spontaneous reaction.

From ΔGo = -RTlnKeq, a positive ΔGo implies that -RTlnKeq is positive. Since R and T are always positive, lnKeq must be negative. A negative natural logarithm means that Keq < 1.

Therefore, the correct relationship is ΔGo > 0; Keq < 1.