Textbook Question
For the following reactions we have not seen yet, which side, if either, would be favored by increasing the temperature?
(d)
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6. Thermodynamics and Kinetics
Gibbs Free Energy
3:19 minutesProblem 7b
Textbook Question
For the following equilibrium processes and the corresponding ∆G° , indicate whether you expect the equilibrium constant to be greater than, equal to, or less than 1. Justify your expectation in words.
(b) 
Verified step by step guidance1
Step 1: Understand the relationship between Gibbs free energy change (∆G°) and the equilibrium constant (K). The equation that connects these two is ΔG° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.
Step 2: Analyze the given ∆G° value. In this case, ∆G° = 0.0 kcal/mol. This indicates that there is no free energy difference between the reactants and products.
Step 3: Interpret the equilibrium constant (K) based on ∆G°. When ∆G° = 0, the equation ΔG° = -RT ln(K) simplifies to ln(K) = 0, which means K = 1.
Step 4: Consider the chemical structures provided. The two structures are conformational isomers (chair conformations of cyclohexane with a methyl group in axial and equatorial positions). Since ∆G° = 0, both conformations are equally stable, and the equilibrium constant reflects this balance.
Step 5: Conclude that the equilibrium constant is equal to 1 because the free energy difference is zero, indicating that the forward and reverse reactions occur at the same rate under standard conditions.
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3mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Gibbs Free Energy (∆G)
Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A negative ∆G indicates a spontaneous process, while a positive ∆G suggests non-spontaneity. When ∆G is zero, as in this case, the system is at equilibrium, meaning the forward and reverse reactions occur at the same rate.
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Equilibrium Constant (K)
The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction. If K > 1, products are favored; if K < 1, reactants are favored. At equilibrium, when ∆G = 0, K is equal to 1, indicating that the concentrations of reactants and products are equal.
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Relationship between ∆G and K
The relationship between Gibbs Free Energy (∆G) and the equilibrium constant (K) is described by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. This equation shows that if ∆G° is zero, then ln(K) is also zero, leading to K = 1. This indicates that at equilibrium, the concentrations of reactants and products are equal, reflecting a balance in the reaction.
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