Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics

Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition

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Mullins 1st Edition

Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics

Problema 7a

Capitolo 4, Problema 7a

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.
(a)

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Understand the relationship between the Gibbs free energy change (∆G°) and the equilibrium constant (K) using the equation:

∆G° = -RT ln(K)

, where R is the gas constant and T is the temperature in Kelvin.

Analyze the sign of ∆G°: If ∆G° is negative, the reaction is spontaneous in the forward direction, and K will be greater than 1. If ∆G° is positive, the reaction is non-spontaneous in the forward direction, and K will be less than 1. If ∆G° is zero, the system is at equilibrium, and K will equal 1.

For each equilibrium process provided, determine the sign of ∆G° (positive, negative, or zero) based on the given value or description.

Use the relationship between ∆G° and K to predict whether the equilibrium constant is greater than, equal to, or less than 1 for each process.

Justify your prediction in words by explaining how the sign of ∆G° influences the equilibrium constant, referencing the thermodynamic principles outlined in step 2.

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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 that a reaction is spontaneous and favors the formation of products, while a positive ∆G° suggests that the reaction is non-spontaneous and favors the reactants.

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Breaking down the different terms of the Gibbs Free Energy equation.

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 at a specific temperature. If K > 1, products are favored at equilibrium; if K < 1, reactants are favored. The relationship between K and ∆G° is given by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.

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The relationship between equilibrium constant and pKa.

Relationship between ∆G° and K

The relationship between Gibbs Free Energy (∆G°) and the equilibrium constant (K) is crucial for predicting the direction of a reaction. If ∆G° is negative, K will be greater than 1, indicating a product-favored reaction. Conversely, if ∆G° is positive, K will be less than 1, indicating a reactant-favored reaction. This relationship allows chemists to assess the favorability of reactions based on thermodynamic data.

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Same atoms, same connectivity, 1 chiral center.

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Concetti chiave

Gibbs Free Energy (∆G°)

Equilibrium Constant (K)

Relationship between ∆G° and K

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.
(a)