Ch. 5 - Alkenes: Structure, Nomenclature, and an Introduction to Reactivity • Thermodynamics and Kinetics

Bruice8th EditionOrganic ChemistryISBN: 9780135213711당신이 사용하는 게 아니라요?교과서 변경

Bruice 8th Edition

Ch. 5 - Alkenes: Structure, Nomenclature, and an Introduction to Reactivity • Thermodynamics and Kinetics

문제 50c,d

5장, 문제 50c,d

In a reaction in which reactant A is in equilibrium with product B at 25 °C, what relative amounts of A and B are present at equilibrium if ∆G° at 25 °C is
c. -2.72 kcal/mol?
d. -0.65 kcal/mol?

검증된 단계별 안내

Step 1: Understand the relationship between Gibbs free energy change (∆G°) and the equilibrium constant (K). The formula to use is:

∆G ° = - R T ln K

, where R is the gas constant (1.987 cal/(mol·K)), T is the temperature in Kelvin, and K is the equilibrium constant.

Step 2: Convert the temperature from Celsius to Kelvin. Since the temperature is given as 25 °C, add 273 to convert it to Kelvin:

T = 25 + 273 = 298 K

Step 3: Rearrange the formula to solve for K (the equilibrium constant):

K = exp (- ∆G ° / R T)

. Substitute the values for R, T, and ∆G° into the equation for each case.

Step 4: For case c (-2.72 kcal/mol), convert ∆G° from kcal to cal (1 kcal = 1000 cal):

∆G ° = - 2.72 \times 1000 = - 2720 cal/mol

. Substitute this value into the formula for K.

Step 5: For case d (-0.65 kcal/mol), similarly convert ∆G° from kcal to cal:

∆G ° = - 0.65 \times 1000 = - 650 cal/mol

. Substitute this value into the formula for K. Once K is calculated for both cases, interpret the relative amounts of A and B based on the magnitude of K (large K indicates more B, small K indicates more A).

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주요 개념

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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, favoring the formation of products, while a positive ∆G suggests that reactants are favored. The magnitude of ∆G also provides insight into the extent of the reaction at equilibrium.

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. It is derived from the Gibbs Free Energy change, where a negative ∆G corresponds to a K value greater than 1, indicating that products are favored. Conversely, a positive ∆G results in a K value less than 1, favoring reactants.

Relationship between ∆G° and K

The relationship between standard Gibbs Free Energy change (∆G°) and the equilibrium constant (K) is given by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. This equation allows us to calculate the equilibrium constant from the Gibbs Free Energy change and vice versa. Understanding this relationship is crucial for predicting the relative amounts of reactants and products at equilibrium.

In a reaction in which reactant A is in equilibrium with product B at 25 °C, what relative amounts of A and B are present at equilibrium if ∆G° at 25 °C isc. -2.72 kcal/mol?d. -0.65 kcal/mol?