Ch.4 - The Study of Chemical Reactions

Wade9th EditionOrganic ChemistryISBN: 9780135213728Not the one you use?Change textbook

Wade 9th Edition

Ch.4 - The Study of Chemical Reactions

Problem 6a

Chapter 4, Problem 6a

Under base-catalyzed conditions, two molecules of acetone can condense to form diacetone alcohol. At room temperature (25 °C), about 5% of the acetone is converted to diacetone alcohol. Determine the value of ΔG° for this reaction.

Verified step by step guidance

Step 1: Understand the reaction. The reaction involves the base-catalyzed aldol condensation of two molecules of acetone to form diacetone alcohol. The equilibrium constant (K) can be determined from the given information that 5% of acetone is converted to diacetone alcohol.

Step 2: Calculate the equilibrium constant (K). If 5% of acetone is converted to diacetone alcohol, then at equilibrium, 95% of acetone remains unreacted. Let the initial concentration of acetone be 1 (arbitrary unit). At equilibrium, the concentration of diacetone alcohol is 0.05, and the concentration of acetone is 0.95. Use the equilibrium expression: K = [diacetone alcohol] / [acetone]^2.

Step 3: Use the relationship between ΔG° and the equilibrium constant (K). The standard Gibbs free energy change (ΔG°) is related to the equilibrium constant by the equation: ΔG° = -RT ln(K), where R is the gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin (25 °C = 298 K).

Step 4: Substitute the value of K into the ΔG° equation. Use the calculated value of K from Step 2 and substitute it into the equation ΔG° = -RT ln(K). Ensure that the units are consistent (R in J/(mol·K), T in Kelvin).

Step 5: Interpret the result. The sign and magnitude of ΔG° will indicate whether the reaction is thermodynamically favorable under standard conditions. A negative ΔG° suggests the reaction is spontaneous, while a positive ΔG° suggests it is non-spontaneous.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy (ΔG°)

Gibbs Free Energy (ΔG°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It indicates the spontaneity of a reaction: a negative ΔG° suggests that the reaction can occur spontaneously, while a positive ΔG° indicates non-spontaneity. The value of ΔG° can be calculated using the standard free energies of formation of the reactants and products.

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. It is related to ΔG° by the equation ΔG° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. A larger K value indicates a greater tendency for the reaction to favor products, while a smaller K suggests a preference for reactants.

Base-Catalyzed Condensation

Base-catalyzed condensation is a reaction where a base facilitates the combination of two molecules, resulting in the formation of a larger molecule and the release of a small molecule, often water. In this case, acetone molecules react under basic conditions to form diacetone alcohol. Understanding the mechanism of this reaction is crucial for predicting the products and calculating thermodynamic properties like ΔG°.

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Base Catalyzed

Related Practice

Textbook Question

The following reaction has a value of ΔG° = –2.1 kJ/mol (–0.50 kcal/mol).

CH₃Br + H₂S ⇌ CH₃SH + HBr

b. Starting with a 1 M solution of CH3Br and H2S, calculate the final concentrations of all four species at equilibrium.

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Textbook Question

When ethene is mixed with hydrogen in the presence of a platinum catalyst, hydrogen adds across the double bond to form ethane. At room temperature, the reaction goes to completion. Predict the signs of ΔH° and ΔS° for this reaction. Explain these signs in terms of bonding and freedom of motion.

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Textbook Question

Free-radical chlorination of hexane gives very poor yields of 1-chlorohexane, while cyclohexane can be converted to chlorocyclohexane in good yield.

a. How do you account for this difference?

b. What ratio of reactants (cyclohexane and chlorine) would you use for the synthesis of chlorocyclohexane?

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Textbook Question

Draw a reaction-energy diagram for the propagation steps of the free-radical addition of HBr to isobutylene. Draw curves representing the reactions leading to both the Markovnikov and the anti-Markovnikov products. Compare the values of ∆Gº and Ea and for the rate-limiting steps, and explain why only one of these products is observed.

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Textbook Question

The following reaction has a value of ΔG° = –2.1 kJ/mol (–0.50 kcal/mol).

CH₃Br + H₂S ⇌ CH₃SH + HBr

a. Calculate K_eq at room temperature (25 °C) for this reaction as written.

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Textbook Question

The dehydrogenation of butane to trans-but-2-ene has ΔH° = +116 kJ/mol (+27.6 kcal/mol) and ΔS° = +117J/kelvin-mol (+28.0 cal/kelvin-mol). a. Compute the value of ΔG° for dehydrogenation at room temperature (25 °C or 298 °K). Is dehydrogenation favored or disfavored?HINT: When you are doing synthesis problems, avoid using these high-temperature industrial methods. They require specialized equipment, and they produce variable mixtures of products.