The industrial solvent ethyl acetate is produced by the reac-tion of acetic acid with ethanol:CH3CO2H1soln2 + CH3CH2OH1soln2 ∆CH3CO2CH2CH31soln2 + H2O1soln2Ethyl acetate (b) A solution prepared by mixing 1.00 mol of acetic acid and 1.00 mol of ethanol contains 0.65 mol of ethyl ace- tate at equilibrium. Calculate the value of Kc. Explain why you can calculate K without knowing the volume of the solution.

Verified step by step guidance

1. Identify the balanced chemical equation for the reaction: \( \text{CH}_3\text{CO}_2\text{H} + \text{CH}_3\text{CH}_2\text{OH} \rightleftharpoons \text{CH}_3\text{CO}_2\text{CH}_2\text{CH}_3 + \text{H}_2\text{O} \).
2. Determine the initial concentrations of reactants: 1.00 mol of acetic acid and 1.00 mol of ethanol.
3. Calculate the change in concentration for each species at equilibrium. Since 0.65 mol of ethyl acetate is formed, the change for ethyl acetate is +0.65 mol, and for acetic acid and ethanol, it is -0.65 mol each.
4. Determine the equilibrium concentrations: \([\text{CH}_3\text{CO}_2\text{H}] = 1.00 - 0.65\), \([\text{CH}_3\text{CH}_2\text{OH}] = 1.00 - 0.65\), \([\text{CH}_3\text{CO}_2\text{CH}_2\text{CH}_3] = 0.65\), and \([\text{H}_2\text{O}] = 0.65\).
5. Write the expression for the equilibrium constant \(K_c\) and substitute the equilibrium concentrations: \(K_c = \frac{[\text{CH}_3\text{CO}_2\text{CH}_2\text{CH}_3][\text{H}_2\text{O}]}{[\text{CH}_3\text{CO}_2\text{H}][\text{CH}_3\text{CH}_2\text{OH}]}\). Calculate \(K_c\) using these values. Note that the volume cancels out in the \(K_c\) expression, so it is not needed.

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the formula Kc = [products]/[reactants], where the concentrations are raised to the power of their coefficients in the balanced equation. A Kc value greater than 1 indicates that products are favored, while a value less than 1 suggests that reactants are favored.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. In this case, the balanced equation shows that one mole of acetic acid reacts with one mole of ethanol to produce one mole of ethyl acetate and one mole of water. Understanding stoichiometry is essential for determining the concentrations of reactants and products at equilibrium, which are necessary for calculating Kc.

Concentration Independence from Volume

In the context of calculating Kc, the actual volume of the solution does not affect the equilibrium constant because Kc is a ratio of concentrations. When calculating concentrations, the volume cancels out, as both the numerator and denominator are divided by the same volume. Therefore, knowing the number of moles of each substance at equilibrium is sufficient to determine Kc, making it independent of the solution's volume.