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Ch.15 - Chemical Equilibrium
All textbooksMcMurry 8th EditionCh.15 - Chemical EquilibriumProblem 96
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Chapter 15, Problem 96

The value of Kc for the reaction of acetic acid with ethanol is 3.4 at 25°C: CH3CO2H1soln2 + CH3CH2OH1soln2 ∆ Acetic acid Ethanol CH3CO2CH2CH31soln2 + H2O1soln2 Kc = 3.4 (a) How many moles of ethyl acetate are present in an equi- librium mixture that contains 4.0 mol of acetic acid, 6.0 mol of ethanol, and 12.0 mol of water at 25 °C?

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Identify the balanced chemical equation for the reaction: \( \text{CH}_3\text{CO}_2\text{H} + \text{CH}_3\text{CH}_2\text{OH} \rightleftharpoons \text{CH}_3\text{CO}_2\text{CH}_2\text{CH}_3 + \text{H}_2\text{O} \).
Write the expression for the equilibrium constant \( K_c \): \( K_c = \frac{[\text{CH}_3\text{CO}_2\text{CH}_2\text{CH}_3][\text{H}_2\text{O}]}{[\text{CH}_3\text{CO}_2\text{H}][\text{CH}_3\text{CH}_2\text{OH}]} \).
Substitute the known values into the \( K_c \) expression: \( 3.4 = \frac{x \cdot 12.0}{(4.0 - x)(6.0 - x)} \), where \( x \) is the moles of ethyl acetate at equilibrium.
Rearrange the equation to solve for \( x \), which represents the moles of ethyl acetate.
Use algebraic methods to solve the equation for \( x \), ensuring to check for any assumptions or approximations made during the process.

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Key Concepts

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

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction provided, Kc = [ethyl acetate][water] / [acetic acid][ethanol]. Understanding Kc helps predict the extent of the reaction and the concentrations of species at equilibrium.
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Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. In this case, the stoichiometric coefficients from the balanced equation indicate the molar relationships between acetic acid, ethanol, ethyl acetate, and water, which are essential for determining the moles of ethyl acetate formed at equilibrium.
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Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is disturbed, the system will shift in a direction that counteracts the disturbance. This principle can be applied to predict how changes in concentration of reactants or products will affect the equilibrium position, which is relevant when analyzing the equilibrium mixture of acetic acid, ethanol, and ethyl acetate.
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