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Ch.15 - Chemical Equilibrium
All textbooksMcMurry 8th EditionCh.15 - Chemical EquilibriumProblem 105
Chapter 15, Problem 105

The equilibrium constant Kp for the gas-phase thermal decomposition of tert-butyl chloride is 3.45 at 500 K: CH3C(CH3)2Cl(g) ↔ CH2=C(CH3)2(g) + HCl(g). (b) Calculate the molar concentrations of reactants and products in an equilibrium mixture obtained by heating 1.00 mol of tert-butyl chloride in a 5.00-L vessel at 500 K. (c) A mixture of isobutylene (0.400 atm partial pressure at 500 K) and HCl (0.600 atm partial pressure at 500 K) is allowed to reach equilibrium at 500 K. What are the equilibrium partial pressures of tert-butyl chloride, isobutylene, and HCl?

Verified step by step guidance
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Step 1: For part (b), start by writing the expression for the equilibrium constant Kp in terms of partial pressures: \( K_p = \frac{P_{\text{isobutylene}} \times P_{\text{HCl}}}{P_{\text{tert-butyl chloride}}} \).
Step 2: Assume that x moles of tert-butyl chloride decompose at equilibrium. The initial moles of tert-butyl chloride are 1.00 mol, so at equilibrium, the moles of tert-butyl chloride are \(1.00 - x\).
Step 3: Calculate the equilibrium partial pressures using the ideal gas law: \( P = \frac{nRT}{V} \). For tert-butyl chloride, \( P_{\text{tert-butyl chloride}} = \frac{(1.00 - x)RT}{5.00} \). For isobutylene and HCl, \( P_{\text{isobutylene}} = P_{\text{HCl}} = \frac{xRT}{5.00} \).
Step 4: Substitute the expressions for the partial pressures into the Kp expression and solve for x: \( K_p = \frac{(\frac{xRT}{5.00})^2}{\frac{(1.00 - x)RT}{5.00}} = 3.45 \).
Step 5: For part (c), use the initial partial pressures of isobutylene and HCl to set up the equilibrium expression. Let y be the change in pressure for the reaction to reach equilibrium. The equilibrium pressures will be \(0.400 - y\) for isobutylene, \(0.600 - y\) for HCl, and y for tert-butyl chloride. Substitute these into the Kp expression and solve for y.

Key Concepts

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

Equilibrium Constant (Kp)

The equilibrium constant Kp is a numerical value that expresses the ratio of the partial pressures of the products to the partial pressures of the reactants at equilibrium for a given reaction at a specific temperature. For the reaction involving tert-butyl chloride, Kp = (P_CH2=C(CH3)2 * P_HCl) / (P_CH3C(CH3)2Cl). A higher Kp indicates a greater tendency for products to form at equilibrium.
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Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. It can be calculated using the ideal gas law, where the total pressure is the sum of the partial pressures of all gases present. In the context of the question, the partial pressures of isobutylene and HCl are crucial for determining the equilibrium state of the system.
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ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations or pressures, the changes that occur as the system reaches equilibrium, and the final equilibrium concentrations or pressures. This systematic approach helps in calculating the equilibrium concentrations of reactants and products by tracking how the system shifts in response to changes in conditions, such as temperature or concentration.
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Related Practice
Textbook Question
At 1000 K, the value of Kc for the reaction C1s2 + H2O1g2 ∆ CO1g2 + H21g2 is 3.0 * 10-2. Calculate the equilibrium concentrations of H2O, CO2, and H2 in a reac- tion mixture obtained by heating 6.00 mol of steam and an excess of solid carbon in a 5.00-L container. What is the molar composition of the equilibrium mixture?
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Textbook Question
At 100 °C, Kc = 4.72 for the reaction 2 NO21g2 ∆ N2O41g2. An empty 10.0-L flask is filled with 4.60 g of NO2 at 100 °C. What is the total pressure in the flask at equilibrium?
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