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

1. Step 1: For part (b), start by writing the expression for the equilibrium constant Kp in terms of partial pressures: \( K_p = \frac{P_{\text{isobutylene}} \times P_{\text{HCl}}}{P_{\text{tert-butyl chloride}}} \).
2. 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 \(1.00 - x\).
3. 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, \( P_{\text{isobutylene}} = P_{\text{HCl}} = \frac{xRT}{5.00} \).
4. Step 4: Substitute the expressions for the partial pressures into the Kp expression and solve for x: \( K_p = \frac{(\frac{xRT}{5.00})^2}{\frac{(1.00 - x)RT}{5.00}} = 3.45 \).
5. 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.