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Ch.15 - Chemical Equilibrium
All textbooksMcMurry 8th EditionCh.15 - Chemical EquilibriumProblem 103
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Chapter 15, Problem 103

When 1.000 mol of PCl5 is introduced into a 5.000-L container at 500 K, 78.50% of the PCl5 dissociates to give an equilibrium mixture of PCl5, PCl3, and Cl2: PCl5(g) ⇌ PCl3(g) + Cl2(g). (a) Calculate the values of Kc and Kp.

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Step 1: Determine the initial concentration of PCl_5. Use the formula for concentration: \([\text{Concentration}] = \frac{\text{moles}}{\text{volume}}\). Here, the initial moles of PCl_5 is 1.000 mol and the volume is 5.000 L.
Step 2: Calculate the change in concentration of PCl_5 due to dissociation. Since 78.50% of PCl_5 dissociates, calculate the moles of PCl_5 that dissociate and convert this to concentration.
Step 3: Determine the equilibrium concentrations of PCl_5, PCl_3, and Cl_2. Use the stoichiometry of the reaction: PCl_5(g) ⇌ PCl_3(g) + Cl_2(g). The change in concentration for PCl_5 will be equal to the increase in concentration for both PCl_3 and Cl_2.
Step 4: Calculate the equilibrium constant K_c. Use the expression \(K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]}\) and substitute the equilibrium concentrations found in Step 3.
Step 5: Calculate the equilibrium constant K_p. Use the relation \(K_p = K_c(RT)^{\Delta n}\), where \(\Delta n\) is the change in moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
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