Kc and Kp Knowledge-Based Practice

Questions

1. 1.

   The mathematical relationship $K_p = K_c(RT)^{\Delta n_g}$ is derived by expressing the partial pressure of each gaseous species in terms of its molar concentration. Which fundamental gas equation directly provides this substitution?

   • A) Dalton's law of partial pressures relating total pressure to gas mole fractions
   • B) Graham's law of effusion relating effusion rates to molar masses
   • C) The ideal gas equation in the form $P_i = [i]RT$
   • D) Raoult's law relating vapor pressure lowering to solute concentration
2. 2.

   For the homogeneous gaseous equilibrium $2\text{A}(g) + \text{B}(g) \rightleftharpoons 2\text{C}(g) + x\text{D}(g)$, the relationship between the equilibrium constants is established as $K_p = K_c(RT)$. What is the value of the stoichiometric coefficient $x$?

   • A) 0
   • B) 1
   • C) 2
   • D) 3
3. 3.

   At 500 K, the equilibrium constant $K_c$ for the reaction $\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)$ is $2.0 \times 10^{-2}$. What is the value of $K_p$ for this reaction at the same temperature? (Use $R = 0.082\text{ L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$)

   • A) $4.9 \times 10^{-4}$
   • B) $2.0 \times 10^{-2}$
   • C) $0.82$
   • D) $8.2$
4. 4.

   For the heterogeneous equilibrium $2\text{C}(s) + \text{O}_2(g) \rightleftharpoons 2\text{CO}(g)$, which mathematical expression correctly relates $K_p$ to $K_c$ at temperature $T$?

   • A) $K_p = K_c(RT)^{-1}$
   • B) $K_p = K_c$
   • C) $K_p = K_c(RT)$
   • D) $K_p = K_c(RT)^2$
5. 5.

   For which of the following gaseous equilibrium systems does the relationship $K_p = K_c(RT)^{-1}$ hold at a given temperature $T$?

   • A) $\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)}$
   • B) $\text{H}_2\text{(g)} + \text{I}_2\text{(g)} \rightleftharpoons 2\text{HI(g)}$
   • C) $2\text{SO}_2\text{(g)} + \text{O}_2\text{(g)} \rightleftharpoons 2\text{SO}_3\text{(g)}$
   • D) $\text{PCl}_5\text{(g)} \rightleftharpoons \text{PCl}_3\text{(g)} + \text{Cl}_2\text{(g)}$

Answers and step-by-step solutions appear after you finish the test.