Question

For the system $$ \mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) $$ \(K\) is 26 at \(300^{\circ} \mathrm{C}\). In a \(10.0-\mathrm{L}\) flask at \(300^{\circ} \mathrm{C}\), a gaseous mixture consists of all three gases with the following partial pres- $$ \text { sures: } P_{\mathrm{PCl}_{5}}=0.026 \mathrm{~atm}, P_{\mathrm{PCl}_{3}}=0.65 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.33 \mathrm{~atm} $$ (a) Is the system at equilibrium? Explain. (b) If the system is not at equilibrium, in which direction will the system move to reach equilibrium?

Short answer

If not, which direction will the reaction move to reach equilibrium? Answer: (a) The system is not at equilibrium. (b) The reaction will proceed in the forward direction (to the right) in order to reach equilibrium.

Step-by-step solution

Calculate the reaction quotient Q

The reaction quotient (Q) can be calculated using the formula, $$Q = \frac{[\mathrm{PCl}_{3}][\mathrm{Cl}_{2}]}{[\mathrm{PCl}_{5}]}$$ Here, [X] represents the partial pressure of gas X. We can plug in the given values to calculate Q. $$Q = \frac{0.65\ \mathrm{atm} \times 0.33\ \mathrm{atm}}{0.026\ \mathrm{atm}} = 8.27$$

Compare Q with K

Now, we will compare the calculated reaction quotient (Q) with the given equilibrium constant (K). Q = 8.27 K = 26 Since Q < K, the system is not at equilibrium.

Determine the direction of the reaction

If Q < K, the reaction will shift in the forward direction to reach equilibrium. This means the concentration of PCl5 will decrease, and the concentrations of PCl3 and Cl2 will increase. So, the reaction will proceed as follows: $$\mathrm{PCl}_5(g) \rightarrow \mathrm{PCl}_3(g) + \mathrm{Cl}_2(g)$$ In conclusion, (a) The system is not at equilibrium. (b) The reaction will proceed in the forward direction (to the right) in order to reach equilibrium.