The equilibrium constant \(K_{P}\) for the reaction $$\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$ is 1.05 at \(250^{\circ} \mathrm{C}\). The reaction starts with a mixture of \(\mathrm{PCl}_{5}, \mathrm{PCl}_{3},\) and \(\mathrm{Cl}_{2}\) at pressures \(0.177 \mathrm{~atm},\) 0.223 atm, and 0.111 atm, respectively, at \(250^{\circ} \mathrm{C}\). When the mixture comes to equilibrium at that temperature, which pressures will have decreased and which will have increased? Explain why.

Short Answer

Expert verified
The pressure of \(PCl_5\) will decrease, while the pressures of \(PCl_3\) and \(Cl_2\) will increase until equilibrium is reached at \(K_p = 1.05\).

Step by step solution

01

Set up the reaction equation and the expression for Kp

\[\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\]\nKp is defined as \[K_{P}=\frac{[\text { Pressure of PCl3 }] \times [\text { Pressure of Cl2 }] }{[\text { Pressure of PCl5 }] }\] For a reaction, when it reaches equilibrium, its Kp equals to the equilibrium constant provided, here it is 1.05
02

Insert the initial pressures into Kp

Calculate Kp based on the initial pressure of each component in the reaction, and determine if the system is at equilibrium. \[Kp = \frac{(0.223 atm)(0.111 atm)}{0.177 atm} \approx 0.140 < 1.05\] Since Kp is less than the equilibrium constant, the system is not at equilibrium.
03

Determine the direction of the shift

According to Le Chatelier's Principle, the reaction will shift towards the side with fewer molecules to reach equilibrium. In this case, the number of moles of reactant and product are equal, thus the reaction shifts towards the products side (PCl3 and Cl2) to increase Kp. Therefore, the pressure of PCl5 will decrease, while the pressures of PCl3 and Cl2 will increase.

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Most popular questions from this chapter

Consider this equilibrium reaction in a closed container: $$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$ What will happen if the following occurs? (a) The volume is increased. (b) Some \(\mathrm{CaO}\) is added to the mixture. (c) Some \(\mathrm{CaCO}_{3}\) is removed. (d) Some \(\mathrm{CO}_{2}\) is added to the mixture. (e) A few drops of a \(\mathrm{NaOH}\) solution are added to the mixture. (f) A few drops of a \(\mathrm{HCl}\) solution are added to the mixture (ignore the reaction between \(\mathrm{CO}_{2}\) and water). (g) Temperature is increased.

In 1899 the German chemist Ludwig Mond developed a process for purifying nickel by converting it to the volatile nickel tetracarbonyl \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\) (b.p. \(\left.=42.2^{\circ} \mathrm{C}\right)\) $$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g)$$ (a) Describe how you can separate nickel and its solid impurities. (b) How would you recover nickel? \(\left[\Delta H_{\mathrm{f}}^{\circ}\right.\) for \(\mathrm{Ni}(\mathrm{CO})_{4}\) is \(\left.-602.9 \mathrm{~kJ} / \mathrm{mol} .\right]\)

Explain the difference between physical equilibrium and chemical equilibrium. Give two examples of each.

A reaction vessel contains \(\mathrm{NH}_{3}, \mathrm{~N}_{2},\) and \(\mathrm{H}_{2}\) at equilibrium at a certain temperature. The equilibrium concentrations are \(\left[\mathrm{NH}_{3}\right]=0.25 M,\left[\mathrm{~N}_{2}\right]=0.11 M\) and \(\left[\mathrm{H}_{2}\right]=1.91 \mathrm{M} .\) Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the synthesis of ammonia if the reaction is represented as (a) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) (b) \(\frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g)\)

Consider the potential energy diagrams for two types of reactions \(\mathrm{A} \rightleftharpoons \mathrm{B}\). In each case, answer the following questions for the system at equilibrium. (a) How would a catalyst affect the forward and reverse rates of the reaction? (b) How would a catalyst affect the energies of the reactant and product? (c) How would an increase in temperature affect the equilibrium constant? (d) If the only effect of a catalyst is to lower the activation energies for the forward and reverse reactions, show that the equilibrium constant remains unchanged if a catalyst is added to the reacting mixture.

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