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Chapter 13: Problem 85

Suppose \(K=4.5 \times 10^{-3}\) at a certain temperature for the reaction $$ \mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) $$ If it is found that the concentration of \(\mathrm{PCl}_{5}\) is twice the concentration of \(\mathrm{PCl}_{3}\), what must be the concentration of \(\mathrm{Cl}_{2}\) under these conditions?

Short Answer

Expert verified
The concentration of Cl2 under these conditions can be expressed in terms of the concentration of PCl3 as follows: $$ [\mathrm{Cl}_2] = 9.0 \times 10^{-3} [\mathrm{PCl}_3] $$

Step by step solution

01

Write the balanced equation

The given chemical reaction is: $$ \mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) $$
02

Write the equilibrium constant expression

For the given reaction, the equilibrium constant expression (K) is: $$ K = \frac{[\mathrm{PCl}_3][\mathrm{Cl}_2]}{[\mathrm{PCl}_5]} $$ Where [] denotes the concentration of each substance at equilibrium.
03

Substitute the given relationship between the concentrations into the equilibrium expression

It is given that the concentration of PCl5 is twice the concentration of PCl3, i.e., $$ [\mathrm{PCl}_5] = 2[\mathrm{PCl}_3] $$ So, let's substitute this into the equilibrium expression and also substitute the given value of \(K = 4.5 \times 10^{-3}\): $$ 4.5 \times 10^{-3} = \frac{[\mathrm{PCl}_3][\mathrm{Cl}_2]}{(2[\mathrm{PCl}_3])} $$
04

Solve for the concentration of Cl2 in terms of the concentration of PCl3

To find the concentration of Cl2, we must first rearrange the equation: $$ [\mathrm{Cl}_2] = \frac{4.5 \times 10^{-3} (2[\mathrm{PCl}_3])}{[\mathrm{PCl}_3]} $$ Then, simplify the equation: $$ [\mathrm{Cl}_2] = 9.0 \times 10^{-3} [\mathrm{PCl}_3] $$ Since we are not given any numerical value for the concentration of PCl3 or PCl5, we can only express the concentration of Cl2 in terms of the concentration of PCl3, which is: $$ [\mathrm{Cl}_2] = 9.0 \times 10^{-3} [\mathrm{PCl}_3] $$

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Most popular questions from this chapter

The equilibrium constant \(K_{\mathrm{p}}\) for the reaction $$ \mathrm{CCl}_{4}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{Cl}_{2}(g) $$ at \(700^{\circ} \mathrm{C}\) is \(0.76 .\) Detemine the initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of \(1.20 \mathrm{~atm}\) at \(700^{\circ} \mathrm{C}\).

A 1.00-L flask was filled with \(2.00\) moles of gaseous \(\mathrm{SO}_{2}\) and \(2.00\) moles of gaseous \(\mathrm{NO}_{2}\) and heated. After equilibrium was reached, it was found that \(1.30\) moles of gaseous NO was present. Assume that the reaction $$ \mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g) $$ occurs under these conditions. Calculate the value of the equilibrium constant, \(K\), for this reaction.

Which of the following statements is(are) true? Correct the false statement(s). a. When a reactant is added to a system at equilibrium at a given temperature, the reaction will shift right to reestablish equilibrium. b. When a product is added to a system at equilibrium at a given temperature, the value of \(K\) for the reaction will increase when equilibrium is reestablished. c. When temperature is increased for a reaction at equilibrium, the value of \(K\) for the reaction will increase. d. When the volume of a reaction container is increased for a system at equilibrium at a given temperature, the reaction will shift left to reestablish equilibrium. e. Addition of a catalyst (a substance that increases the speed of the reaction) has no effect on the equilibrium position.

An initial mixture of nitrogen gas and hydrogen gas is reacted in a rigid container at a certain temperature by the reaction $$ 3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ At equilibrium, the concentrations are \(\left[\mathrm{H}_{2}\right]=5.0 \mathrm{M},\left[\mathrm{N}_{2}\right]=\) \(8.0 M\), and \(\left[\mathrm{NH}_{3}\right]=4.0 M .\) What were the concentrations of nitrogen gas and hydrogen gas that were reacted initially?

At a given temperature, \(K=1.3 \times 10^{-2}\) for the reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ Calculate values of \(K\) for the following reactions at this temperature. a. \(\frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g)\) b. \(2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\) c. \(\mathrm{NH}_{3}(g) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g)\) d. \(2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2}(g) \rightleftharpoons 4 \mathrm{NH}_{3}(g)\)
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