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Chapter 13: Problem 95

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 is \(9\times10^{-3}\) M.

Step by step solution

01

Write the given information as algebraic expressions

Given that the concentration of PCl5 is twice the concentration of PCl3, we express it as: $$ [\mathrm{PCl_5}] = 2 [\mathrm{PCl_3}] $$ Now we need to find the concentration of Cl2.
02

Substitute the given information into the equilibrium expression

Insert the given relationship and the unknown concentration of Cl2 into the equilibrium expression: $$ K=\frac{[\mathrm{PCl_3}][\mathrm{Cl_2}]}{(2 [\mathrm{PCl_3}])} $$
03

Solve the expression for the unknown concentration of Cl2

We want to isolate the unknown concentration of Cl2, so we will first multiply both sides of the equation by \(2[\mathrm{PCl_{3}}]\): $$ 2 [\mathrm{PCl_{3}}]K = [\mathrm{PCl{3}}][\mathrm{Cl_2}] $$ Now, divide both sides of the equation by \([\mathrm{PCl_3}]\): $$ 2K = [\mathrm{Cl_2}] $$
04

Substitute the given value of K

Substitute the given value of K into the equation: $$ 2(4.5\times10^{-3}) = [\mathrm{Cl_2}] $$
05

Calculate the concentration of Cl2

Multiply to solve for the concentration of Cl2: $$ [\mathrm{Cl_2}] = 9\times10^{-3}\mathrm{M} $$ So, the concentration of Cl2 under these conditions is \(9\times10^{-3}\) M.

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Most popular questions from this chapter

At \(900^{\circ} \mathrm{C}, K_{\mathrm{p}}=1.04\) for the reaction $$ \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$ At a low temperature, dry ice (solid \(\mathrm{CO}_{2}\) ), calcium oxide, and calcium carbonate are introduced into a 50.0-L reaction chamber. The temperature is raised to \(900^{\circ} \mathrm{C}\), resulting in the dry ice converting to gaseous \(\mathrm{CO}_{2} .\) For the following mixtures, will the initial amount of calcium oxide increase, decrease, or remain the same as the system moves toward equilibrium at \(900{ }^{\circ} \mathrm{C}\) ? a. \(655 \mathrm{~g} \mathrm{CaCO}_{3}, 95.0 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=2.55 \mathrm{~atm}\) b. \(780 \mathrm{~g} \mathrm{CaCO}_{3}, 1.00 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=1.04 \mathrm{~atm}\) c. \(0.14 \mathrm{~g} \mathrm{CaCO}_{3}, 5000 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=1.04 \mathrm{~atm}\) d. \(715 \mathrm{~g} \mathrm{CaCO}_{3}, 813 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=0.211 \mathrm{~atm}\)

At a particular temperature, \(K=3.75\) for the reaction $$ \mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g) $$ If all four gases had initial concentrations of \(0.800 M\), calculate the equilibrium concentrations of the gases.

Old-fashioned "smelling salts" consist of ammonium carbonate, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3} .\) The reaction for the decomposition of ammonium carbonate $$ \left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}(s) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ is endothermic. Would the smell of ammonia increase or decrease as the temperature is increased?

The reaction $$ 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) $$ has \(K_{\mathrm{p}}=109\) at \(25^{\circ} \mathrm{C}\). If the equilibrium partial pressure of \(\mathrm{Br}_{2}\) is \(0.0159\) atm and the equilibrium partial pressure of \(\mathrm{NOBr}\) is \(0.0768\) atm, calculate the partial pressure of \(\mathrm{NO}\) at equilibrium.

The following equilibrium pressures were observed at a certain temperature for the reaction $$ \begin{array}{c} \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \\\ P_{\mathrm{NH}_{3}}=3.1 \times 10^{-2} \mathrm{~atm} \\ P_{\mathrm{N}_{2}}=8.5 \times 10^{-1} \mathrm{~atm} \\ P_{\mathrm{H}_{2}}=3.1 \times 10^{-3} \mathrm{~atm} \end{array} $$ Calculate the value for the equilibrium constant \(K_{\mathrm{p}}\) at this temperature. If \(P_{\mathrm{N}_{2}}=0.525 \mathrm{~atm}, P_{\mathrm{NH}_{3}}=0.0167 \mathrm{~atm}\), and \(P_{\mathrm{H}_{2}}=0.00761\) atm, does this represent a system at equilibrium?
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