Question #377c6

You are dealing with the following equilibrium reaction

#"PCl"_ (5(g)) rightleftharpoons "PCl" _ (3(g)) + "Cl"_ (2(g))#

You also know that the equilibrium constant for this reaction at #327^@"C"# is equal to

#K_(eq) = 2.24 * 10^(-2)#

Notice that you have #K_(eq) < 1#; this should tell you that at equilibrium, the reaction vessel should contain more reactant than products.

In other words, you can expect the equilibrium concentration of phosphorus pentachloride, #"PCl"_5#, to decrease only slightly compared to its initial value.

You will have less reactant at equilibrium than what you started with because the vessel doesn't contain chlorine gas, #"Cl"_2#, so right from the start, you can predict that the reaction will produce some chlorine gas.

Given the value of #K_(eq)#, we can expect a very low concentration of chlorine gas at equilibrium.

Since the vessel has a volume of #"1.00 L"#, you can treat moles and molarity interchangeably. Set up an ICE table to help you find the equilibrium concentration of the three species

#" ""PCl"_ (5(g)) " "rightleftharpoons" " "PCl" _ (3(g))" " + " ""Cl"_ (2(g))#

#color(purple)("I")color(white)(aaaacolor(black)(0.235)aaaaaaaaaacolor(black)(0.174)aaaaaaaaacolor(black)(0)#
#color(purple)("C")color(white)(aaacolor(black)((-x))aaaaaaaaaacolor(black)((+x))aaaaaacolor(black)((+x))#
#color(purple)("E")color(white)(aacolor(black)(0.235-x)aaaaaaacolor(black)(0.174+x)aaaaaaacolor(black)(x)#

By definition, the equilibrium constant is equal to

#K_(eq) = (["PCl"_3] * ["Cl"_2])/(["PCl"_5])#

In your case, you will have

#2.24 * 10^(-2) = ((0.174 + x) * x)/(0.235 - x)#

This is equivalent to

#x^2 + 0.1964x - 0.005264 = 0#

Tis quadratic equation ahs two solutiuons, one positive and one negative. Since #x# represents concentration, discard the negative value and go with

#x = 0.0239#

Therefore, you can say that at equilibrium, the reaction vessel will contain

#color(darkgreen)(ul(color(black)(["Cl"_2] = "0.0239 M")))#

The answer is rounded to three sig figs.

As predicted, the equilibrium concentration of chlorine gas is significantly lower than that of phosphorus pentachloride and that of phosphorus trichloride.