The Foundations of Chemistry

Kc1.9

[Cl 2 ]0.82 M

Often we know the starting concentrations and want to know how much of each reac-

tant and each product would be present at equilibrium. The next two examples illustrate

this important kind of calculation.

EXAMPLE 17-6 Finding Equilibrium Concentrations

For the following reaction, the equilibrium constant is 49.0 at a certain temperature. If 0.400

mol each of A and B are placed in a 2.00-liter container at that temperature, what concentra-

tions of all species are present at equilibrium?

AB 34 CD

Plan

First we find the initial concentrations. Then we write the reaction summary and represent

the equilibrium concentrations algebraically. Finally we substitute the algebraic representa-

tions of equilibrium concentrations into the Kc expression and find the equilibrium

concentrations.

Solution

The initial concentrations are

[A]0.

2

4

.

0

0

0

0

m

L

ol

0.200 M [C]^0 M

[B]0.

2

4

.

0

0

0

0

m

L

ol

0.200 M [D]^0 M

We know that the reaction can only proceed to the right because only “reactants” are present.

The reaction summary includes the values, or symbols for the values, of (1) initial concentra-

tions, (2) changes in concentrations, and (3) concentrations at equilibrium.

Let xmoles per liter of A that react; then xmoles per liter of B that react and x

moles per liter of C and D that are formed.

A  B 34 C  D

initial 0.200 M 0.200 M 0 M 0 M

change due to rxn x M x M x M x M

at equilibrium (0.200x)M (0.200x)Mx Mx M

Now Kcis known, but concentrations are not. But the equilibrium concentrations have all been

expressed in terms of the single variable x.We substitute the equilibrium concentrations (not

the initial ones) into the Kcexpression and solve for x.

Kc49.0

49.0

This quadratic equation has a perfect square on both sides. We solve it by taking the square

roots of both sides of the equation and then rearranging for x.

x^2



(0.200x)^2

(x)(x)



(0.200x)(0.200x)

[C][D]



[A][B]

(0.25)



(1.9)(0.16)

[PCl 5 ]



Kc[PCl 3 ]

[PCl 5 ]



[PCl 3 ][Cl 2 ]

We have represented chemical
formulas by single letters to simplify
the notation in these calculations.

The coefficients in the equation are
all 1’s, so the reaction ratio must be
1
1
1
1.

718 CHAPTER 17: Chemical Equilibrium