The Foundations of Chemistry

In Example 17-4 we calculate the value for Qand compare it with the knownvalue of
Kcto predict the direction of the reaction that leads to equilibrium.

EXAMPLE 17-4 The Reaction Quotient

At a very high temperature, Kc65.0 for the following reaction.

2HI(g) 34 H 2 (g)I 2 (g)

The following concentrations were detected in a mixture. Is the system at equilibrium? If not,
in which direction must the reaction proceed for equilibrium to be established?

[HI]0.500 M,[H 2 ]2.80 M, and [I 2 ]3.40 M

Plan

We substitute these concentrations into the expression for the reaction quotient to calculate
Q.Then we compare Qwith Kcto see whether the system is at equilibrium.

Solution

Q38.1

But Kc65.0, so Q Kc. The system is notat equilibrium. For equilibrium to be established,
the value of Qmust increaseuntil it equals Kc. This can occur only if the numerator increases
and the denominator decreases.Thus, the forward (left-to-right) reaction must occur to a greater
extent than the reverse reaction; that is, some HI must react to form more H 2 and I 2 to reach
equilibrium.

You should now work Exercises 38, 40, and 42.

USES OF THE EQUILIBRIUM CONSTANT, Kc

We have seen (Section 17-2) how to calculate the value of Kcfrom one set of equilibrium
concentrations. Once that value has been obtained, the process can be turned around to
calculate equilibrium concentrationsfrom the equilibrium constant.

EXAMPLE 17-5 Finding Equilibrium Concentrations

The equation for the following reaction and the value of Kcat a given temperature are given.
An equilibrium mixture in a 1.00-liter container contains 0.25 mol of PCl 5 and 0.16 mol of
PCl 3. What equilibrium concentration of Cl 2 must be present?

PCl 3 (g)Cl 2 (g) 34 PCl 5 (g) Kc1.9

Plan

We write the equilibrium constant expression and its value. Only one term, [Cl 2 ], is unknown.
We solve for it.

Solution

Because the volume of the container is 1.00 liter, the molar concentration (mol/L) of each
substance is numerically equal to the number of moles. The equilibrium constant expression
and its numeric value are

17-5

(2.80)(3.40)



(0.500)^2

[H 2 ][I 2 ]



[HI]^2

These concentrations could be present

if we started with a mixture of HI, H 2 ,

and I 2.

17-5 Uses of the Equilibrium Constant, Kc 717

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 16.10, Estimating Equilibrium

Concentrations.

The equilibrium constant is a

“constant” only if the temperature

does not change.

Reaction proceeds to the right

Increasing Q

Q = 38.1 K = 65.0