Page 245 - Theory and Problems of BEGINNING CHEMISTRY

234 RATES AND EQUILIBRIUM [CHAP. 16

EXAMPLE 16.6. What effect would an increase in volume have on the following system at equilibrium at 500 C, where
◦
all the reagents are gases?
−→
H 2 + I 2 ←− 2HI
Ans. The increase in volume would decrease the pressure on each of the gases (Chap. 12). The equilibrium would not
shift, however, because there are equal numbers of moles of gases on the two sides. Neither possible shift would
cause an increase in pressure.

Presence of a Catalyst
Addition of a catalyst to a system at equilibrium will not cause any change in the position of the equilibrium;
it will shift neither left nor right. (Addition of the catalyst speeds up both the forward reaction and the reverse
reaction equally.)

16.4. EQUILIBRIUM CONSTANTS
Although Le Chˆatelier’s principle does not tell us how much an equilibrium will be shifted, there is a way
to determine the position of an equilibrium once data have been determined for the equilibrium experimentally.
At a given temperature the ratio of concentrations of products to reactants, each raised to a suitable power, is
constant for a given equilibrium reaction. The letters A, B, C, and D are used here to stand for general chemical
species. Thus, for a chemical reaction in general,

aA + bB ←− cC + dD
−→
The following ratio always has the same value at a given temperature:
c
[C] [D] d
K =
a
[A] [B] b
Here the square brackets indicate the concentration of the chemical species within the bracket. That is, [A] means
a
the concentration of A, and so forth. [A] means the concentration of A raised to the power a, where a is the
value of the coefficient of A in the balanced equation for the chemical equilibrium. The value of the ratio of
concentration terms is symbolized by the letter K, called the equilibrium constant. For example, for the reaction
of hydrogen and nitrogen referred to in Sec. 16.3,

−→
3H 2 + N 2 ←− 2NH 3
the ratio is
[NH 3 ] 2
K =
3
[H 2 ] [N 2 ]
The exponents 2 and 3 are the coefficients of ammonia and hydrogen, respectively, in the balanced equation.
Please note carefully the following points about the equilibrium constant expression:
1. This is a mathematical equation. Its values are numbers, involving the concentrations of the chemicals and
their coefficients.
2. Each concentration is raised to the power given by the coefficient in the chemical equation.
3. The concentrations of the products of the reaction are written in the numerator of the equilibrium constant
expression; the concentrations of the reactants are in the denominator.
4. The terms are multiplied together, not added.
5. Each equilibrium constant expression is associated with a particular chemical reaction written in a given
direction.

EXAMPLE 16.7. Write the equilibrium constant expression for the reaction
−→
2NH 3 ←− 3H 2 + N 2