## Equilibrium Constants and Chemical Equations

### Skills to develop

• Write the expression for the equilibrium constant K for a given chemical reaction equiation.
• Express the equilibrium constant for a chemical equation in terms of equilibrium constant(s) for one or more related equations.
• Calculate the equilibrium constant for a chemical equation from equilibrium constant(s) for one or more related equations.
• ## Equilibrium Constants and Chemical Equations

The equilibrium constnat depends on the way we write the chemical reaction equation. When we change the equation, we need to change the value of the equalibrium for the new equation.

### Law of Mass Action, a review

The law of mass action gives an equilibrium constant expression for any chemical reaction equation. The law suggests that for a general chemical reaction equation between a moles of A and b moles of B producing c moles of C and d moles of D,

a A + b B --> c C + d D

where

A, B - represent reactants
C, D - represent products
a, b, c, d - are the coefficients for a balanced chemical equation.

If the system is at equilibrium at a given temperature, then the following ratio is a constant.

```       [C]c    [D]d
----------------  =  Keq
[A]a    [B]b
```
When a mixture of A, B, C, D is enclosed in a closed system, the law of mass action suggests that the system try to maitain a state such that K is a constant.

You can write the equilibrium constant (K) expression for any reaction equation according to the las of mass action. This has been done in the module on the Law of Mass Action.

The following rules are obvious for manipulating the K's when you change the equations.

#### Rule 1

If Kf is the equilibrium constant for the equation A + B -> C + D, then 1/Kf is the equilibrium constant for the reverse equation, C + D -> A + B.

Example
If the equilibrium constant K = 2 for

A + B = C then the equilibrium constant K = 1/2 = 0.5 for C = A + B

#### Rule 2.

If you double the number of moles of the reactants and products in an equation, then the equilibrium constant must be raised to a power of 2.

Example
If the equilibrium constant K = 2 for

A + B = C then the equilibrium constant K = 22 = 4 for 2 A + 2 B = 2 C

#### Rule 3

When you add equations (1) and (2) to give an overall reaction equation (3), then K3 = K1 * K2 where K1, K2 and K3 are equilibrium constants for the reaction equations (1), (2) and (3) respectively.

Example
If the equilibrium constant K = 2 for

A + B = C and that the equilibrium constant K = 3 for C + D = X + Y then the equilibrium constant K = 2*3 = 6 for A + B + D = X + Y
The reasons for the above rules is the relationship between the K and the enthalpy change, dH, of a reaction equation. This relationship is expressed by the Van't Hoff Equation,
```               dH
ln K  = - ---- + B
R T
```
where B is a constant. For example if you double the number of moles of the reactants and products, the value for dH doubles, resulting in the new equilibrium constant having its value squared. The reasons behind the other rules follow similar arguments.

#### Summary of Skills

• Write the expression for the equilibrium constant K for a given chemical reaction equiation.

• Express the equilibrium constant for a chemical equation in terms of equilibrium constant(s) for one or more related equations.

• Calculate the equilibrium constant for a chemical equation from equilibrium constant(s) for one or more related equations.

### Confidence Building Questions

• If the equilibrium constant for the reaction equation I2 = 2 I is 0.010, what is the equilibrium constant for the reaction equation 2 I = I2?

Hint...

Consider...
You have learned rule 1.

• If the equilibrium constant is 1E9 for the reaction equation H2 + (1/2)O2 = H2O, what is the equilibrum constant for the reaction equation 2 H2 + O2 = 2 H2O?

Hint...
Review rule 2

Consider...
The value may be higher, but the computer can not handle a very high value.

• If the equilibrium constant K1 = 1e11 for H2SO4 = H+ + HSO4-, and the equilibrium constant K2 = 6e-8 for HSO4- = H+ + SO42-, what is the equilibrium constant Koverall for H2SO4 = 2 H+ + SO42-?

Hint...
The third equation is the sum of the first two. Apply rule 3 in the Instructions of this tutorial. Try K1*K2, K1 * K2, or K1K2.

Consider...
H2SO4 is a strong acid; and K1 is very large. You have learned rule 3.

• The equilibrium constant is a quantity depending on how the equation is written. Any change in the equation should be reflected in the expression for the equilibrium constant. True or false? (t/f)