Question

Explain the difference between K, K_p, and Q.

Short answer

In the equilibrium reaction, the Q value is calculated for both initial conditions and equilibrium conditions while the K and K_p values is calculated for only equilibrium conditions.

Step-by-step solution

Write the expressions for K, Kp and Q.

Consider a general chemical reaction as shown below:

$\text{mM+nN}\stackrel{}{\rightleftharpoons }\text{qQ+rR}$ …(1)

Here,

M and N are the reactant species.

Q and R are the product species.

m, n, q and r are the coefficients of M, N, Q and R respectively.

According to the law of mass action, the equilibrium constant expressions for the above reaction at equilibrium can be represented as follows:

For K in terms of concentrations:

$\mathrm{K}=\frac{{\left[\mathrm{Q}\right]}^{\mathrm{q}}{\left[\mathrm{R}\right]}^{\mathrm{r}}}{{\left[\mathrm{M}\right]}^{\mathrm{m}}{\left[\mathrm{N}\right]}^{\mathrm{n}}}$ …(2)

For K_p in terms of partial pressures:

${\mathrm{K}}_{\mathrm{p}}=\frac{\left({{\mathrm{P}}_{\mathrm{Q}}}^{\mathrm{q}}\right)\left({{\mathrm{P}}_{\mathrm{R}}}^{\mathrm{r}}\right)}{\left({{\mathrm{P}}_{\mathrm{M}}}^{\mathrm{m}}\right)\left({{\mathrm{P}}_{\mathrm{N}}}^{\mathrm{n}}\right)}$ …(3)

The expression for the reaction quotient, Q for this reaction is shown below:

$\mathrm{Q}=\frac{{\left[\mathrm{Q}\right]}^{\mathrm{q}}{\left[\mathrm{R}\right]}^{\mathrm{r}}}{{\left[\mathrm{M}\right]}^{\mathrm{m}}{\left[\mathrm{N}\right]}^{\mathrm{n}}}$ …(4)

The difference between K, Kp, and Q are described.

Q is the reaction quotient whereas K and K_p are equilibrium constants. All are calculated by the law of mass action. Q is used for any set of conditions while K and K_p are used for equilibrium conditions only. When the reaction is at equilibrium, the reaction quotient becomes the equilibrium constant. The equilibrium constant value does not change for the equilibrium reaction at a specific temperature but the reaction quotient value changes with changing the reaction conditions.