Equilibrium constant Kp for homogeneous systems (A-level only) revision notes

Understanding Kp

Definition of Partial Pressure

Partial pressure is the pressure that a gas in a mixture would exert if it occupied the entire volume alone. It is calculated using the formula:

$$ P_i = X_i \times P_{total} $$

where:

• $P_i$ is the partial pressure of gas $i$,
• $X_i$ is the mole fraction of gas $i$,
• $P_{total}$ is the total pressure of the gas mixture.

Calculating Mole Fractions

The mole fraction of a component in a gas mixture is given by:

$$ X_i = \frac{n_i}{n_{total}} $$

where:

• $n_i$ is the number of moles of component $i$,
• $n_{total}$ is the total number of moles in the mixture.

Constructing Kp Expressions

For a general reaction:

$$ aA + bB \rightleftharpoons cC + dD $$

The equilibrium constant Kp is expressed as:

$$ K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b} $$

where $P_X$ represents the partial pressure of species $X$ at equilibrium.

Calculating Kp and Units

To calculate Kp, substitute the equilibrium partial pressures into the Kp expression. The units of Kp depend on the stoichiometry of the reaction and can be derived from the expression itself.

Interpreting Kp Values

• If Kp >> 1, the equilibrium position favors products.
• If Kp << 1, the equilibrium position favors reactants.
• If Kp = 1, concentrations of reactants and products are similar at equilibrium.