5.3.1 Kp Expressions

What are Kp Expressions?

The equilibrium constant $K_p$ is used to express the equilibrium position of gaseous reactions in terms of partial pressures. It is derived from the balanced equation of a reversible reaction and calculated using the partial pressures of the gases involved. $K_p$ remains constant at a given temperature but changes if the temperature is altered.

Mole Fraction and Partial Pressure

Mole Fraction ($x$):

The mole fraction of a gas $A$ in a mixture is defined as the ratio of the moles of $A$ to the total moles of all gases in the mixture.

For a gas $A$ in an equilibrium mixture with gases $B$ and $C$:

$$x_A = \frac{\text{moles of } A}{\text{total moles of all gases}} = \frac{n_A}{n_A + n_B + n_C}$$

The mole fractions of all gases in the mixture add up to 1.

Partial Pressure ($p$):

The partial pressure of a gas in a mixture is calculated by multiplying its mole fraction by the total pressure of the gas mixture:

$$p_A = x_A \times \text{total pressure}$$

Writing the $K_p$ Expression

For a general reaction in the gas phase:

$$aA(g) + bB(g) \leftrightarrow cC(g) + dD(g)$$

The expression for K_p is written as:

$$K_p = \frac{(p_C)^c \times (p_D)^d}{(p_A)^a \times (p_B)^b}$$

where:

• $p_A$, $p_B$, $p_C$, and $p_D$ are the partial pressures of gases $A$, $B$, $C$ and $D$
• $a$, $b$, $c$, and $d$ are the coefficients from the balanced equation.

Important Points for $K_p$

• Temperature Dependence: $K_p$ is constant at a fixed temperature but changes with temperature.
• No Units for Mole Fraction: Mole fractions are unitless, simplifying calculations.
• Effect of Changes in Pressure: Changing the overall pressure does not affect $K_p$ as long as temperature is constant.