Equilibrium (2) Calculation of Kp using partial pressures

Edexcel A level Chemistry (2017)

Topic 11: Equilibrium II:

Here is the first learning objective:

1. To be able to deduce an expression for Kp, for homogeneous and heterogeneous systems, in terms of equilibrium partial pressures in atmospheres.

Mathematical skills that could be developed in this topic include constructing expressions for Kc and Kp and calculating values with relevant units, estimating the change to the value of an equilibrium constant when a variable changes.

Calculating K_p for an homogenous equilibrium:

K_p is the equilibrium constant expressed in terms of partial pressures.

The partial pressure of a gas is the pressure of a gas in a mixture of gases that the gas would exert if it alone occupied the space.

The partial pressure of a gas depends on the gas’s mole fraction in its mixture. 

For example:

Given we have the partial pressures of each gas in a homogenous equilibrium we can then use each value to calculate the equilibrium constant K_p. 

For the homogenous ammonia equilibrium system:

N₂(g)    +     3H₂(g)   ⇌      2NH₃(g)

Partial pressures are:

p_N2    =  2.31 atm  

p_H2    =  4.62 atm

p_NH3  =  8.08 atm

So calculating Kp

Determining the units of K_p   in this example:

this reduces down to

  

For a heterogenous equilibrium only the species in the gaseous state affect the equilibrium.

e.g. CaCO₃(s)      ⟶       CaO(s)       +      CO₂(g)

so the decomposition of calcium carbonate depends on the partial pressure of carbon dioxide in the kiln.

K_p     =     p_CO2          Units of Kp are Atmospheres (atm)

since all other reacting species are in the solid state and do not exert a partial pressure.