Calculating Kp, the equilibrium constant, for a gaseous system.

For reversible reactions taking place in the gaseous phase it is more straightforward to think in terms of pressure rather than concentration.

3H_2(g) + N_2(g) ⇌ 2NH_3(g)

At equilibrium, hydrogen, nitrogen and ammonia all contribute to the total pressure in the container.

We can write an equilibrium expression to represent this in exactly the same way as we would for K_c, but instead of working with concentration we are working with the partial pressure of each gas in the system.

Partial pressure = mole fraction of the gas x total pressure

Units are kPa, atm or Pa; 1 atm = 101 kPa

The units for K_p have to be worked out for each expression in the same way as we did for K_c.

If we had 25.1g of ammonia, 12.8g of hydrogen, 59.6g of nitrogen at equilibrium, and the total pressure of the system was 12.0 atm at 150K, we could calculate the partial pressure of each gas as follows:

Now that we know the partial pressures for each gas in the equilibriium mixture, we can calculate a value for K_p and determine where the position of equilibrium lies for this reaction.

The position of equilibrium lies strongly to the left at this temperature! The video below runs through another example.

Practice questions

1. Ammonium aminomethanoate decomposes readily at 298K to form ammonia and carbon dioxide.

NH₂CO₂NH_4(s)    ⇌    2NH_3(g)  +  CO_2(g)

(a)  Explain why the expression for K_p will not include ammonium aminomethanoate

(b)  Given that in a system with a total pressure of 1.85 atm there were 0.224 mol of carbon dioxide, 0.142 mol of ammonia, calculate K_p.

2. A sample of dinitrogen tetroxide was found to be 55% dissociated at a pressure of 100kPa and 330K.  Calculate K_p for this equilibrium.

N₂O_4(g)    ⇌    2NO_2(g)

3. Hydrogen can be produced from a reaction between carbon and steam at 1000K.

C_(s)   +    H₂O_(g)    ⇌    CO_(g)   +    H_2(g)      K_p = 3.72 atm

Calculate the total pressure needed to obtain an equilibrium mixture of 2.0 mol of carbon monoxide, 1.0 mol of hydrogen and 4.0 mol of water. 

Answers

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