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 – part 1

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. 

Practice questions – part 2 (exam style)

1. An equilibrium mixture was found to contain 0.013 mol of carbon dioxide and 0.024 mol of carbon monoxide at 600K.  Calculate the total pressure in the system. 

C_(s)   +   CO_2(g)    ⇌    2CO_(g)           K_p = 192 kPa

2. An equilibrium mixture was found to contain 0.20 mol PCl₅, 0.010 mol PCl₃ and 3.8 mol Cl₂ at 260K and 3.0 atm.  

PCl_5(g)   ⇌   PCl_3(g)   +   Cl_2(g)

(a)   Calculate K_p for the system.

(b)   Calculate the average molar mass of the mixture.

3. 2.00 mol of steam was reacted with excess carbon at 800K and a total pressure of 4 atm.  At equilibrium 1.62 mol of hydrogen was present in the mixture.  Calculate K_p. 

H₂O_(g)  +  C_(s)   ⇌   H_2(g)   +   CO_(g)

4. 1.00 mol of nitrogen and 3.00 mol of hydrogen were mixed in a sealed container at 500K and a total pressure of 150kPa.  At equilibrium the mole fraction of ammonia was 0.80. Calculate K_p for this system. 

N_2(g)   +   3H_2(g)   ⇌   2NH_3(g)

5. 10.1 mol of carbon monoxide and 12.2 mol of hydrogen were placed in a sealed tube at 400K and an equilibrium was established.

CO_(g)   +  2H_2(g)   ⇌   CH₃OH_(g)

At equilibrium, the mixture contained 1.08 mol of methanol under a total pressure of 320kPa.  Calculate K_p for the system. 

**EXTENSION**

6. 0.20 mol of carbon dioxide was heated with excess carbon in a sealed tube and allowed to achieve equilibrium.  The average molar mass of the gaseous equilibrium mixture was 36.0 gmol^-1.

CO_2(g)   +   C_(s)    ⇌  2CO_(g)

1. Calculate the mole fraction of carbon monoxide at equilibrium.
2. Calculate K_p given that the total pressure at equilibrium was 12 atm.
3. Calculate the mole fraction of carbon monoxide present in the equilibrium mixture if the total pressure was reduced to 2 atm at the same temperature. 

Answers to part 1 questions

Answers to part 2 questions