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Question 7

The reaction between carbon monoxide, CO(g)\text{CO}(\text{g})CO(g), and hydrogen, H2(g)\text{H}_2(\text{g})H2​(g), forms methanol vapour, CH3OH(g)\text{CH}_3\text{OH}(\text{g})CH3​OH(g), according to the following equilibrium:

CO(g)+2H2(g)⇌CH3OH(g) \text{CO}(\text{g}) + 2\text{H}_2(\text{g}) \rightleftharpoons \text{CH}_3\text{OH}(\text{g}) CO(g)+2H2​(g)⇌CH3​OH(g)

An industrial chemist conducts an investigation into this equilibrium:

  • The chemist fills a 6.0 dm36.0\text{ dm}^36.0 dm3 container with CO(g)\text{CO}(\text{g})CO(g) at room temperature and pressure (RTP), and then adds 1.20 g1.20\text{ g}1.20 g of H2(g)\text{H}_2(\text{g})H2​(g). (Assume 1 mol1\text{ mol}1 mol of gas occupies 24.0 dm324.0\text{ dm}^324.0 dm3 at RTP and the molar mass of H2\text{H}_2H2​ is 2.0 g mol−12.0\text{ g mol}^{-1}2.0 g mol−1).
  • The mixture is heated with a catalyst and allowed to reach equilibrium at a total pressure of 4.00 bar4.00\text{ bar}4.00 bar and a temperature of 500 K500\text{ K}500 K.
  • A sample of the equilibrium mixture is analysed and found to contain 0.150 mol0.150\text{ mol}0.150 mol of CH3OH(g)\text{CH}_3\text{OH}(\text{g})CH3​OH(g).
a.

Write an expression for KpK_{\text{p}}Kp​ for this equilibrium, including its units.

[2]
b.

Determine the value of KpK_{\text{p}}Kp​ at 500 K500\text{ K}500 K. Show your working and give your answer to 3 significant figures.

[6]

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