Methanol gas can be manufactured in the chemical industry by the catalytic hydrogenation of carbon monoxide. This is a reversible reaction shown in equilibrium 20.1 below.

$$CO(g)+2H_2(g)\rightleftharpoons {CH}_{3}OH(g)\Delta H=-91{kJ\; mol}^{-1}$$

Explain, in terms of Le Chatelier's principle, the conditions of pressure and temperature for a maximum yield of methanol from equilibrium 20.1, and explain why the operational conditions used by the chemical industry may be different.

A chemist investigates the equilibrium reaction between sulfur dioxide, oxygen, and sulfur trioxide, shown below.

$$2{SO}_2(g)+O_2(g)\rightleftharpoons 2{SO}_3(g)$$

• The chemist mixes together ${SO}_2$ and $O_2$ with a catalyst.
• The chemist compresses the gas mixture to a volume of $250{cm}^3$.
• The mixture is heated to a constant temperature and is allowed to reach equilibrium without changing the total gas volume.

The equilibrium mixture contains $0.0240mol$ of ${SO}_2$ and $0.0150mol$ of $O_2$.

At the temperature used, the numerical value for $K_c$ is $1.25\times 10^3{dm}^3{mol}^{-1}$.

Write the expression for $K_c$ and the units of $K_c$ for this equilibrium.

Determine the amount, in $mol$, of ${SO}_3$ in the equilibrium mixture at this temperature.

Give your final answer to an appropriate number of significant figures. Show all your working.