Sulfur trioxide (${SO}_3$) is an essential intermediate manufactured in the chemical industry for the production of sulfuric acid. This is achieved via the reversible oxidation of sulfur dioxide (${SO}_2$) shown in equilibrium 20.1 below.

$$2{SO}_2(g)+O_2(g)\rightleftharpoons 2{SO}_3(g)\Delta H=-197{kJ\; mol}^{-1}$$

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

A chemist investigates the gas-phase equilibrium reaction between nitrogen monoxide and bromine, producing nitrosyl bromide, shown below.

$$2NO(g)+{Br}_2(g)\rightleftharpoons 2NOBr(g)$$

• The chemist mixes together $NO$ and ${Br}_2$ in a sealed vessel.
• 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 $NO$ and $0.0125mol$ of ${Br}_2$.

At the temperature used, the numerical value for $K_c$ is $2.00\times 10^3{dm}^3{mol}^{-1}$.

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

Determine the amount, in $mol$, of $NOBr$ in the equilibrium mixture at this temperature.

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