Question

Nitrogen and hydrogen gases react to form ammonia gas as follows: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ At a certain temperature and pressure, \(1.2 \mathrm{~L}\) of \(\mathrm{N}_{2}\) reacts with \(3.6 \mathrm{~L}\) of \(\mathrm{H}_{2}\). If all the \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) are consumed, what volume of \(\mathrm{NH}_{3}\), at the same temperature and pressure, will be produced?

Short answer

The volume of ammonia gas produced at the same temperature and pressure will be \(2.4 \: \text{L}\).

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the reaction between nitrogen gas and hydrogen gas to form ammonia gas is given by: \[ \mathrm{N}_{2}(g) + 3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \]

Calculate the mole ratio of reactants and products

From the balanced chemical equation, we can see that 1 mole of \(\mathrm{N}_{2}(g)\) reacts with 3 moles of \(\mathrm{H}_{2}(g)\) to produce 2 moles of \(\mathrm{NH}_{3}(g)\). Stated in the form of mole ratios: \[ 1 \: \text{mol N}_2 : 3 \: \text{mol H}_2 : 2 \: \text{mol NH}_3 \]

Relate the volumes of the reactants using the mole ratios

Since the temperature and pressure are constant throughout the reaction, the volumes of the reactants and products are directly proportional to their mole ratios. Therefore, we can use the mole ratio to find the volume of ammonia gas produced. First, we write an expression relating the volumes of each reactant and product: \[ \frac{V_{N_2}}{1} = \frac{V_{H_2}}{3} = \frac{V_{NH_3}}{2} \]

Calculate the volume of ammonia gas produced

We are given that the volume of nitrogen gas, \(V_{N_2}\), is 1.2 L, and the volume of hydrogen gas, \(V_{H_2}\), is 3.6 L. Using these values, we can find the volume of ammonia gas, \(V_{NH_3}\): \[ \frac{1.2 \: \text{L}}{1} = \frac{3.6 \: \text{L}}{3} \] Since the ratio is consistent based on the balanced chemical equation, we can use either ratio to find the volume of ammonia gas: \[ V_{NH_3} = 2 \times 1.2 \: \text{L} = 2.4 \: \text{L} \] So, the volume of ammonia gas produced at the same temperature and pressure will be 2.4 liters.