Question

In the Haber process for the production of ammonia, $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ what is the relationship between the rate of production of ammonia and the rate of consumption of hydrogen?

Short answer

The relationship between the rate of production of ammonia (NH3) and the rate of consumption of hydrogen (H2) in the Haber process is given by: \(\text{rate of consumption of H}_{2} = \frac{3}{2} \times \text{rate of production of NH}_{3}\). This means that for every 1 mole of ammonia produced, 3/2 moles of hydrogen are consumed.

Step-by-step solution

Identify the balanced chemical equation

First, let's identify the balanced chemical equation for the Haber process for the production of ammonia: \[ \mathrm{N}_{2}(g) + 3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \]

Determine the stoichiometric coefficients

We can see the stoichiometric coefficients for each component in the reaction: - For nitrogen (N2), the coefficient is 1. - For hydrogen (H2), the coefficient is 3. - For ammonia (NH3), the coefficient is 2. These coefficients represent the molar ratio of the reactants and products in the reaction.

Establish the relationship between the rate of consumption and production in the reaction

The rate of a chemical reaction can be expressed in terms of the rate of change of concentration (in moles per unit time) of the reactants and products. In this case, we are looking for the relationship between the rate of consumption of hydrogen (H2) and the rate of production of ammonia (NH3). Using the stoichiometric coefficients, we can write the relationship as follows: \[ \frac{\text{rate of consumption of H}_{2}}{3} = -\frac{1}{3}\frac{d[\mathrm{H}_{2}]}{dt} = \frac{\text{rate of production of NH}_{3}}{2} \]

Solve for the rate of consumption of hydrogen

Now, we will solve for the rate of consumption of hydrogen (H2) in terms of the rate of production of ammonia (NH3): \[ \text{rate of consumption of H}_{2} = 3\left(\frac{\text{rate of production of NH}_{3}}{2}\right) \]

Write the final relationship

The final relationship between the rate of production of ammonia and the rate of consumption of hydrogen is given by: \[ \text{rate of consumption of H}_{2} = \frac{3}{2} \times \text{rate of production of NH}_{3} \] This means that for every 1 mole of ammonia produced, 3/2 moles of hydrogen are consumed in the Haber process.