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 and the rate of consumption of hydrogen is given by: \[ R_{H_2} = \frac{3}{2} R_{NH_3} \] This means that for every 2 moles of ammonia produced, 3 moles of hydrogen are consumed.

Step-by-step solution

Identify stoichiometric coefficients

The balanced chemical equation for the Haber process is given by: \[ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \] The stoichiometric coefficients are as follows: - Nitrogen (N₂): 1 - Hydrogen (H₂): 3 - Ammonia (NH₃): 2

Write the rates of substances

Let's define the rate of production of ammonia as \(R_{NH_3}\), the rate of consumption of hydrogen as \(R_{H_2}\), and the rate of consumption of nitrogen as \(R_{N_2}\). Now we will use the stoichiometric coefficients to write the rates for each substance in the reaction: \[ -R_{N_2} = \frac{-1}{1} \cdot R_{NH_3} \] \[ -R_{H_2} = \frac{-3}{2} \cdot R_{NH_3} \]

Find the relationship between ammonia and hydrogen rates

Now that we have the rates of ammonia and hydrogen written in terms of their stoichiometric coefficients, we can find the relationship between these two rates by comparing their equations. Using the equation for hydrogen, we get: \[ R_{H_2} = \frac{3}{2} \cdot R_{NH_3} \] So, the relationship between the rate of production of ammonia and the rate of consumption of hydrogen is: \[ R_{H_2} = \frac{3}{2} R_{NH_3} \] This means that for every 2 moles of ammonia produced, 3 moles of hydrogen are consumed.