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 (\(R_{NH_3}\)) and the rate of consumption of hydrogen (\(R_{H_2}\)) in the Haber process is given by: \( R_{NH_3}=\frac{2}{3} R_{H_2} \). This means that the rate of production of ammonia is 2/3 times the rate of consumption of hydrogen.

Step-by-step solution

Analyze the balanced chemical equation

For the Haber process, the balanced chemical equation is given by: \[ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \] The stoichiometry of the equation tells us that 1 mole of nitrogen (N₂) reacts with 3 moles of hydrogen (H₂) to produce 2 moles of ammonia (NH₃).

Express the rate of production of ammonia as a function of the rate of consumption of hydrogen

We can use the stoichiometry to write the relationship between the rate of production of ammonia (NH₃) and the rate of consumption of hydrogen (H₂). 1 mole of N₂ reacts with 3 moles of H₂ to produce 2 moles of NH₃, which means that the ratio of moles of NH₃ produced to moles of H₂ consumed is 2:3. Let's denote the rate of production of ammonia by \(R_{NH_3}\) and the rate of consumption of hydrogen by \(R_{H_2}\). Therefore, the relationship between the rate of production of ammonia and the rate of consumption of hydrogen is given by: \( \frac{R_{NH_3}}{2}=\frac{R_{H_2}}{3} \)

Solve for the rate of production of ammonia

Now, let's solve for the rate of production of ammonia, \(R_{NH_3}\), in terms of the rate of consumption of hydrogen, \(R_{H_2}\). We can rearrange the equation in Step 2 to find the rate of production of ammonia: \(R_{NH_3}=2\times\frac{R_{H_2}}{3}\)

Write the final relationship

The relationship between the rate of production of ammonia and the rate of consumption of hydrogen in the Haber process is given by: \[ R_{NH_3}=\frac{2}{3} R_{H_2} \] This equation states that the rate of production of ammonia is 2/3 times the rate of consumption of hydrogen.

Key concepts

Ammonia Production

The Haber process is a critical industrial reaction for producing ammonia. Ammonia is essential for fertilizers, which are widely used in agriculture to enhance crop yields. The process involves combining nitrogen gas (\( \text{N}_2(g) \)) from the air with hydrogen gas (\( \text{H}_2(g) \)) under high pressure and temperature, in the presence of an iron catalyst. This setup makes the Haber process highly efficient, ensuring that large amounts of ammonia can be produced. The reaction is represented by the equation: \( \text{N}_2(g) + 3\text{H}_2(g) \longrightarrow 2\text{NH}_3(g) \). This shows that one molecule of nitrogen reacts with three molecules of hydrogen to form two molecules of ammonia. Understanding this process is essential for industries focused on supplying fertilizers.

Stoichiometry

Stoichiometry is the calculus behind chemical reactions. It helps determine the relationship between reactants and products. In the Haber process equation, \( \text{N}_2(g) + 3 \text{H}_2(g) \longrightarrow 2 \text{NH}_3(g) \), the stoichiometric coefficients (1, 3, and 2) provide the ratio of molecules involved. It means that for every mole of nitrogen gas, three moles of hydrogen gas are required to produce two moles of ammonia.

• This ratio is crucial for calculating material quantities needed in industrial settings.
• It helps optimize resource usage, minimizing waste, and reducing costs.

By mastering stoichiometry, engineers can ensure efficient chemical productions and maintain a balanced resource input and output.

Reaction Rates

Reaction rates describe how quickly reactants transform into products in a chemical reaction. For the Haber process, the reaction rate is crucial for optimizing the production of ammonia. In the given balanced equation, \( \text{N}_2(g) + 3 \text{H}_2(g) \longrightarrow 2 \text{NH}_3(g) \), one key focus is the rate at which ammonia is produced compared to the rate hydrogen is consumed.

• According to the stoichiometric relationship, for every three moles of hydrogen consumed, two moles of ammonia are formed.
• This gives us the relationship: \( R_{NH_3} = \frac{2}{3} R_{H_2} \).

This formula can help chemists adjust conditions like pressure and temperature to achieve optimal ammonia production rates.

Balanced Chemical Equation

Balancing a chemical equation is a fundamental skill in chemistry. It ensures that atoms are conserved during a reaction. In the Haber process, the balanced equation is crucial for understanding how reactants and products relate. The equation is:\( \text{N}_2(g) + 3\text{H}_2(g) \longrightarrow 2\text{NH}_3(g) \), where the balancing coefficients (1, 3, and 2) show the molar relationship.

• Each side of the equation has an equal number of nitrogen (N) and hydrogen (H) atoms.
• This balance adheres to the law of conservation of mass, meaning atoms are neither created nor destroyed.

Understanding and applying balanced equations ensures that calculations and experimental setups are accurate, leading to successful chemical processing.