Question

Consider the reaction: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ Suppose that at a particular moment during the reaction molecular hydrogen is reacting at the rate of \(0.082 \mathrm{M} / \mathrm{s}\). (a) At what rate is ammonia being formed? (b) At what rate is molecular nitrogen reacting?

Short answer

(a) 0.0547 M/s; (b) 0.0273 M/s.

Step-by-step solution

Identify the Stoichiometry

The balanced chemical equation given is \( \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g) \). This means that for every 1 mole of \( \mathrm{N}_{2} \), 3 moles of \( \mathrm{H}_{2} \) are consumed to produce 2 moles of \( \mathrm{NH}_{3} \).

Calculate the Rate of Ammonia Formation

Given that hydrogen is reacting at \( 0.082 \mathrm{M/s} \), use the stoichiometry of the reaction to find the rate of ammonia formation. According to the reaction, \( 3 \mathrm{H}_{2} \) forms \( 2 \mathrm{NH}_{3} \), so the rate of ammonia formation is \( \frac{2}{3} \times 0.082 = 0.0547 \mathrm{M/s} \).

Calculate the Rate of Nitrogen Reaction

Use the stoichiometry given: 1 mole of \( \mathrm{N}_{2} \) reacts for every 3 moles of \( \mathrm{H}_{2} \). So, the rate of \( \mathrm{N}_{2} \) reacting is \( \frac{1}{3} \times 0.082 = 0.0273 \mathrm{M/s} \).

Key concepts

Rate of Reaction

The rate of reaction describes how fast or slow a reaction takes place. It's essential for understanding how quickly products are formed or reactants are used up in a chemical process. You can think of it as the speed at which the chemical transformations occur. The rate is often measured in molarity per second (M/s), indicating the concentration change over time.

To determine these rates, we utilize stoichiometry from the balanced chemical equation. For the reaction \( \mathrm{N}_{2}(g) + 3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g) \), the rates can be interrelated:

• The rate of hydrogen reacting helps us determine the rate of ammonia formation using molar ratios.
• A higher stoichiometric coefficient in the reaction equation means a faster rate of consumption or formation, relative to components with smaller coefficients.

Understanding the rate of reaction is crucial for predicting how long a reaction takes to reach completion, optimizing industrial processes, and safely conducting experiments.

Ammonia Formation

Ammonia formation is a critical process with wide industrial applications, notably in fertilizers. The chemical equation for this process is \( \mathrm{N}_{2}(g) + 3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g) \).

To find the rate at which ammonia is formed, we use the given rate of hydrogen consumption and apply stoichiometry:

• Given: Hydrogen reacts at \( 0.082 \mathrm{M/s} \).
• According to the stoichiometric ratios, 3 moles of hydrogen form 2 moles of ammonia.
• Thus, the rate of ammonia formation is \( \frac{2}{3} \times 0.082 \approx 0.0547 \mathrm{M/s} \).

This calculation helps predict how quickly we can obtain ammonia under given conditions, making it vital for ensuring efficiency in chemical production.

Chemical Equilibrium

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction. For ammonia formation, the equilibrium is dynamic, meaning reactions are continuously happening in both directions, but at equal rates.

Key features of chemical equilibrium include:

• No net change in the concentrations of reactants and products over time.
• Equilibrium can be shifted by changing factors like temperature, pressure, or concentration (Le Châtelier's principle).
• In ammonia formation, optimizing these conditions increases yield.

Understanding equilibrium helps in controlling reaction conditions to maximize product formation while minimizing waste, essential in industrial-scale production.