In the given balanced chemical equation:

$\text{N}_2(g) + 3 \text{H}_2(g) \rightarrow 2 \text{NH}_3(g)$

The rate of reaction with respect to nitrogen $[N_2]$ is defined as the change in concentration of $N_2$ over time. Since the stoichiometry of the reaction involves one mole of nitrogen reacting with three moles of hydrogen to produce two moles of ammonia, we can express the rate of reaction in terms of nitrogen as:

$\text{Rate} = -\frac{d[\text{N}_2]}{dt}$

The negative sign indicates that the concentration of nitrogen is decreasing as the reaction proceeds.

Relative Rates of Other Species:

• For $\text{H}_2$, the rate of reaction is:

  $\text{Rate} = -\frac{1}{3} \frac{d[\text{H}_2]}{dt}$

• For $\text{NH}_3$, the rate of reaction is:

  $\text{Rate} = \frac{1}{2} \frac{d[\text{NH}_3]}{dt}$

All of these rates are related through the stoichiometric coefficients of the balanced equation.

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Would you like more details on how to calculate the rate, or clarification on any specific part?

Here are 5 questions to extend your understanding:

1. How do you experimentally determine the rate of reaction?
2. What factors affect the rate of reaction for this system?
3. How do the rates of formation of $NH_3$ and consumption of $H_2$ compare?
4. How does temperature affect the rate of this reaction?
5. What role do catalysts play in the reaction rate for this equation?

Tip: Always remember that the rate of a reaction is influenced by the concentrations of the reactants and may vary over time.