For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product: (c) N21g2 + 3 H21g2¡2 NH31g2

Verified step by step guidance

1. Write the balanced chemical equation for the reaction: N2(g) + 3 H2(g) → 2 NH3(g).
2. Identify the stoichiometric coefficients from the balanced equation: 1 for N2, 3 for H2, and 2 for NH3.
3. Apply the relationship that the rate of disappearance of reactants is proportional to their stoichiometric coefficients. For N2, the rate of disappearance is -\(\frac{d[N2]}{dt}\) and for H2, it is -\(\frac{d[H2]}{dt}\).
4. Apply the relationship that the rate of appearance of products is also proportional to their stoichiometric coefficients. For NH3, the rate of appearance is +\(\frac{d[NH3]}{dt}\).
5. Relate the rates using the stoichiometric coefficients: \(\frac{1}{1}\frac{d[N2]}{dt} = \frac{1}{3}\frac{d[H2]}{dt} = \frac{1}{2}\frac{d[NH3]}{dt}\). This shows how the disappearance of N2 and H2 is related to the appearance of NH3.

Key Concepts

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the balanced chemical equation, which indicates the proportions in which substances react and are produced. In the given reaction, the coefficients (1 for N2, 3 for H2, and 2 for NH3) dictate how the rates of disappearance and appearance are related.

Rate of Reaction

The rate of reaction refers to the speed at which reactants are converted into products. It can be expressed in terms of the change in concentration of a reactant or product over time. For the reaction provided, the rate of disappearance of N2 and H2 will be related to the rate of appearance of NH3, following the stoichiometric coefficients.

Rate Law

The rate law is an equation that relates the rate of a reaction to the concentration of its reactants, often expressed in the form rate = k[A]^m[B]^n, where k is the rate constant and m and n are the orders of the reaction with respect to each reactant. Understanding the rate law helps in determining how changes in concentration affect the rates of disappearance and appearance in the reaction.