This reaction is first order in N₂O₅: N₂O₅(g) → NO₃(g) + NO₂(g) The rate constant for the reaction at a certain temperature is 0.053/s. b. What would the rate of the reaction be at the concentration indicated in part a if the reaction were second order? Zero order? (Assume the same numerical value for the rate constant with the appropriate units.)

Verified step by step guidance

1. First, recall the rate law expressions for different orders of reactions. For a first-order reaction, the rate is given by: \( \text{Rate} = k[N_2O_5] \). For a second-order reaction, the rate is given by: \( \text{Rate} = k[N_2O_5]^2 \). For a zero-order reaction, the rate is given by: \( \text{Rate} = k \).
2. Next, identify the given rate constant \( k = 0.053 \text{ s}^{-1} \) for the first-order reaction. Assume the same numerical value for the rate constant for the second-order and zero-order reactions, but with appropriate units.
3. For the second-order reaction, the units of the rate constant \( k \) should be \( \text{M}^{-1}\text{s}^{-1} \). Use the rate law for a second-order reaction: \( \text{Rate} = k[N_2O_5]^2 \). Substitute the given concentration of \( N_2O_5 \) from part a into this equation to find the rate.
4. For the zero-order reaction, the units of the rate constant \( k \) should be \( \text{M}\text{s}^{-1} \). Use the rate law for a zero-order reaction: \( \text{Rate} = k \). The rate is independent of the concentration of \( N_2O_5 \).
5. Finally, calculate the rate for both the second-order and zero-order reactions using the appropriate rate laws and units for the rate constant.

Key Concepts

Reaction Order

Reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction. It indicates how the rate of reaction depends on the concentration of reactants. For example, a first-order reaction depends linearly on the concentration of one reactant, while a second-order reaction depends on the square of the concentration of that reactant. Understanding reaction order is crucial for predicting how changes in concentration affect the reaction rate.

Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentration of its reactants, each raised to a power corresponding to its order in the reaction. For a first-order reaction, the rate is directly proportional to the concentration of the reactant, while for a second-order reaction, the rate is proportional to the square of the concentration. The rate constant, which is specific to the reaction and temperature, is also included in the rate law, allowing for the calculation of reaction rates under different conditions.

Units of Rate Constant

The units of the rate constant (k) vary depending on the order of the reaction. For a first-order reaction, the units are typically s⁻¹, indicating that the rate is directly proportional to concentration. For a second-order reaction, the units are M⁻¹s⁻¹, reflecting that the rate depends on the product of two concentrations. Understanding these units is essential for correctly applying the rate law and calculating reaction rates for different orders.