What are the units of k for each type of reaction?
a. first-order reaction
b. second-order reaction
c. zero-order reaction

Verified step by step guidance

1. Identify the type of reaction: In this case, it's a second-order reaction.
2. Understand the rate law for a second-order reaction: The rate law for a second-order reaction can be expressed as \(rate = k[A]^2\) or \(rate = k[A][B]\), where [A] and [B] are the concentrations of the reactants.
3. Analyze the units of rate and concentration: The rate of reaction is typically measured in \(\text{mol L}^{-1} \text{s}^{-1}\), and concentration is measured in \(\text{mol L}^{-1}\).
4. Set up the equation to find the units of k: Using the rate law, substitute the units into the equation. For example, if the rate law is \(rate = k[A]^2\), then substituting the units gives \(\text{mol L}^{-1} \text{s}^{-1} = k(\text{mol L}^{-1})^2\).
5. Solve for the units of k: Rearrange the equation to isolate k, which results in the units of k being \(\text{L mol}^{-1} \text{s}^{-1}\) for a second-order reaction.

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 second-order reaction means that the rate is proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. Its units vary depending on the order of the reaction. For a second-order reaction, the units of k are typically expressed as M^-1 s^-1, indicating that the rate depends on the concentration squared.

Units of Measurement in Chemistry

Units of measurement in chemistry are essential for quantifying concentrations, rates, and other properties. In the context of reaction kinetics, understanding how to derive the units of k based on the reaction order is crucial. For second-order reactions, the units of k reflect the need to balance the rate (M/s) with the concentration terms, leading to the specific units of M^-1 s^-1.