2.7
Rate Law and Reaction Order
The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressio…
For any reaction, the relationship between the reaction rate and the reactant concentrations can be expressed mathematically using a rate law or the rate equation.
In a rate law, ‘k’ is the proportionality constant, or the rate constant, and ‘n’ is the reaction order with respect to a single reactant, whose value is often an integer. In rate laws for multi-reactant reactions, the overall reaction order is the sum of all reactant orders.
For each reactant, the reaction rate, rate constant, concentration, and the reaction order are all determined experimentally.
Individual reactant orders commonly take the values 0, 1, or 2, and based on the overall reaction order, chemical reactions can be categorized as zero-order, first-order, or second-order reactions.
A single-reactant, or unimolecular, chemical reaction for which the reaction rate remains constant throughout its duration is a zero-order reaction. The reactant order in a zero-order reaction is zero, and the reactant concentration is raised to the zeroth power.
Since the value of any number raised to the zeroth power is one, the reaction rate of a zero-order reaction is equal to the rate constant and, hence, independent of the reactant concentration.
A unimolecular chemical reaction where the reaction rate is directly proportional to the reactant's concentration is a first-order reaction. The reactant order for a first-order reaction is one, and as per the rate law, the reactant’s concentration is raised to the first power.
Since the value of any number raised to the power of one remains the same, the reaction rate of a first-order reaction directly depends on the reactant concentration. As the reactant concentration decreases, the reaction rate decreases proportionally in a linear manner.
A unimolecular chemical reaction where the reaction rate is dependent on the square of the reactant’s concentration is a second-order reaction. As the reactant concentration decreases, the reaction rate decreases exponentially in a quadratic manner.
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Q1: What is a rate law and how does it relate to reaction rate?
A rate law is a mathematical expression describing the relationship between reaction rate and reactant concentrations. It takes the form rate = k[A]m[B]n, where k is the rate constant, and m and n are reaction orders determined experimentally. The rate constant is specific to a particular reaction at a specific temperature and is independent of reactant concentrations.
Q2: How is reaction order determined experimentally?
Reaction order is determined through the method of initial rates, which involves measuring reaction rates for multiple trials using different initial reactant concentrations. By comparing measured rates across trials, chemists determine individual reaction orders for each reactant and calculate the rate constant. Rate laws are determined by experiment only and cannot be reliably predicted by reaction stoichiometry.
Q3: What is the difference between zero-order and first-order reactions?
In a zero-order reaction, the reaction rate remains constant throughout and is independent of reactant concentration because the concentration is raised to the zeroth power. In a first-order reaction, the reaction rate is directly proportional to reactant concentration. As reactant concentration decreases, the first-order reaction rate decreases proportionally in a linear manner.
Q4: How does reactant concentration affect second-order reaction rates?
In a second-order reaction, the reaction rate depends on the square of the reactant's concentration. As the reactant concentration decreases, the reaction rate decreases exponentially in a quadratic manner, not linearly. This exponential relationship distinguishes second-order reactions from first-order reactions.
Q5: What is the overall reaction order and how is it calculated?
The overall reaction order is the sum of individual reaction orders for all reactants in a rate law. For example, in the rate law rate = k[A]1[B]2, the reaction is first order in A and second order in B, making it third order overall (1 + 2 = 3). Overall reaction order determines how the combined concentrations affect the total reaction rate.
Q6: Can reaction orders be fractional or negative values?
Yes, reaction orders can be fractional, negative, or zero, though positive integers are most common. Fractional orders occur in complex reactions, while negative reaction orders are sometimes observed when an increase in one reactant's concentration causes a decrease in reaction rate. These unusual orders are determined experimentally and reflect the actual mathematical dependence of rate on concentration.
Q7: Why does the rate constant vary with temperature?
The rate constant k is independent of reactant concentrations but varies with temperature because higher temperatures provide more molecular energy. This temperature dependence is described by the Arrhenius equation and relates to bond dissociation energy and activation energy. Understanding the effect of temperature change on reaction rate is essential for predicting reaction behavior under different conditions.