13.3
Concentration and Rate Law
The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressio…
The rate of a reaction often depends on the reactant concentrations. 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. The rate law expresses the relationship between all these parameters.
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 according to the rate law, 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. Therefore, in a zero-order reaction, even as the reactant's concentration decreases, the reaction rate does not slow down.
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. The reactant order is two, and the reactant concentration is raised to the second power.
Accordingly, the reaction rate in a second-order reaction directly depends on the square of the reactant concentration. 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 reactant concentration?
A rate law is a mathematical expression describing the relationship between reaction rate and reactant concentrations. It expresses how the rate depends on the concentration of each reactant raised to a specific power, called the reaction order. The rate law includes the rate constant k, which is specific to a particular reaction at a given temperature, and the reaction orders for each reactant, which are determined experimentally.
Q2: How are reaction orders and the rate constant determined experimentally?
Reaction orders and the rate constant are determined by observing how the reaction rate changes as reactant concentrations vary. A common experimental approach is the method of initial rates, which involves measuring reaction rates using different initial reactant concentrations. Comparing these measured rates allows chemists to determine the reaction orders and subsequently calculate the rate constant to formulate the rate law.
Q3: What happens to the reaction rate in a zero-order reaction as reactant concentration decreases?
In a zero-order reaction, the reaction rate remains constant throughout and is independent of reactant concentration. Since the reactant concentration is raised to the zeroth power in the rate law, any number raised to zero equals one, making the rate equal to the rate constant alone. Therefore, even as the reactant concentration decreases, the reaction rate does not slow down.
Q4: How does reactant concentration affect the rate of a first-order reaction?
In a first-order reaction, the reaction rate is directly and linearly proportional to reactant concentration. The reactant concentration is raised to the first power in the rate law, so the rate depends directly on the concentration value. As the reactant concentration decreases, the reaction rate decreases proportionally in a linear manner.
Q5: Why does a second-order reaction rate decrease exponentially as concentration drops?
In a second-order reaction, the reactant concentration is raised to the second power in the rate law, making the rate dependent on the square of the concentration. This quadratic relationship means small changes in concentration produce larger changes in rate. As reactant concentration decreases, the reaction rate decreases exponentially rather than linearly, following the squared concentration term.
Q6: What is the overall reaction order and how is it calculated?
The overall reaction order is the sum of the individual reaction orders for all reactants in the rate law. For example, in a reaction that is first-order in reactant A and second-order in reactant B, the overall reaction order is three (1 + 2 = 3). The overall order determines the mathematical dependence of the reaction rate on all reactant concentrations combined.
Q7: Can reaction orders be predicted from the stoichiometric coefficients of a reaction?
No, reaction orders cannot be reliably predicted from stoichiometric coefficients. Rate laws are determined by experiment only and must be established through direct observation of how reaction rates change with concentration. Reaction orders can be integers, fractions, negative, or zero, and this experimental determination is essential for accurately describing reaction kinetics.