13.4
Determining Order of Reaction
Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k…
For a chemical reaction, the rate law expresses the relationship between the reaction rate and reactant concentration. The exponents of the reactant concentrations influence the reaction rate individually and are called reaction orders.
The reaction order is determined experimentally by employing the method of initial rates, where a chemical reaction is repeated multiple times with varying reactant concentrations to measure the initial reaction rates.
An increase in the reactant concentration, producing a linearly-proportional increase in the reaction rate, characterizes a first-order reaction. If doubling the reactant concentration quadruples the initial rate, then a second-order reaction is observed.
However, if the change of reactant concentrations does not affect the initial rate values, then a zero-order reaction is observed.
When the obtained data of initial rates present an indiscernible relationship between the change in initial reactant concentration and the corresponding rate, a ratio of rate laws is calculated.
Here, any two concentration values of the reactant and their corresponding reaction rates are used to determine the reaction order.
But what about reactions with multiple reactants? First, using the method of initial rates, the reaction order of each reactant is determined individually.
Next, the individual reaction orders are expressed as exponents to their respective reactant concentrations to formulate the rate law. Lastly, the summation of individual exponents from the rate law determines the overall reaction order.
While the reaction order depicts the reaction rate’s dependence on the reactant concentration, a direct measure of the relative reaction speed is indicated by the rate constant.
The rate constant k, is the proportionality coefficient relating the reaction rate to the product of reactant concentrations.
The unit of a rate constant depends on the overall reaction order and can be determined by rearranging the rate law to solve for the rate constant. For a zero-order reaction, k has the unit molarity per seconds. The unit for a first-order reaction is 1/s, and for a second-order reaction it is 1/M·s.
A large rate constant indicates a fast reaction. Conversely, a smaller rate constant indicates a slow reaction. A value of zero signifies the absence of any chemical reaction.
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Q1: What is the method of initial rates and how is it used to determine reaction order?
The method of initial rates involves repeating a chemical reaction multiple times with varying reactant concentrations to measure initial reaction rates. By comparing how the rate changes when concentration changes, you can determine the reaction order for each reactant. If doubling concentration doubles the rate, the reaction is first-order; if it quadruples the rate, it is second-order.
Q2: How do you determine the overall reaction order for a reaction with multiple reactants?
First, use the method of initial rates to determine the reaction order of each reactant individually by varying one reactant while keeping others constant. Then express these individual orders as exponents in the rate law equation. The overall reaction order equals the sum of all individual exponents from the rate law.
Q3: What does the rate constant represent and how does its value relate to reaction speed?
The rate constant k is the proportionality coefficient in the rate law that relates reaction rate to reactant concentrations. A large rate constant indicates a fast reaction, while a smaller rate constant indicates a slow reaction. A value of zero signifies the absence of any chemical reaction.
Q4: Why do rate constant units vary depending on the overall reaction order?
Rate constant units depend on the overall reaction order because the rate law must always produce rate units of mol/L·s. For zero-order reactions, k has units of mol/L·s. For first-order, k is 1/s. For second-order, k is 1/M·s. The units adjust so that multiplying k by concentration terms yields the correct rate units.
Q5: What is a ratio of rate laws and when is it used?
A ratio of rate laws is an algebraic approach used when initial rate data does not directly show the relationship between concentration and rate. By dividing one rate law equation by another using data from two different trials, concentration terms cancel out, allowing you to solve for the reaction order without calculating the rate constant first.
Q6: How do you calculate the rate constant once you know the reaction order?
Once you determine the reaction order and formulate the rate law, substitute the concentration and rate values from any experimental trial into the rate law equation. Solve algebraically for k. The units of k are determined by rearranging the rate law so that rate units of mol/L·s are produced when k is multiplied by the concentration terms.
Q7: Can reaction orders be predicted from the stoichiometric coefficients in a chemical equation?
No. Although reaction orders sometimes coincidentally match stoichiometric coefficients, this is not reliable. Rate laws may exhibit fractional orders or negative orders, and they are determined experimentally only. Stoichiometry alone cannot predict how reactant concentration affects reaction rate. The integrated rate law the dependence of concentration on time provides predictive tools instead.