Question

The type of rate law for a reaction, either the differential rate law or the integrated rate law, is usually determined by which data is easiest to collect. Explain.

Short answer

The reaction rate is the measure of the change of concentration of reactants or products during the progression of a chemical reaction. Different rate laws are used to explain the reaction progress. These rate laws are expressed as mathematical relationships between different parameters

Step-by-step solution

Determine the differential rate law or integrated rate law. 

Differential rate law and integrated rate law are two forms of rate laws. The key difference between differential rate law and integrated rate law is that differential rate law gives the rate of a chemical reaction as a function of the change in concentration of one or more reactants during a particular time period, whereas integrated rate law gives the rate of a chemical reaction as a function of the initial concentration of one or more reactants after a specific period of time.

Determine the differential rate law equation

The differential rate law for the below chemical reaction can be given as a mathematical expression.

A → B + C

Rate = – {d[A] / dt} = k[A]ⁿ

Here, [A] is the concentration of reactant “A” and “k” is the rate constant. “n” gives the order of reaction. The differential rate law equation can be integrated to obtain a clear relationship between [A] and time “t”. This integration gives the integrated rate law.

Determine the integrated rate law equation

For the chemical reaction A → B + C, integrated rate law can be expressed as a mathematical expression as given below.

ln[A] = -kt + ln[A]₀

Here, [A]₀ is the initial concentration of the reactant A and [A] is the concentration of reactant “A” after “t” time has passed. However, integrated rate laws are different from each other based on the order of the reaction “n”. The above equation is given for zero order chemical reactions.

For first order reactions, the rate law equation is,

[A] = [A]e^-kt

For second order reactions, the rate law equation is,

1/[A] = 1/[A]₀ + kt

In order to determine the rate constant of a reaction, above equations can be used as follows.

For first order reactions,

$k=\left\{In\left[A\right]–In{\left[A\right]}_0\right\}/t$

For second order reactions,

$k=\left\{1/\left[A\right]–1/{\left[A\right]}_0\right\}/t$