Question

The rate constant of a reaction is $K = 3.4 \times {10^{ - 4}}mo{l^{ - 1}}L{\sec ^{ - 1}}$ . What is the order of the reaction?

Answer 1

Hint: Rate constant is simply the measure of the rate of reaction. Greater is the value of rate constant, faster is the reaction. Rate constant may be defined as the rate of the reaction when the concentration of each reactant is taken as unity.

Complete answer:
Rate law is the expression which expresses the rate of reaction in terms of molar concentrations of the reactants with each term raised to some power, which may or may not be the same as the stoichiometric coefficient of that reactant in the balanced chemical equation.
The sum of the exponents to which the concentration terms in the rate law equations are raised to express the observed rate of the reaction is called the order of the reaction.
Let’s consider a reaction;
$A \to B$
According to rate law;
$Rate$ $\alpha $ ${[A]^n}$ (where n= order of the reaction)
$Rate = K{[A]^n}$ (K= rate constant)
We know that the rate of reaction is change in concentration of any one of the reactant or product per unit time. Thus, we can write
$\dfrac{{concentration}}{{time}} = K{[concentration]^n}$
$K = {[concentration]^{1 - n}}{[time]^{ - 1}}$ ( concentration is usually in $mol{L^{ - 1}}$ and time is in sec)
We can use the units of rate constant $\left( K \right)$ in order to find the order of the reaction.
The rate constant given in the question is;
$K = 3.4 \times {10^{ - 4}}mo{l^{ - 1}}L{\sec ^{ - 1}}$
Using the formula;
Let’s put the value of n = $2$
$K = {[mol{L^{ - 1}}]^{1 - 2}}{[\sec ]^{ - 1}}$
We’ll get; $K = mo{l^{ - 1}}L{\sec ^{ - 1}}$
Which is exactly equal to the units of rate constant given in the question.
Thus, the order of the reaction is $2$

Note:
The order of the reaction can be easily determined by looking at the units of rate constant. $K = mol{L^{ - 1}}{\sec ^{ - 1}}$ is for zero order reaction. $K = {\sec ^{ - 1}}$ unit of rate constant corresponds to the first order reaction.