Question

For a chemical reaction, \[mA \to xB\], the rate law is $r = k{[A]^2}$. If the concentration of A is doubled, the reaction rate will be:
A. Unchanged
B. Increases by $8$ times
C. Quadrupled
D. Doubled

Answer 1

Hint: As we know that the rate of a reaction depends on the concentration of the reactant and the order of reaction is the power which is raised in different concentration terms in rate expression. Here, the order of reaction is $2$.

Complete step by step solution:
As we have already discussed, the rate of any reaction is the rate of change of concentration of any one of the reactants. As we know that it depends upon the concentration of its reactants, so if we change the concentration, the rate of reaction will automatically change.
Now, in the question we are provided with the rate law as $r = k{[A]^2}$. And, in the rate law, the rate is expressed in terms of concentration which actually influences the rate of reaction.
So, let us assume that the initial concentration of A is \[x\]. Hence, we can write the rate of the reaction as:
 ${r_{initial}} = k{[x]^2}$

But if we increase the concentration of A and double it, then the rate of the reaction will become as:
${r_{final}} = k{[2x]^2}$
${r_{final}} = k \times 4{x^2}$
Now comparing both the rates of the reaction we would get:
$\dfrac{{{r_{initial}}}}{{{r_{final}}}} = \dfrac{{k{x^2}}}{{4k{x^2}}}$
${r_{final}} = 4 \times {r_{initial}}$
Thus, from the above explanation we can say that if the concentration of A is doubled, then the rate of reaction becomes quadrupled.

Therefore, the correct answer is option C.

Note: Always remember that the rate law is the expression in which reaction rate is given in terms of molar concentrations of reactants with each term raised to some power which may or may not be the same as stoichiometric coefficient of the reacting species in a balanced chemical equation. And the reaction rate depends upon the nature of reactant, concentration of the reactant, temperature and catalyst. When temperature is increased, reaction rate increases.