Question

The rate constant is numerically the same for the reactions of first , second and third order respectively. Which one is true for the rates of the three reactions if the concentration of the reactant is greater than $1M$ ?
A . ${r_1} = {r_2} = {r_3}$
B. ${r_1} > {r_2} > {r_3}$
C. ${r_1} < {r_2} < {r_3}$
D. None of the above

Answer 1

Hint: We all know that rate of a reaction can be written as $R = k{[M]^n}$ , where $R = $ rate of the reaction, $k = $ rate constant of the reaction , $M = $ concentration of the reactant , $n = $ order of the reaction. The unit of the rate constant of a reaction is $mo{l^{(1 - n)}}{L^{(n - 1)}}{s^{ - 1}}$.

Complete step by step solution:
As in the question, the given information and data are that the rate constant is numerically the same for the reactions of first ,second and third order respectively. The concentration of the reactant is greater than $1M$ . Now we have to find the relation between the rate of the given three reactions.
Rate of a reaction can be written as : $r = k{[M]^n}$ ,
According to question the value of $k$ is equal for the reactions and the value of concentration is greater than $1M$ .
So the rate of reaction of the given reaction will be ${r_1} = k{[M]^1},{r_2} = k{[M]^2},{r_3} = k{[M]^3}$.
As concentration of the reactant is greater than $1M$ this implies ${r_3} > {r_2} > {r_1}$ .
So according to above explanation and calculation

The correct answer of the question is C.

Additional information:
The definition of rate of reaction is that at what rate or speed the reaction is happening .In other words at what rate the reactants are being converted to products. The order of a reaction is the power dependence of the rate on reactant.

Note: Always remember that the rate of a reaction is given by $R = k{[M]^n}$ . The unit of rate constant depends on the order of the reaction. If we are given a particular rate law equation and asked to identify the order of the reaction , we can directly find out by observing the unit if the rate constant. The rate constant is $mo{l^{(1 - n)}}{L^{(n - 1)}}{s^{ - 1}}$ . Here $n$ is the order of the reaction and $n$ will be $1$ for first order , $2$ for second order and so on.