Question
Consider the reaction $aX \rightarrow bY$, for which the rate constant at $30^{\circ}C$ is $1 \times 10^{- 3}{\text{ }mol}^{- 1}{Ls}^{- 1}$. Which of the following statements are true?
A. When concentration of ' X ' is increased to four times, the rate of reaction becomes 16 times.
B. The reaction is a second order reaction.
C. The half-life period is independent of the concentration of X.
D. Decomposition of $N_{2}O_{5}$ is an example of the above reaction.
E. 
is valid for the above reaction.
Choose the correct answer from the options given below:
Options
Solution
Sol. [Key Concept: The unit of $k$ fixes the order ($n = 2$ here); then test each statement.]
Rate of constant $(k) = 10^{- 3}M^{- 1}\sec^{- 1}$
$\because 1 - n = - 1$ [unit of $k = M^{1 - n}\sec^{- 1}$ ]
$n = 2 \Rightarrow 2^{\text{nd}\text{~}}$ order reaction
rate $= k\lbrack A\rbrack^{2}$
A) If concentration of A is 4 times then reaction will become 16 times.
B) Order of reaction is 2
C) Half-life of the reaction is independent of the concentration of the reactant for $1^{\text{st}\text{~}}$ order, not for $2^{\text{nd}\text{~}}$ order reaction.
D) Decomposition of $N_{2}O_{5}$ is example of $1^{\text{st}\text{~}}$ order reaction
E) Graph of $\mathcal{l}n\frac{\lbrack R\rbrack_{0}}{\lbrack R\rbrack_{t}}$ vs t is straight line for $1^{\text{st}\text{~}}$ order not for $2^{\text{nd}\text{~}}$ order reaction.
So, statement (A)& (B) are correct
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