Q42 / 180 · COMEDK 2025 (10 May Shift 3) · Chemistry
Choose the correct statement.
- AMolecularity of a chemical reaction is always greater than order of the reaction.
- BThe plot of [A] versus time "t" for a zero order reaction is a horizontal line parallel to the x -axis which represents " t "
- Correct answerCFor a first order reaction the time taken for $3 / 4^{\text {th }}$ completion is 2 times the half-life period.
- DFor a second order reaction the rate of reaction with respect to reactant becomes 27 times when its concentration is tripled.
Solution
Molecularity is the number of reacting species taking part in an elementary reaction and is always a positive integer, whereas order of reaction can be fractional or zero. Thus, molecularity is not always greater than the order of reaction.
For a zero order reaction, the rate law is $[A] = [A]_0 - kt$. The plot of $[A]$ versus $t$ is a straight line with a negative slope $-k$ and y-intercept $[A]_0$, not a horizontal line.
For a first order reaction, the half-life is $t_{1/2} = \dfrac{\ln 2}{k}$. The time for $3/4^{th}$ completion is $t_{3/4} = \dfrac{1}{k} \ln \left( \dfrac{[A]_0}{[A]_0/4} \right) = \dfrac{\ln 4}{k} = \dfrac{2 \ln 2}{k} = 2 t_{1/2}$. This statement is correct.
For a second order reaction, the rate is $r = k[A]^2$. If the concentration is tripled, the new rate becomes $r' = k(3[A])^2 = 9k[A]^2 = 9r$. The rate becomes 9 times, not 27 times.
Answer: For a first order reaction the time taken for $3 / 4^{\text {th }}$ completion is 2 times the half-life period.
For a zero order reaction, the rate law is $[A] = [A]_0 - kt$. The plot of $[A]$ versus $t$ is a straight line with a negative slope $-k$ and y-intercept $[A]_0$, not a horizontal line.
For a first order reaction, the half-life is $t_{1/2} = \dfrac{\ln 2}{k}$. The time for $3/4^{th}$ completion is $t_{3/4} = \dfrac{1}{k} \ln \left( \dfrac{[A]_0}{[A]_0/4} \right) = \dfrac{\ln 4}{k} = \dfrac{2 \ln 2}{k} = 2 t_{1/2}$. This statement is correct.
For a second order reaction, the rate is $r = k[A]^2$. If the concentration is tripled, the new rate becomes $r' = k(3[A])^2 = 9k[A]^2 = 9r$. The rate becomes 9 times, not 27 times.
Answer: For a first order reaction the time taken for $3 / 4^{\text {th }}$ completion is 2 times the half-life period.
Hence, the correct answer is option: 'C'.