The ratio of t_{0.75} and t_{0.5} for a first | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a first-order reaction,the time $t$ required for a fraction of reaction to complete is given by $t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$

Vedclass · Accepted Answer

$2 : 1$

Vedclass · Answer

(C) For a first-order reaction,the time $t$ required for a fraction of reaction to complete is given by $t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$.For $t_{0.5}$ (half-life),$[A]_t = 0.5[A]_0$,so $t_{0.5} = \frac{2.303}{k} \log 2$.For $t_{0.75}$,$[A]_t = 0.25[A]_0$,so $t_{0.75} = \frac{2.303}{k} \log \frac{[A]_0}{0.25[A]_0} = \frac{2.303}{k} \log 4 = \frac{2.303}{k} \log 2^2 = 2 	imes \frac{2.303}{k} \log 2$.Therefore,$t_{0.75} = 2 	imes t_{0.5}$.The ratio $\frac{t_{0.75}}{t_{0.5}} = \frac{2}{1}$ or $2 : 1$.

The ratio of $t_{0.75}$ and $t_{0.5}$ for a first-order reaction is:

Similar Questions

The half-life period of a first order reaction is $15 \ minutes$. The amount of substance left after one hour will be

An organic compound undergoes first order decomposition. If the time taken for the $60 \%$ decomposition is $540 \ s$,then the time required for $90 \%$ decomposition will be $.......... \ s$. (Nearest integer). Given : $\ln 10 = 2.3 ; \log 2 = 0.3$

For which order reaction,the unit of rate constant is $\text{time}^{-1}$?

The half-life of a first order reaction $X \to Y$ is $100 \ min$. The concentration of $X$ would be reduced to $10 \%$ of the initial concentration in .......... $min$.

The plot of $t_{1/2}$ versus $[R]_0$ for a reaction is a straight line parallel to the $x$-axis. The unit for the rate constant of this reaction is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module