Medium INTEGER +4 / -1 PYQ · JEE Mains 2024

Consider the two different first order reactions given below

$$\begin{aligned} & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C} \text { (Reaction 1) } \\ & \mathrm{P} \rightarrow \mathrm{Q} \text { (Reaction 2) } \end{aligned}$$

The ratio of the half life of Reaction 1 : Reaction 2 is $5: 2$ If $t_1$ and $t_2$ represent the time taken to complete $2 / 3^{\text {rd }}$ and $4 / 5^{\text {th }}$ of Reaction 1 and Reaction 2 , respectively, then the value of the ratio $t_1: t_2$ is _________ $\times 10^{-1}$ (nearest integer). [Given : $\log _{10}(3)=0.477$ and $\log _{10}(5)=0.699$]

Answer (integer) 17

Solution

<p>$\mathrm{A+B \rightarrow C}$ Reaction .... (1)</p> <p>$\mathrm{P} \rightarrow \mathrm{Q} \quad$ Reaction .... (2)</p> <p>$$\frac{\left(t_{\frac{1}{2}}\right)_1}{\left(t_{\frac{1}{2}}\right)_2}=\frac{k}{k_1}= \frac{5}{2}$$</p> <p>$$\begin{aligned} & \frac{\frac{t_2}{3}}{t_{\frac{4}{5}}^5}=\frac{k_2}{k_1} \frac{\log 3}{\log 5} \\ & =\left(\frac{5}{2}\right) \frac{0.477}{0.699}=1.7 \\ & =17 \times 10^{-1} \\ & =x=17 \end{aligned}$$</p>

About this question

Subject: Chemistry · Chapter: Chemical Kinetics · Topic: Rate of Reaction

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