For a first order reaction,the time required | vedclass

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

Question

(C) For a first order reaction,the rate constant $K$ is given by $K = \frac{0.693}{t_{1/2}}$.The time $t$ required for a reaction to complete $90 \%$

Vedclass · Accepted Answer

$3.32$

Vedclass · Answer

(C) For a first order reaction,the rate constant $K$ is given by $K = \frac{0.693}{t_{1/2}}$.The time $t$ required for a reaction to complete $90 \%$ is given by $t_{90\%} = \frac{2.303}{K} \log \left( \frac{100}{100 - 90} ight) = \frac{2.303}{K} \log 10 = \frac{2.303}{K}$.Substituting $K = \frac{\ln 2}{t_{1/2}} = \frac{0.693}{t_{1/2}}$ into the equation:$t_{90\%} = \frac{2.303}{0.693} 	imes t_{1/2}$.Since $2.303 \approx \ln 10$ and $0.693 \approx \ln 2$,we have $t_{90\%} = \frac{\ln 10}{\ln 2} 	imes t_{1/2} = \frac{2.303}{2.303 	imes 0.3010} 	imes t_{1/2} = \frac{1}{0.3010} 	imes t_{1/2} \approx 3.32 	imes t_{1/2}$.Therefore,$x = 3.32$.

$S$.No.	Time	Total pressure in Pascal
$1$.	At the end of $10 \ min$	$300$
$2$.	After completion	$200$

For a first order reaction,the time required for completion of $90 \%$ reaction is '$x$' times the half life of the reaction. The value of '$x$' is $........$. (Given: $\ln 10 = 2.303$ and $\log 2 = 0.3010$)

Similar Questions

The following data is obtained during the first order thermal decomposition of $2A_{(g)} \longrightarrow B_{(g)} + C_{(s)}$ at constant volume and temperature. The rate constant in $min^{-1}$ is:
$S$.No. Time Total pressure in Pascal
$1$. At the end of $10 \ min$ $300$
$2$. After completion $200$

For a first order reaction $A \rightarrow \text{Products}$,initial concentration of $A$ is $0.1 \, M$,which becomes $0.001 \, M$ after $5 \, \min$. Rate constant for the reaction in $\min^{-1}$ is .... .

The time of completion of $90\%$ of a first order reaction is approximately

The rate equation for a first-order reaction is given by $[R] = [R]_0 e^{-kt}$. $A$ straight line with a positive slope is obtained by plotting: ($[R]_0 =$ initial concentration of reactant,$[R] =$ concentration of reactant at time $t$)

In a first order reaction,the concentration of the reactant is reduced to $25\%$ in one hour. The half-life period of the reaction is: (in $hr$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module