(C) For a first order reaction,the rate law is given by $-\frac{d[A]}{dt} = k[A]$.Integrating this expression from time $t=0$ (where $[A] = a$) to tim

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$k = \frac{2.303}{t} \log \frac{a}{a-x}$

(C) For a first order reaction,the rate law is given by $-\frac{d[A]}{dt} = k[A]$.Integrating this expression from time $t=0$ (where $[A] = a$) to time $t$ (where $[A] = a-x$),we get:$k = \frac{2.303}{t} \log \frac{a}{a-x}$where '$a$' is the initial concentration and '$a-x$' is the concentration at time '$t$'.

Class 12 Chemistry Chemical Kinetics First Order reaction

Medium

$A$ first order reaction is given as $A \rightarrow \text{products}$. Its integrated rate equation is:

MHT CET 2011 All MHT CET

A
$k = \frac{2.303}{t} \log \frac{a-x}{a}$
B
$k = \frac{1}{t} \log \frac{a}{a-x}$
C
$k = \frac{2.303}{t} \log \frac{a}{a-x}$
D
$-k = \frac{1}{t} \log \frac{a-x}{a}$

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Chemical Kinetics

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First Order reaction

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The following data were obtained during the first order thermal decomposition of $N_{2}O_{5(g)}$ at constant volume:
$2N_{2}O_{5(g)} \rightarrow 2N_{2}O_{4(g)} + O_{2(g)}$

$S.No.$ Time $/$ $s$ Total pressure $/$ $atm$

$1.$ $0$ $0.5$

$2.$ $100$ $0.512$

Calculate the rate constant.

Difficult

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If the half-life of a first-order reaction is $4 \ min$,then after how many minutes will the reaction be $99.9 \%$ complete?

Medium

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The decomposition of $N_2O_5$ is a first order reaction represented by $N_2O_5 \to N_2O_4 + \frac{1}{2} O_2$. After $15 \ min$,the volume of $O_2$ produced is $9 \ mL$ and at the end of the reaction,it is $35 \ mL$. The rate constant is equal to:

Medium

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Identify $True$ $(T)$ and $False$ $(F)$ statements for the following equations related to a first-order reaction $R \rightarrow P$:
$(i) \ln [R] = -kt + \ln [R]_{0}$
$(ii) \ln [R] = +kt + \ln [R]_{0}$

Easy

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The thermal decomposition of a compound is of first order. If a sample of the compound decomposes $50\%$ in $120 \, minutes$,in what time will it undergo $90\%$ decomposition?

Medium

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$S.No.$	Time $/$ $s$	Total pressure $/$ $atm$
$1.$	$0$	$0.5$
$2.$	$100$	$0.512$

$A$ first order reaction is given as $A \rightarrow \text{products}$. Its integrated rate equation is:

Similar Questions

The following data were obtained during the first order thermal decomposition of $N_{2}O_{5(g)}$ at constant volume:$2N_{2}O_{5(g)} \rightarrow 2N_{2}O_{4(g)} + O_{2(g)}$ $S.No.$ Time $/$ $s$ Total pressure $/$ $atm$ $1.$ $0$ $0.5$ $2.$ $100$ $0.512$ Calculate the rate constant.

If the half-life of a first-order reaction is $4 \ min$,then after how many minutes will the reaction be $99.9 \%$ complete?

The decomposition of $N_2O_5$ is a first order reaction represented by $N_2O_5 \to N_2O_4 + \frac{1}{2} O_2$. After $15 \ min$,the volume of $O_2$ produced is $9 \ mL$ and at the end of the reaction,it is $35 \ mL$. The rate constant is equal to:

Identify $True$ $(T)$ and $False$ $(F)$ statements for the following equations related to a first-order reaction $R \rightarrow P$:$(i) \ln [R] = -kt + \ln [R]_{0}$$(ii) \ln [R] = +kt + \ln [R]_{0}$

The thermal decomposition of a compound is of first order. If a sample of the compound decomposes $50\%$ in $120 \, minutes$,in what time will it undergo $90\%$ decomposition?

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The following data were obtained during the first order thermal decomposition of $N_{2}O_{5(g)}$ at constant volume:
$2N_{2}O_{5(g)} \rightarrow 2N_{2}O_{4(g)} + O_{2(g)}$

$S.No.$ Time $/$ $s$ Total pressure $/$ $atm$

$1.$ $0$ $0.5$

$2.$ $100$ $0.512$

Calculate the rate constant.

Identify $True$ $(T)$ and $False$ $(F)$ statements for the following equations related to a first-order reaction $R \rightarrow P$:
$(i) \ln [R] = -kt + \ln [R]_{0}$
$(ii) \ln [R] = +kt + \ln [R]_{0}$