For a first order reaction R longrightarrow P | vedclass

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(B) For a first order reaction $R \longrightarrow P$,the rate law is given by: $	ext{Rate} = -\frac{d[R]}{dt} = k[R]$.Rearranging the terms,we get: $

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$[R_0] e^{-kt}$

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(B) For a first order reaction $R \longrightarrow P$,the rate law is given by: $	ext{Rate} = -\frac{d[R]}{dt} = k[R]$.Rearranging the terms,we get: $\frac{d[R]}{[R]} = -k dt$.Integrating both sides: $\int \frac{d[R]}{[R]} = -\int k dt \Rightarrow \ln[R] = -kt + C$.At $t = 0$,$[R] = [R_0]$,so $\ln[R_0] = C$.Substituting $C$ back into the equation: $\ln[R] = -kt + \ln[R_0]$.Rearranging: $\ln \frac{[R]}{[R_0]} = -kt$.Taking the exponential of both sides: $\frac{[R]}{[R_0]} = e^{-kt}$.Therefore,the concentration at time $t$ is: $[R] = [R_0] e^{-kt}$.

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

$S. No.$	$Time$ $(s)$	$Total$ $pressure$ $(atm)$
$1$	$0$	$0.5$
$2$	$100$	$0.6$

For a first order reaction $R \longrightarrow P$,the rate constant is $k$. If the initial concentration of $R$ is $[R_0]$,the concentration of $R$ at any time $t$ is given by the expression:

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$1$ $0$ $0.5$
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Calculate the rate constant.

Consider the first order reaction $R \to P$. The fraction of molecules decomposed in the given first order reaction can be expressed as:

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