The rate equation for a first-$order$ reaction is given by $R = R_0 e^{-kt}$. $A$ straight line with positive slope is obtained by plotting which of the following? ($R_0 =$ Initial concentration of the reactant,$R =$ concentration of the reactant at time $t$)
- A$\log(R_0/R)$ vs time
- B$R$ vs time
- C$\log R$ vs time
- D$\log(R/R_0)$ vs time
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In a first order reaction, $20 \text{ mmol}$ of reactant is reduced to $10 \text{ mmol}$ in $0.3010 \text{ min}$. Find the rate constant of the reaction. (in $\text{ min}^{-1}$)
DifficultMHT CET 2026
View SolutionCalculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$. If the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$,find the half-life in $\text{min}$.
Medium
View SolutionIf the half-life $(t_{1/2})$ of a first-order reaction is $20 \ minutes$,what fraction of the reactant remains after $40 \ minutes$?
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View SolutionFor a first order reaction,the half-life period is independent of
For a first order reaction $A \rightarrow B$, the data is provided in the table below. Find $x$ in minutes. (Nearest integer)
$t/\text{min}$ $[A]/M$ $0$ $0.6500$ $x$ $0.0650$ $20$ $0.00065$
| $t/\text{min}$ | $[A]/M$ |
|---|---|
| $0$ | $0.6500$ |
| $x$ | $0.0650$ |
| $20$ | $0.00065$ |
DifficultJEE MAIN 2026
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