(A) For a first-$order$ reaction,the rate equation is $R = R_0 e^{-kt}$.Taking the natural logarithm on both sides: $\ln R = \ln R_0 - kt$.This can be

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(A) For a first-$order$ reaction,the rate equation is $R = R_0 e^{-kt}$.Taking the natural logarithm on both sides: $\ln R = \ln R_0 - kt$.This can be rearranged as $\ln(R_0/R) = kt$.Converting to base $10$: $\log(R_0/R) = \frac{kt}{2.303}$.Comparing this with the equation of a straight line $y = mx + c$,where $y = \log(R_0/R)$ and $x = t$,the slope is $m = \frac{k}{2.303}$,which is positive.Therefore,plotting $\log(R_0/R)$ vs time gives a straight line with a positive slope.

Class 12 Chemistry Chemical Kinetics First Order reaction

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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 $t$)

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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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Chemical Kinetics

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First Order reaction

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Regarding the half-life period of a first-order reaction,which one of the following statements is generally false?

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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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If the rate constant of a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$,then find the time required for $400 \ g$ of the reactant to reduce to $50 \ g$. (in $min$)

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For a first order reaction,the rate constant is given as $\log_{10} K = 12 - \frac{6 \times 10^3}{T}$. What will be the value of temperature if its half-life period is $6.93 \times 10^{-3} \, \text{min}$ (in $, K$)?

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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 $t$)

Similar Questions

Regarding the half-life period of a first-order reaction,which one of the following statements is generally false?

Which equation represents the $1/4^{th}$ life for a first-order reaction?

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:

If the rate constant of a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$,then find the time required for $400 \ g$ of the reactant to reduce to $50 \ g$. (in $min$)

For a first order reaction,the rate constant is given as $\log_{10} K = 12 - \frac{6 \times 10^3}{T}$. What will be the value of temperature if its half-life period is $6.93 \times 10^{-3} \, \text{min}$ (in $, K$)?

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