For a first-order reaction,which of the following statements is correct?

  • A
    The degree of dissociation is equal to $(1 - e^{-kt})$.
  • B
    The pre-exponential factor in the Arrhenius equation has the dimensions of time.
  • C
    The plot of reciprocal concentration versus time is a straight line.
  • D
    Both $A$ and $B$.

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Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:
$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$
$S. No.$$Time$ $(s)$$Total$ $pressure$ $(atm)$
$1$$0$$0.5$
$2$$100$$0.6$

Calculate the rate constant.

$PCl_{5(g)} \rightarrow PCl_{3(g)} + Cl_{2(g)}$
In the above first order reaction,the concentration of $PCl_{5}$ reduces from an initial concentration of $50 \ mol \ L^{-1}$ to $10 \ mol \ L^{-1}$ in $120 \ minutes$ at $300 \ K$. The rate constant for the reaction at $300 \ K$ is $X \times 10^{-2} \ min^{-1}$. The value of $X$ is $......$
$[$ Given $\log 5 = 0.6989 ]$

For a first-order reaction at $100\,^oC$,the rate constant is $K = 1.5 \times 10^{-2} \, s^{-1}$. If the initial concentration of the reactant is $100 \, mol \, L^{-1}$,what will be the concentration of the reactant after $10 \, min$?

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What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.8 \ mol \ dm^{-3}$ to $0.2 \ mol \ dm^{-3}$ is $12 \ hour$ (in $hour$)?

What is the half-life of a first-order reaction if the rate constant is $4.2 \times 10^{-2} \text{ day}^{-1}$ (in $\text{ days}$)?

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