If $C_{o} =$ initial concentration of the reactant, $C_{t} =$ concentration of the reactant at time t and k $=$ rate constant of the reaction, then the equation applicable for a first order reaction is:

C_{t} = C_{0} e^{- K t}

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C_{t} = C_{0} e^{K t}

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C_{0} = C_{t} e^{- K t}

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\frac{C_{0}}{C_{t}} = 1

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Solution

The correct option is A $C_{t} = C_{0} e^{- K t}$
$k = \frac{1}{t} l n [\frac{C_{0}}{C_{t}}]$
$k t = l n \frac{C_{0}}{C_{t}}$
$\frac{C_{t}}{C_{0}} = e^{- k t}$
$C_{t} = C_{0} e^{- k t}$
Thus, The integrated form for the first order reaction is $C_{t} = C_{o} e^{- K t}$ .
Here, $C_{o} =$ represents initial concentration of the reactant, $C_{t}$ represents the concentration of the reactant at time t and k is the rate constant of the reaction.
Other forms of the integrated rate law are $l n \frac{C_{t}}{C_{o}} = - k t$ and $k = \frac{2.303}{t} l o g \frac{c}{c - x}$ .

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If Co=initial concentration of the reactant, Ct= concentration of the reactant at time t and k=rate constant of the reaction, then the equation applicable for a first order reaction is:

If $C_{o} =$ initial concentration of the reactant, $C_{t} =$ concentration of the reactant at time t and k $=$ rate constant of the reaction, then the equation applicable for a first order reaction is: