What are the units of the rate constant of a reaction in which the half life is doubled by halving the initial concentration of reactants.

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$M^{- 1} s^{- 1}$

$\sec^{- 1}$

$M - s^{- 1}$

$M^{- 2} s^{- 1}$

answer is B.

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Detailed Solution

$for 2^{nd} order \begin{aligned} t_{\frac{1}{2}} = \frac{1}{{ka}_{0}} \\ a_{0} \to \frac{a_{0}}{2} \\ t_{\frac{1}{2}} \to 2 t_{\frac{1}{2}} \end{aligned} so, \frac{dx}{dt} = k [A]^{2} \begin{aligned} k = \frac{1}{MS} \\ k = M^{- 1} S^{- 1} \end{aligned}$

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