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(C) The rate constant $k = 1 	imes 10^{-2} \ s^{-1}$,initial concentration $[A]_0 = 20 \ g$,and final concentration $[A]_t = 5 \ g$. For a first orde

Vedclass · Accepted Answer

$138.6$

Vedclass · Answer

(C) The rate constant $k = 1 	imes 10^{-2} \ s^{-1}$,initial concentration $[A]_0 = 20 \ g$,and final concentration $[A]_t = 5 \ g$. For a first order reaction,the time $t$ is given by the formula: $t = \frac{2.303}{k} \log_{10} \frac{[A]_0}{[A]_t}$ Substituting the values: $t = \frac{2.303}{1 	imes 10^{-2}} \log_{10} \frac{20}{5}$ $t = 2.303 	imes 10^2 	imes \log_{10}(4)$ Since $\log_{10}(4) \approx 0.602$: $t = 230.3 	imes 0.602 \approx 138.6 \ s$ Therefore,the correct option is $C$.

$A$ first order reaction has a rate constant of $1 \times 10^{-2} \ s^{-1}$. How much time will it take for $20 \ g$ of reactant to reduce to $5 \ g$ (in $s$)?

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