The half-life of a zero order reaction A righ | vedclass

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Question

(A) For a zero order reaction,the rate constant $k$ is given by the formula $k = \frac{[A]_0 - [A]_t}{t}$.First,calculate $k$ using the half-life form

Vedclass · Accepted Answer

$1/4$

Vedclass · Answer

(A) For a zero order reaction,the rate constant $k$ is given by the formula $k = \frac{[A]_0 - [A]_t}{t}$.First,calculate $k$ using the half-life formula $t_{1/2} = \frac{[A]_0}{2k}$.Given $t_{1/2} = 0.5 \ hr$ and $[A]_0 = 4 \ mol \ L^{-1}$,we have $0.5 = \frac{4}{2k}$,which gives $k = \frac{4}{1} = 4 \ mol \ L^{-1} \ hr^{-1}$.Now,to find the time $t$ for the concentration to change from $[A]_1 = 2.0 \ mol \ L^{-1}$ to $[A]_2 = 1.0 \ mol \ L^{-1}$,use the integrated rate law: $t = \frac{[A]_1 - [A]_2}{k}$.Substituting the values: $t = \frac{2.0 - 1.0}{4} = \frac{1.0}{4} = 0.25 \ hr$.Thus,$t = 1/4 \ hr$.

The half-life of a zero order reaction $A \rightarrow \text{products}$ is $0.5 \ hr$. The initial concentration of $A$ is $4 \ mol \ L^{-1}$. How much time (in $hr$) does it take for its concentration to come from $2.0 \ mol \ L^{-1}$ to $1.0 \ mol \ L^{-1}$?

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