The half-life for a zero-order reaction having 0.02 M initial concentration of reactant is 100 s. The rate con

Question

The half-life for a zero-order reaction having 0.02 M initial concentration of reactant is 100 s. The rate constant (in mol L⁻¹ s⁻¹) for the reaction is:

Accepted Answer

For a zero-order reaction, the half-life ($t_{1/2}$) is directly proportional to the initial concentration of the reactant ($[R]_0$) and inversely proportional to the rate constant ($k$). The relationship is given by the equation:
$$ t_{1/2} = \frac{[R]_0}{2k} $$

To find the rate constant ($k$), we rearrange the formula:
$$ k = \frac{[R]_0}{2t_{1/2}} $$

Given:
*   Initial concentration, $[R]_0 = 0.02 	ext{ M}$
*   Half-life, $t_{1/2} = 100 	ext{ s}$

Substituting the values:
$$ k = \frac{0.02 	ext{ mol L}^{-1}}{2 	imes 100 	ext{ s}} $$
$$ k = \frac{0.02}{200} $$
$$ k = 1.0 	imes 10^{-4} 	ext{ mol L}^{-1} 	ext{ s}^{-1} $$

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