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, $[R]_0 = 0.02 \text{ M}$ Half-life, $t_{1/2} = 100 \text{ s}$

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