For a first order reaction \( \text{A} \longrightarrow \text{Products} \), initial concentration of \( \text{A} \) is \( 0.1 \text{ M} \), which becomes \( 0.001 \text{ M} \) after 5 minutes. Rate constant for the reaction in \( \text{min}^{-1} \) is

For a first-order reaction, the integrated rate equation is given by: \( k = \frac{2.303}{t} \log \frac{[A]_0}{[A]} \) \n\nGiven data: \n- Initial concentration, \( [A]_0 = 0.1 \text{ M} \) \n- Final concentration after time \( t \), \( [A] = 0.001 \text{ M} \) \n- Time, \( t = 5 \text{ min} \) \n\nSubstituting the given values into the formula: \n\( k = \frac{2.303}{5} \log \frac{0.1}{0.001} \) \n\( k = \frac{2.303}{5} \log(10^2) \) \n\( k = \frac{2.303 \times 2}{5} \) \n\( k = \frac{4.606}{5} = 0.9212 \text{ min}^{-1} \) \n\nTherefore, the correct option is 4.