For a first-order reaction, the integrated rate law is expressed as: \[ \ln \left( \frac{[A]_0}{[A]_t} \right) = kt \] Variables are defined as: - \([A]_0 = 1.0 \, \text{mol L}^{-1}\) (initial concentration) - \([A]_t = 0.25 \, \text{mol L}^{-1}\) (concentration at time \(t\)) - \(k\) denotes the rate constant - \(t = 60 \, \text{minutes} = 1 \, \text{hour}\) The rate constant \(k\) is computed using the integrated rate law: \[ \ln \left( \frac{1.0}{0.25} \right) = k \times 60 \] \[ \ln (4) = k \times 60 \] \[ 0.693 = k \times 60 \] \[ k = \frac{0.693}{60} \approx 0.01155 \, \text{mol L}^{-1} \, \text{min}^{-1} \] Consequently, the initial rate of the reaction is \(0.0115 \, \text{mol L}^{-1} \, \text{min}^{-1}\).