First-order reaction => r = - dC / dt k * C^m
Where: m is the order of the reaction, which is 1, r is the rate of reaction, k is the rate constant, C is the concentration, and dC / dt is the derivative of the concentration respect time.
=> - dC/dt = K * C
Solving: dC / C = k dt
=> - [ln(C) - ln Co] = kt, where Co is the initial concentration (at t = 0)
=> - ln (C / Co) = kt
Concentration dropo to half => C / Co = 1/2
=> - ln (1/2) = k * 7.30 min
=> k = ln(2) / 7.30 min = 0.095 M / min
Answer: k = 0.095 M / min
