(Solved): Half-lifo equation for first-order reactione: \[ t_{1 / 2}=\frac{0.093}{k} \] where \( t_{1 / 2} \) ...

Half-lifo equation for first-order reactione: \[ t_{1 / 2}=\frac{0.093}{k} \] where \( t_{1 / 2} \) is the half-life in seconds \( (s) \), and \( k \) is the rate constant in inverse seconds \( \left(\mathrm{s}^{-1}\right) \). Part A To calculate the half-life, plug the value for \( k \) into the half-life equation and solve. What is the half-life of a first-order reaction with a rate constant of \( 8.80 \times 10^{-4} \mathrm{~s}^{-1} \) ? Express your answer with the appropriate units. What is the rate constant of a first-order reaction that takes 193 seconds for the reactant concentration to drop to half of its initial value? Express your answer with the appropriate units. A certain first-order reaction has a rate constant of \( 2.00 \times 10^{-3} \mathrm{~s}^{-1} \). How long will it take for the reactant concentration to drop to \( \frac{1}{8} \) of its initial value? Express your answer with the appropriate units.