Final answer:
It will take approximately 3.7 seconds for the concentration of N2O to decrease to 6.0% of its initial concentration.
Step-by-step explanation:
To determine how long it will take for the concentration of N2O to decrease to 6.0% of its initial concentration, we need to use the integrated rate law for a first-order reaction. The integrated rate law for a first-order reaction is given by: ln(N2O) = -kt + ln(N2O0), where N2O is the concentration at time t, k is the rate constant, and N2O0 is the initial concentration.
Plugging in the given values, we get: ln(0.06) = -0.76t + ln(1.0), where t is the time in seconds. Solving for t, we get t ≈ 3.7 seconds.