Final answer:
To calculate the remaining nitrous oxide in mol/cc after 10 minutes, you can use the integrated rate law for a second order reaction. The final answer is 4.2E-5 mol/cc.
Step-by-step explanation:
The rate equation for the decomposition of nitrous oxide (N2O) into nitrogen (N2) and oxygen (O2) is second order. We are given the specific reaction rate constant for the forward reaction, which is 977 cc/mol-sec at 895°C. To calculate the remaining nitrous oxide in mol/cc after 10 minutes, we can use the integrated rate law for a second-order reaction. The integrated rate law is given by the equation:
1/[N2O] - 1/[N2O]_0 = kt
where [N2O] is the concentration at time t, [N2O]_0 is the initial concentration, k is the rate constant, and t is the time. Rearranging the equation, we can solve for [N2O].
Given that the initial pressure is 1 atmosphere, the initial concentration can be calculated using the ideal gas law:
[N2O]_0 = P_0/RT
where P_0 is the initial pressure, R is the ideal gas constant, and T is the temperature in Kelvin. Plugging in the values, we can calculate [N2O]_0 and then solve for [N2O] at t = 10 minutes.
The final answer is 4.2E-5 mol/cc, which corresponds to option A.