Question

N2O undergoes thermal decomposition at 730°C to nitrogen (N2) and oxygen (O2) via first-order kinetics with a half-life of 3.58 x 103 minutes. Calculate the time required for 90% of a sample of N2O to decompose at 730°C.

Answer 1

I think this is the easiest way.
k = 0.693/t_1/2 and substitute k into the following:

ln(No/N) = kt.
I would call No = 100, then
N = 10 (if 90% is gone)
k from above
t = solve for this. The unit will be the unit used for the half life to solve for k.

Answer 2

i am so sad