The rate constant for the first order decomposition of a at 500oc is 9.2 x 10-3 s-1. how long will it take for 90.8% of a 0.500 m sample of a to decompose? question options:

For this problem, we assume a first-order kinetics which has a kinetics expression written as:

ln(Ca/Cao) = -kt

We use this formula to solve for time, t. First we list the needed values,
k = 9.2 x 10-3 s-1
Cao = 0.500 M 
Xa = 90.8% = 1 - (Ca/Cao) 
Ca = 0.046 M

ln(0.046/0.500) = -9.2 x 10-3 s-1(t)
t = 259.34 s

Me i need

Ithink ahopefully im correct