A question on reaction half life?

Question

I'm a bit stuck at this - can anyone help please!
The question is;

At 320C, the rate constant for the 1st order reaction

SO2Cl2 ---> SO2 + Cl2

is k=2.2 x 10^-5 s-1.

What percentage of SO2Cl2 will decompose in 90 minutes?

I know that to work out the half life it is;

t1/2 = 0.693/k

but how do I then calculate the percentage in 90 mins?

Thanks to anyone who can help!

Answer 1

For first order what remains is

C=C0*e^(-kt) =>
C/C0= e^(-kt) is the fraction remaining
t=90 min =90*60=5400 s

so C/C0=e^(-5400*2.2*10^-5)= 0.88798 = 0.888 =88.8% remains
so 100-88.8= 11.2% decomposes