Question

The decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5

Answer 1

The reaction is first order reaction so we can use the following relation:
ln[A] = -kt + ln[Ao]

Where [A] = conc / pressure after time t
k = 4.5 X 10 ^-2
t = 58 seconds
lnAo = ln(400)
ln[A] = -(4.5 X 10 ^-2)(58) + ln[400]
= (-2.61) + (5.99)
lnA= 3.38

Taking antilog
[A] = 29.37torr

Part B:

t_1/2 = 0.693 / K

     t_1/2    = 0.693 / 4.5 X 10 ^-2

t_{1/2 =} 15.4 seconds

so for one fourth value the time will be two half lives

time = 30.8 seconds