The following data in the table were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume: SO2Cl2(g) → SO2(g) + Cl2(g) Calculate the rate constant. (Given: log4=0.6021, log2=0.3010)

The thermal decomposition of SO2Cl2 at a constant volume is represent by the following reaction.
SO2Cl2(g) → SO2(g) + Cl2(g)
At t=0 P0 0 0
At t=t P0-p p p
After time t, total pressure, Pt = (P0-p) + p + p
Pt = P0 + p
which on rearrangement gives:
p = Pt - P0
Therefore, P0-p = P0 - (Pt - P0) = 2P0 - Pt
For a first-order reaction,
k = 2.303/t log P0 / (2P0 - Pt) = 2.303/100 log 0.4/0.1 = 1.38 × 10⁻²; s⁻¹