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Question:

The following data 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) Experiment Time(s⁻¹) Total pressure (atm) 1 0 0.42 100 0.7

Solution:

The thermal decomposition of SO2Cl2 at a constant volume is represented by the following equation.
SO2Cl2(g) → SO2(g) + Cl2(g)
At t=0 P0
At t=t P0-p
After time t, total pressure is given as,
Pt = (P0 - p) + p + p
Pt = P0 + p
which on rearrangement gives:
p = Pt - P0
∴ P0 - p = P0 - (Pt - P0) = 2P0 - Pt
For a first-order reaction,
k = (2.303/t)log(P0/(P0 - p)) = (2.303/t)log(P0/(2P0 - Pt))
t = 100s
k = (2.303/100)log(0.42/(2*0.42 - 0.7)) = 1.386 x 10⁻² s⁻¹