Question

The following data were obtained during the first order thermal decomposition of SO₂Cl₂ at a constant volume.
SO₂Cl_2(g) → SO_2(g) + Cl_2(g).

Experiment	Time/ s	Total pressure/ atm
1	0	0.5
2	100	0.6

Calculate the rate of reaction when total pressure is 0.65 atm.

Answer 1

SO₂Cl_2(g) → SO_2(g) + Cl_2(g)

Total pressure after time ‘t
P_t = (P₀ – x) + x + x
P_t = P₀ + x
x = P_t – P₀
Initial pressure = P₀
Final pressure = P₀ – x
= P₀ – (P_t – P₀)
= 2P₀ – P_t

k = 2.2316 x 10^-3s^-1
P_t = 0.65 atm
i.e., (P₀ + P) = 0.65 atm
P = 0.65 – P₀ = 0.65 – 0.50
P = 0.15 atm
Pressure of SO₂Cl₂ at time t
P_SO2Cl2 = P₀ – P
= 0.50 – 0.15
= 0.35 atm
At time ‘t
Rate = k x P_SO2Cl2
= 2.2316 x 10^-3 x 0.35
= 7.8 x 10^-4 atm s^-1
Hence when total pressure is 0.65 atm then the rate will be 7.8 x 10^-4 atm s^-1