The following data were obtained during the first order thermal decomposition of SO₂Cl₂ at a constant volume.

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

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

The thermal decomposition of SO₂Cl₂ at a constant volume is represented by the following equation.

After time, t, total pressure,

Therefore,

= 2 P₀ − P_t

For a first order reaction,

When t = 100 s,

= 2.231 × 10⁻³ s⁻¹

When P_t = 0.65 atm,

P₀ + p = 0.65

⇒ p = 0.65 − P₀

= 0.65 − 0.5

= 0.15 atm

Therefore, when the total pressure is 0.65 atm, pressure of SOCl₂ is

= P₀ − p

= 0.5 − 0.15

= 0.35 atm

Therefore, the rate of equation, when total pressure is 0.65 atm, is given by,

Rate = k()

= (2.23 × 10⁻³ s⁻¹) (0.35 atm)

= 7.8 × 10⁻⁴ atm s⁻¹