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–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

When t = 0, the total partial pressure is P₀ = 0.5 atm

When time t = t, the total partial pressure is P_t = P₀ + p

P₀-p = P_t-2p, but by the above equation, we know p = P_t-P₀

Hence, P₀-p = P_t-2(P_t-P₀)

Thus, P₀-p = 2P₀ – P_t

We know that time

Where, k- rate constant

[R]_° -Initial concentration of reactant

[R]-Concentration of reactant at time ‘t’

Here concentration can be replaced by the corresponding partial pressures.

Hence, the equation becomes,

⇒ → equation 1

At time t = 100 s, P_t = 0.6 atm and P₀ = 0.5 atm,

Substituting in equation 1,

⇒

Thus, k = 2.231 × 10^-3 s^-1

The rate of reaction R = k × P_S02Cl2

When total pressure P_t = 0.65 atm and P₀ = 0.5 atm, then

P_S02Cl2 = 2P₀-P_t

Thus, substituting the values, P_S02Cl2 = 2(0.5)-0.6 = 0.35 atm

R = k × P_S02Cl2 = 2.231 × 10^-3 s^–1 × 0.35

Rate of the reaction R = 7.8 × 10^-4atm s^–1