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 of the reaction when total pressure is 0.65 atm.

Question 4.21: 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 of the reaction when total pressure is 0.65 atm.
Answer
Let initial pressure = p_o
And pressure after time t = p_t
Amount of substance = a
Decomposed quantity = x

The thermal decomposition of SO₂Cl₂ at a constant volume is
Use the formula of first order reaction
In this problem we take pressure in place of concentration or quantity
Final pressure due to reactant = p_o - p = 2po - p_t

After calculation we get
K = 2.231 × 10⁻³ sec⁻¹
We have gotten p_t= 0.65 atm
Use above equation again we get
p_o - p = 2po - p_t
then
p = 0.65 − P₀ = 0.65 − 0.5 = 0.15 atm
pressure of SOCl₂ = P₀ − p = 0.5 − 0.15 = 0.35 atm
Use the formula of rate of equation
Rate = k x P_SOCl2
Plug the values we get
Rate =(2.23 × 10⁻³ s⁻¹ x 0.35 atm = 7.8 × 10⁻⁴ atm s⁻¹
Answer
Rate of reaction = 7.8 × 10⁻⁴ atm s⁻¹