Question

The following data were obtained during the first order thermal decomposition of \( SO _{2} Cl _{2} \) at a constant volume : 

\( SO _{2} Cl _{2}(g) \longrightarrow SO _{2}(g)+ Cl _{2}(g) \) \( \begin{array}{ccc}\text { Experiment } & \text { Time/s } & \text { Total pressure/atm } \\ 1 & 0 & 0.5 \\ 2 & 100 & 0.6\end{array} \) 

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

Answer 1

Pressure at time t, 

P_t = P_o - P + P + P

P_t = P_o+ P

⇒ P = P_t  -  P_o

Pressure at reactant at time t = P_o - P 

= P_o - P_t  -  P_o

= 2P_o -  Pt.

K = \(\frac{2.303}{t}\,log\,\frac{P_0}{2P_0 -P_t}\)

= \(\frac{2.303}{100}\,log\,\frac{0.5}{2\times 0.5 -0.6}\)

= \(\frac{2.303}{100}\,log\,1.25\)

K = 2.2318 x 10^-3 S^-1

Pressure of SO₂Cl₂ at time t (\(P_{SO_2Cl_2}\))

= 2P_o - P_t

= 2 x 0.50 - 0.65

= 0.35 atm

Rate of reaction at time t = K [SO₂Cl₂]      ∵ [SO₂Cl₂] \(\propto\) \(P_{SO_2Cl_2}\)

= 2.23 x 10^-3 x 0.35

= 7.8 x 10^-4 atm/s