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Question 21

# The following data were obtained during the first order thermal decomposition of SO2Cl2at a constant volume.SO2Cl2(g)  →  SO2(g) + Cl2(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.

The thermal decomposition of SO2Cl2at a constant volume is represented by the following equation.

After time, t, total pressure,Pt = (Pº - p) + p + p

⇒ Pt = (Pº + p)

p = P - Pº

therefore, Pº - p = Pº  - P - Pº

= 2 Pº -  Pt

For a first order reaction,

k = 2.303/ Log  Pº / Pº  - p

=   2.303/ Log  Pº / 2 Pº  -  Pt

When t= 100 s,

k = 2.303 / 100s log 0.5 / 2x0.5 - 0.6

= 2.231 × 10 - 3s - 1

When Pt= 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

pSOCL2 = 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(pSOCL2)

= (2.23 × 10 - 3s - 1) (0.35 atm)

= 7.8 × 10 - 4atm s - 1

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