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Question
The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.
\[\ce{SO2Cl2_{(g)} -> SO2_{(g)} + Cl2_{(g)}}\]
| 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.
Solution
The thermal decomposition of SO2Cl2 at a constant volume is represented by the following equation.
\[\ce{SO2Cl2_{(g)} -> SO2_{(g)} + Cl2_{(g)}}\]
| At t = 0 | P0 | 0 | 0 |
| At t = t | P0 − p | p | p |
After time t, total pressure, Pt = (P0 − p) + p + p
⇒ Pt = (P0 + p)
⇒ p = Pt − P0
∴ P0 − p = P0 − (Pt − P0)
= 2 P0 − Pt
For a first order reaction,
k = `2.303/"t" log "P"_0/("P"_0 - "p")`
When t = 100 s, k = `2.303/(100s)log 0.5/(2 xx 0.5 - 0.6)`
When Pt = 0.65 atm,
P0 + p = 0.65
⇒ p = 0.65 − P0
= 0.65 − 0.5
= 0.15 atm
∴ When the total pressure is 0.65 atm, pressure of SOCl2 is \[\ce{P_{SO_2Cl_2}}\] = P0 − p
= 0.5 − 0.15
= 0.35 atm
∴ The rate of equation, when total pressure is 0.65 atm, is given by,
Rate = \[\ce{k(P_{SO_2Cl_2)}}\]
= (2.23 × 10−3 s−1) × (0.35 atm)
= 7.8 × 10−4 atm s−1
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