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Question
The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume :
SO2Cl2 (g) → SO2 (g) + Cl2 (g)
| Experiment | Time/s–1 | Total pressure/atm |
| 1 | 0 | 0.4 |
| 2 | 100 | 0.7 |
Calculate the rate constant.
(Given : log 4 = 0.6021, log 2 = 0.3010)
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Solution 1
The given reaction is as follows:
SO2Cl2 (g) → SO2(g)+Cl2(g)
Also given:
| Experiment | Time/s–1 | Total pressure/atm |
| 1 | 0 | 0.4 |
| 2 | 100 | 0.7 |
The rate constant k can be calculated as follows:
`k=2.303/tlog `
when t= 100s, k = `2.303/(100s)log`
`k = 2.303/(100s)log`
`k=2.303/(100s) log 4`
`k = 2.303/(100s)xx0.6021`
k = 1.39 x 10-2s-1
Therefore, the rate constant is 1.39 x 10-2s-1
Solution 2
The thermal decomposition of SO2Cl2 at a constant volume is represented by the following equation:
SO2Cl2→SO2(g) + Cl2(g)
At t =0 P0 0 0
At t=t P0 −p p p
After time t, total pressure is given as:
Pt =(P0−p) + p + p
Pt = P0 + p
This, on rearrangement, gives:
p = Pt − P0
∴ P0−p=P0−(Pt−P0)= 2P0 − Pt
For the first-order reaction, we have:
`k=2.303/tlog P_0/(P_0 - p)`
`=2.303/tlog P_0/(P_0 - p)`
t = 100 s
`k = 2.303/100log 0.42/(0.4 - 0.7) = 1.386 xx 10^(-2)s-1`
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