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)

Answer 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

 

Answer 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`