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) rarr SO_(2)(g) + Cl_(2)(g)`

Calculate the rate constant.
[Given : log 4 = 0.6021, log 2 = 0.3010]

Explanation

`{:(SO_(2)Cl_(2)(g),rarr,SO_(2)(g),+,Cl_(2)(g)),("At t = 0s 0.4 atm",,"0 atm",,"0 atm"),("At t = 100s (0.4 - x) atm",,"x atm",,"x atm"):}`
`pt = 0.4 - x + x + x`
`pt = 0.4 + x`
`0.7 = 0.4 + x`
`x = 0.3`
`k = (2.303)/(t)log.(p_(i))/((2p_(i) - p_(t)))`
`k = (2.303)/(t) log.(0.4)/(0.8-0.7)`
`k = (2.303)/(100) xx 0.6021`
`= 1.39 xx 10^(-2) s^(-1)`