Ethylene is profuced by
`C_(4)H_(8)("cyclobutane")overset(Delta)rarr2C_(2)H_(4)`
The rate constant is `2.48 xx 10^(-4)s^(-1)`. In what time will the molar ratio of the ethylene to cyclobutane in reaction mixture attain the value (a) `1` (b) `100`?

Explanation

`{:(,C_(4)H_(8),,overset(Delta)rarr,2C_(2)H_(4)),(t=0,a,,,0),(t=t,a-x,,,2x):}`
(a) `(2x)/(a-x) = 1, x = (a)/(3)`
`t = (2.303)/(k)log.(a)/(a-(a//3))`
`= (2.303)/(2.48 xx 10^(-4)) log.(3)/(2) = 1635.2 s = 27.25 min`
(b) `(2x)/(a-x) = 100, x = (100a)/(102)`
`t = (2.303)/(2.48 xx 10^(-4))log.((a)/(a-(100a)/(102)))`
`= 15856.9s = 264.2 min`
Analyiss of Some Important First order Reactions