Photochlorination of propane gives `48%` n-propylchloride and `52%` isopropyl chloride. The relative reactivity of perimary and secondary hydrognes on a per-hydrogen basis is expected to be

Options

A. `1:4,43`
B. `1:3.25`
C. `1:5`
D. `1:2.5`

Answer

B

Explanation

`overset(1^(@))(CH_(3))overset(2^(@))(CH_(2))overset(1^(@))(CH_(3))`
Let `r_(p)` and `r_(s)` be the relative rates of substitution of a primary and secondary `H` atom, respectively. Since there are `6` primary `H` atoms, and statistically, each one has an equal chance of being replaced, their total rate of replacement is `6r_(p)`. Similarly, for `2` secondary `H` atoms, their total rate of replacement is `2r_(s)`. Since the amount of each isomers formed depends on its rate of formation,
`"Ratio of rates" = "Ratio of amounts"`
i.e., `(6r_(p))/(2r_(s))=(48)/(52)`
or `(r_(p))/(r_(s))=(2xx48)/(6xx52)=(3.25)/(1)`