Optically pure `(+)-2` -chlorooctane, `[alpha] = +40^@`, reacts with aq. `NaOH` in acetone to give optically pure `(-)-2` -octanol, `[alpha] = -12.0^@`. With partically racemised chloro compound whose `[alpha] = + 30^@`, the `[alpha]` of alcohal product is `- 6.0^@`. Calculate :
(a) The percentage optical purity of partially racemised chloro compound and alcohol.
(b) The percentage of inversion and racemisation.
(c) The percentage of front-side and back-side attacks.
(d) What interference can be drawn from the data in part (a) of the above example, about the mode of `2^@` alky1 halide.
( e) Give the rate expression.
In terms if the expression, decrease the experimental changes for encourage (i) `SN^1`, (ii) `SN^2`,

Explanation

(a) To find the percentage of optical purity (optically active enantiometer), divide the observed specific rotation by that of the pure enantiomer and multiply the quotient by `100 %`. The optical purities are :
Chloride `= (30^@)/(40^@) xx (100 %) = 75%`
Alcohol `= (-6.0^@)/(-12.0^@) xx (100 %) = 50 %`
(b) The percentage of inversion is calculated by dividing the percentage of enantiomer of alchol by that of reacting chloride and multiplying the quotient by `100 %`. The percentage of racemisation is the difference between this percentage and `100 %`
Percentage inversion ` = (50 %)/(75 %) xx 100 % = 66.6 %`
Percentage racemisation `= 100 % - 66.6 % = 33.4 %`
(c) Inversion involves only back-side attack, while recemisation results from equal back-side and front-side attacks. The percentage of back-side attacks. The percentage of back-side attack is the sum of the inversion and one-half of the percentage of racemisation. The percentage of front-side attack is the remaining half of the percentage of racemisation.
Percentage of back-side attack is
`66.6 % + (1)/(2) (33.4 %) = 83.3 %`
Percentage of front-side attack `= (1)/(2) (33.4 %) = 16.7 %`
(d) The larger percentage of inversion shows that `2^@ RX` reacts predominantly by `SN^2` and smaller percentage of racemisation indicates some `SN^1` reaction.
(e) The rate expression is composed of `SN^1` and `SN^2` terms.
Rate `K_1[2^@ RX] + K_2[2^@ RX][overset (Ө) O H]`
(f) (i) At a very low concentration of `[overset (Ө) O H]`, the term `K_2` becomes insignificant and `SN^1` predominates.
(ii) At a higher concentration of `[overset (Ө) O H]`, the term `K_2` becomes more significant and `SN^2` predominates.