A `20cm` length of a certain solution causes right-handed rotation of `38^@`. A `30cm` length of another solution causes left-handed rotation of `24^@`. The optical rotation caused by `30cm` length of a mixture of the above solutions in the volume ratio `1:2` is

Options

A. left handed rotation of `14^(@)`
B. right handed rotation of `14^(@)`
C. left handed rotation of `3^(@)`
D. right handed rotation of `3^(@)`

Answer

D

Explanation

Case I `l_(1) = 20 cm, theta_(1) = 38^(@)`,
concentration = `C_(1)`
`therefore` Specific rotation, `alpha_(1) = (theta)/(l_(1)C_(1)) = (38^(@))/(20 xx C_(1))` Liquid A.
Case II: ` l_(2) = 30 cm, theta_(2) = (-24^(@))/(30 xx C_(2))`. Liquid B.
The mixture has 1 part A and 2 part B.
`therefore C'_(1) : C'_(2) = 1 : 2`
`therefore theta = [alpha_(1)C_(1) + a_(2)C'_(2)]l`
` = {(38)/(20 xx C_(1)) xx (C_(1))/(3) + (-24^(@))/(30 xx C_(2)) xx (2C_(2))/(3)} xx 30 = 19^(@) - 16^(@)`
The new angle of rotation is `+3` in the right hand direction.