What is the observed rotation when `0.1 M` solutions of `(R )-2` butanol is mixed with an equal volume of `0.05M` solution of recemic `2-butnol` and the resulting solution is taken in a cell of `5cm` long tube in a polarimeter? The specific rotation of `(R -2)` butonal is `+13.9^(@)`

Explanation

The racemic `2-` butanol has no contribution to optical activity. So the observed rotation will be due ot `(R )-2` butanol. Only Racemic butanol helps in diluting the solution. Therefore, the concentration of `(R )-2` butanol after dilution is `0.05M`. Molecular weight of `2-` butnol is `74`.
`l= 5 cm= 0.5dm`
`:.` Concentration `=(74xx0.05)/(1000)=3.7xx120^(-3)gm ml^(-1)`
`:. [alpha]=[alpha]_(pure)xxlxxc= 13.9xx0.5xx3.7xx10^(-3)` ltbr `=0.26^(@)`