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

Step-by-step solution

For liquid A L₁=20 ~cm , ₁=38^ ; concentration =C₁ aligned Specific rotation ₁ &= ₁ L₁ C₁ &= 38^ 20 C₁ aligned Similarly, for liquid BL₂=30 ~cm ₂=-24^ , concentration =C₂ Specific rotation ₂= ₂ L₂ C₂ = (-24^ ) 30 C₂ The mixture has 1 part of liquid A and 2 parts of liquid B . aligned C₁^ &: C₂^ =1: 2 &= [ ₁ C₁^ + ₂ C₂^ ] l &= 38^ 20 C₁ C₁ 3 + (-24^ ) 30 C₂ 2 C₂ 3 30 &=19^ -16^ =3^ aligned Thus, the optical rotation of mixture is +3^ in right hand direction