Question

two optical isomers, A and B, having specific rotations of +27.6 deg and -19.5 deg, respectively, are in equilibrium in solution. If the specific rotation of the mixture is 16.2 deg, calculate the equilibrium constant for the process A<-->B

Answer 1

Equilbrium A $\rightleftharpoons$ B

The rate constant is given by K= (γ_α -γ_∞) / (γ_∞ -γ_β)

γ_{α =} specific rotations of A = +27.6 deg

γ_{β =}  specific rotations of B = -19.5 deg

γ_{∞ =} equilibrium specific rotation = + 16.2 deg

K = (27.6-16.2) / (16.2 + 19.5)= 11.4 / 35.7 = 0.319