91Ó°ÊÓ

A specific rotation constitutes a property of the chiral molecule. It can be identified by measuring the energy and temperature of a plane polarized light.The formula used for evaluating the specific rotation of a mixture is:

Specific rotation of the mixture = Specific rotation of A x fraction of D - glucose in the α form + Specific rotation of B x fraction of D - glucose in the β form

Let A denote the fraction of D-glucose in the α from and B denote the fraction of D-glucose in the β form.

A + B = 1

B = 1 - A

The specific rotation of A is 112.2.

The specific rotation of B is 18.7.

The specific rotation of the equilibrium mixture is 52.7.

The specific rotation of the mixture can be found as:

Specific rotation of the mixture = Specific rotation of A x fraction of D - glucose in the α form + Specific rotation of B x fraction of D - glucose in the β form

52.7 = 112.2A+(1-A)18.7

52.7 = 112.2A + 18.7 - 18.7A

34.0 = 93.5A

The value of A can be found as:

A = 34.0/93.5

= 0.36

The value of B can be found as:

B = 1 - A

= 1 - 0.36

= 0.64

This calculation indicates that 36% is in the α-form and 64% is the β-form. This agrees with the values in Section 21.10.