Question

The specific rotation of α -d-galactose is 150.7 and that of β -d-galactose is 52.8. When an aqueous mixture that was initially 70% α -d-galactose and 30% β -d-galactose reaches equilibrium, the specific rotation is 80.2. What is the percentage of α -d-galactose and β -d galactose at equilibrium?

Short answer

The calculation indicates that 13.5% is in the α -D galactose and 76.5% is in the β -D galactose.

Step-by-step solution

Specific rotation

The instrument used for computing the specific rotation caused by polarized light is called a polarimeter. Once the measurement is acquired, it is substituted in the specific rotation formula.

This helps in finding the specific rotation value, which is a property of a particular compound.

Calculating the percentages of α -d-glucose and β -d-glucose present at equilibrium

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

A + B = 1

B = 1 - A

The specific rotation of A is 150.7.

The specific rotation of B is 52.8.

The specific rotation of the equilibrium mixture is 80.2.

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

80.2 = 150.7A+(1-A)52.8

80.2 = 150.7A + 52.8 - 52.8A

27.4 = 203.5A

The value of A can be found as:

A = 27.4/203.5

= 0.135

The value of B can be found as:

B = 1 - A

= 1 - 0.135

= 0.765

This calculation indicates that 13.5% is in the α -D galactose and 76.5% is in the β -D galactose.