When pure alpha-D-galactopyranose is placed in a plane polarimeter it rotates pl

Question

When pure alpha-D-galactopyranose is placed in a plane polarimeter it rotates plane-polarized light +150.7 degrees. The pure beta-anomer rotates plane polarized light to +52.8 degrees. When the pure anomer of either form is left standing, an equilibrium is reached and the observed rotation is +80.2 degrees. What is the percentage of the alpha-form in the equilibrium mixture? Assume the contribution of linear or other cyclic forms is negligible, and report your answer as a percent to the nearest ones.

Explanation / Answer

On standing both the isomers are getting equilibrated by interconversion. This process of interconvertion through open chain structure leading to equilibration is called mutarotation.

alpha isomer <-----> open chain <----> beta anomer

The percentage of each form can be calculated as

equilibrium value = {[ rotation of alpha anomer x % ] + [rotation of beta anomer x %] }/ 100

Substituing the values

+ 80.2 = [ 150.7a + 52.8(100-a)] /100

where a is the percentage of alpha anomer

Solving for a we get a = 27.98

Thus the percentage of alpha anomer in equilibrium mixture is 30.64 % and beta anomer is 72.08

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