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

Pure Alpha-D-Glucose has optical rotation of +150.7

Pure Beta-anomer has optical rotation of +52.8

Observed rotation is +80.2. It is a mixture of Alpha and beta anomer.

Suppose Alpha has fraction A and Beta has fraction B,

Observed rotaion rotaion, +80.2=A*(+150.7)+B*(+52.8)

and

A+B=1 or A=1-B

Overall, equation will be

80.2=(1-B)*(150.7)+B*52.8

80.2=150.7-150.7B+52.8B

                80.2=150.7-97.9B                changing the side

                                97.9B=150.7-80.2

                                                B=70.5/97.9

                                                                              B=0.72

                And

                                A=1-0.72

                                                A=0.28

Finally converting fraction to %

                A=0.28*100=28%

                B=0.72*100=72%

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