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.
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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