Chemists: can you help me with this homework problem? (optical rotation)

[tsarina]

A question from my biochem homework that I have no idea how to answer:

The values of the specific rotation, [alpha]20D, for the alpha and beta anomers of D-galactose are 150.7 and 52.8 degrees, respectively. A mixture that is 20% of alpha-D-galactose and 80% beta-D-galactose is dissolved in water at 20 degrees C. What is its initial specific rotation? After several hours the specific rotation of this mixture has reached an equilibrium value of 80.2 degrees. What is its anomeric composition?

So do I multiply .2 x 150.7 and .8 x 52.8 and do it that way, if the rotations complement each other, or does the beta rotation predominate since there is much more of it? Also, how would i solve the second question given this information?

Thanks for any help you can give me,
- tsarina, confused biochem student.

[aggiej]

it's been a while but...for the first part seems like the rotation would be a sum of the two anomers. e.g. rotation 1 plus rotation 2 with respect to their ratios in solution. i think you've got that one. the second part seems to be missing an equilibrium constant for the equation alpha<----->beta which should be the ratio of the two forms in solution. k=concentration of beta/concentration of alpha. k*(52.8/150.7)=80.2. solve for k.

[Squink]

Don't need k for part 2. You already know that fracalpha + fracbeta = 1.

[mnemosyne]

Optical rotations do cancel each other out, IIRC. All they mean is the degree to which plane polarized light is "turned" by the substance. L (levorotatory) and D (dextrorotatory) (or + and -) just mean they go in opposite directions - levo to the left and dextro to the right. So -100 and +60 = -40 in a 1 to 1 mixture., whereas 60 and 40 would give 100. Fractions are just that - fractions.

I'll let you try solving part b with what Squink gave you, but also because I don't wanna do it :)

mnem - also a biochemistry student :)