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The specific rotation for a pure enantiomer is known to be +158^o g^-1 mL^-1 dm^-1. What will be the specific rotation of mixtures containing:

a.: 25% of the (+) enantiomer and 75% of the (-) enantiomer,
b.: 50% of the (+) enantiomer and 50% of the (-) enantiomer, and,
c.: 75% of the (+) enantiomer and 25% of the (-) enantiomer?

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[a] = ^a_{/(c x l)}

If the fraction of the (+) enantiomer is x, then (1x) gives the fraction of the (-) enantiomer. For any mixture of the two, the apparent specific rotation will be given by:

x(+[a]) + (1x)(-[a]) = [a]_apparent

Solution:

[a] = ^a_{/(c x l)}

If the fraction of the (+) enantiomer is x, then (1x) gives the fraction of the (-) enantiomer. For any mixture of the two, the apparent specific rotation will be given by:

x(+[a]) + (1x)(-[a]) = [a]_apparent

For these mixtures:

a. 0.25(+158^o) + 0.75(-158^o) = -79^o

b. 0.50(+158^o) + 0.50(-158^o) = 0^o (racemic mixture)

c. 0.75(+158^o) + 0.25(-158^o) = +79^o

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