Final answer:
The specific rotation of a solution containing 40% (-) mandelic acid and 60% (+) mandelic acid would be +31.6 degrees.
Step-by-step explanation:
The specific rotation of a solution containing a mixture of enantiomers can be calculated by considering the proportion of each enantiomer and their individual specific rotations. In the case of mandelic acid, we know that (-) mandelic acid has a specific rotation of -158 degrees. If a solution contains 40% (-) mandelic acid and 60% (+) mandelic acid (which would have a specific rotation of +158 degrees, as enantiomers have equal but opposite specific rotations), we can calculate the net specific rotation using the following formula:
Specific rotation of the mixture = (fraction of (-) enantiomer * specific rotation of (-) enantiomer) + (fraction of (+) enantiomer * specific rotation of (+) enantiomer)
Substituting the values:
Specific rotation of the mixture = (0.40 * -158) + (0.60 * 158)
Specific rotation of the mixture = -63.2 + 94.8
Specific rotation of the mixture = +31.6 degrees