Concept explainers
(a) An aqueous solution containing
(b) If this solution were mixed with
Interpretation:
The specific rotation of fructose is to be calculated and the specific rotation of the resulting fructose mixture and its optical rotation is to be calculated.
Concept introduction:
The specific rotation, denoted by
Here,
The optical purity is numerically equal to the percentage enantiomeric excess, which can be determined from the following expression:
The percent enantiomeric excess is the difference between the percentages of each enantiomer.
It can also be calculated according to the following equation:
Where
Mixtures containing equal quantities of enantiomers are called racemic mixtures.
Answer to Problem 43P
Solution:
a) The specific rotation of optically pure fructose is
b) The specific rotation of resulting fructose mixture is
Explanation of Solution
a) Calculation for specific rotation of fructose.
Calculating the concentration of the sample solution as follows:
Now, calculate the length of the polarimeter tube as follows:
The specific rotation for the optically pure enantiomer can be calculated below:
Substitute the required values in the above equation.
Hence the specific rotation of optically pure fructose is
b) The amount of racemic mixture added is
The amount of fructose present as pure enantiomer is
The racemic mixture contains equal amounts of both the enantiomers. The total amount of pure enantiomer is calculated below.
Combined amount of the pure enantiomer is
Thus, the amount of the other enantiomer is
Total volume of solution is
The concentration of the pure enantiomer is calculated as follows:
The concentration of the other enantiomer is calculated as follows:
The enantiomeric excess is given by the expression as follows:
Substitute the required values in the above equation.
Optical purity is equal to the enantiomeric excess. Thus, the specific rotation of the sample is calculated using the following formula given below.
Here, the specific rotation of pure enantiomer of fructose is
Hence the specific rotation of resulting fructose sample is
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Chapter 4 Solutions
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