What is the percentage of the S enantiomer in a sample of carvone that has a specific rotation of 30, given that the specific rotation of (R)-carvone is -61?
How do i set up the problem?
To determine the percentage of the S enantiomer in a sample of carvone, you can use a formula that relates the specific rotation to the percentage of each enantiomer. The formula is:
Specific Rotation = (% S enantiomer × Specific Rotation of S enantiomer) + (% R enantiomer × Specific Rotation of R enantiomer)
Let's set up the problem using this formula:
1. Assign variables:
- % S enantiomer = x
- % R enantiomer = 100 - x (since the percentages of the two enantiomers must add up to 100)
- Specific Rotation of S enantiomer = ? (to be determined)
- Specific Rotation of R enantiomer = -61
2. Plug in the known values:
30 = (x × ?) + ((100 - x) × -61)
3. Solve for x:
Simplify the equation by multiplying the percentages by their respective specific rotations:
30 = (x × ?) - 61(100 - x)
Distribute the -61:
30 = (x × ?) - 6100 + 61x
Combine like terms:
30 = 62x - 6100
Move the constant to the other side:
30 + 6100 = 62x
Simplify:
6130 = 62x
Divide both sides by 62:
x = 6130 / 62
4. Calculate x:
x ≈ 98.871
So, the percentage of the S enantiomer in the carvone sample with a specific rotation of 30 is approximately 98.871%.