A sample of 2-butanol has a specific rotation of -9.75 degrees. Determine the % ee (enantiomeric excess) and the molecular composition of this sample. The specific rotation of pure (+)-2-butanol is +13.0 degrees.
%ee = %1-%2 = ??
If we call the mole fraction of the A isomer x (with specific rotation of +13.0) and the mole fraction of the B isomer 1-x (with a specific rotation of -13.0), then will it not be true that
13.0*x + [-13.0*(1-x)] = -9.75
Solve for x and 1-x.
Multiply those by 100 to change to mole percent.
Then mole percent A - mole percent B = %excess enantiometer. You take the absolute value of this number so the sign at the end doesn't matter. Check my thinking on this.
To determine the percent enantiomeric excess (% ee) and the molecular composition of the sample, we first need to calculate the observed rotation of the sample and then use it to calculate the % ee.
1. Calculate the observed rotation:
Observed rotation = Specific rotation of the sample / Specific rotation of pure (+)-2-butanol
Observed rotation = -9.75 degrees / +13.0 degrees
2. Determine the sign of the specific rotations:
Since the specific rotation of the pure (+)-2-butanol is positive, and the observed rotation is negative, it means that the observed rotation is opposite in sign to the specific rotation of the pure enantiomer.
3. Calculate the % ee:
% ee = (Observed rotation / Specific rotation of pure enantiomer) * 100
% ee = (-9.75 degrees / 13.0 degrees) * 100
4. Determine the molecular composition of the sample:
The molecular composition of the sample cannot be directly determined from the specific rotation alone. It requires additional information, such as the concentration of the sample or the purity of the compound. Please provide more information if you want to determine the molecular composition.
Please note that specific rotations may vary depending on the conditions (e.g., concentration, temperature, solvent) under which the measurements are taken.
To determine the % ee (enantiomeric excess) and the molecular composition of the sample, you need to calculate the optical purity and the molar concentration of each enantiomer. Here's how you can do it step by step:
1. Calculate the observed rotation (OR):
OR = -9.75 degrees
2. Calculate the specific rotation (SR) of (+)-2-butanol:
SR = +13.0 degrees
3. Calculate the % ee (enantiomeric excess):
% ee = (OR / SR) * 100
% ee = (-9.75 / 13.0) * 100
% ee = -75.0%
4. The % ee represents the difference in concentration between the two enantiomers. If the % ee is positive, it means the (+) enantiomer is in excess, and if it is negative, it means the (-) enantiomer is in excess. In this case, since the % ee is negative (-75.0%), the (-) enantiomer is present in excess.
5. To determine the concentrations of each enantiomer, assume a total concentration of 100 grams (or 100 mL).
Let x be the concentration of (+)-2-butanol (in grams or mL),
Let y be the concentration of (-)-2-butanol (in grams or mL).
Since the % ee is -75.0%, we know that:
x - y = -75.0 (Equation 1)
Also, since the total concentration is 100 grams (or 100 mL):
x + y = 100 (Equation 2)
Solve these two equations simultaneously to find the concentrations of each enantiomer.
6. Solve Equations 1 and 2 simultaneously to find the concentrations of each enantiomer.
Subtract Equation 1 from Equation 2:
x + y - (x - y) = 100 - (-75.0)
2y = 175.0
y = 87.5 grams (or mL)
Substitute the value of y into Equation 2 to find x:
x + 87.5 = 100
x = 12.5 grams (or mL)
7. Calculate the molar masses of (+)-2-butanol and (-)-2-butanol to determine the molecular composition.
The molar mass of (+)-2-butanol = M1
The molar mass of (-)-2-butanol = M2
Let n1 be the number of moles of (+)-2-butanol,
Let n2 be the number of moles of (-)-2-butanol.
n1 = x / M1
n2 = y / M2
Divide the number of moles by the total number of moles to find the mole fraction of each enantiomer.
Mole fraction of (+)-2-butanol = n1 / (n1 + n2)
Mole fraction of (-)-2-butanol = n2 / (n1 + n2)
8. Determine the molecular composition based on the mole fractions obtained in step 7.
And that's how you can determine the % ee and molecular composition of the sample of 2-butanol with the given specific rotation.