How am I supposed to do these questions? I'm completely lost.
A 0.120 M solution of an enantiomerically pure chiral compound D has an observed rotation of 0.12° in a 1-dm sample container. The molar mass of the compound is 130.0 g/mol.
(b) What is the observed rotation if this solution is mixed with an equal volume of a solution that is 0.120 M in L, the enantiomer of D?
(c) What is the observed rotation if the solution of D is diluted with an equal volume of solvent?
(d) What is the specific rotation of D after the dilution described in part (c)?
(e) What is the specific rotation of L, the enantiomer of D, after the dilution described in part (c)?
(f) What is the observed rotation of 100 mL of a solution that contains 0.01 mole of D and 0.005 mole of L? (Assume a 1-dm path length.)
Help is greatly appreciated. :)
To solve these questions, you will need to use the concept of specific rotation and the relationship between concentration and observed rotation. Here's how you can approach each part of the question:
(b) To find the observed rotation when the solution of D is mixed with an equal volume of the enantiomer L, you can consider that the concentrations of D and L are now both 0.120 M due to the equal volume mixing. Since the specific rotation is a property of the compound, it remains the same for both D and L. Therefore, the observed rotation will also be the same. You can simply use the observed rotation of 0.12° as the answer for this part.
(c) When the solution of D is diluted with an equal volume of solvent, the concentration of D will be halved, resulting in a concentration of 0.060 M. However, the specific rotation remains the same since it is a property of the compound. To find the observed rotation, you can use the formula:
Observed Rotation = Specific Rotation x Concentration x Path Length
Since the observed rotation is directly proportional to the concentration, you can multiply the initial observed rotation (0.12°) by the concentration ratio (0.060/0.120) to get the answer for this part.
(d) The specific rotation after the dilution described in part (c) remains the same as it is a property of the compound and independent of concentration. Therefore, the specific rotation of D is the same as the specific rotation mentioned in the question.
(e) Similarly, the specific rotation of L (the enantiomer of D) remains the same after the dilution as well. The specific rotation of L is also the same as the specific rotation mentioned in the question.
(f) To find the observed rotation of a solution that contains 0.01 mole of D and 0.005 mole of L, you can use the concept of weighted average specific rotation. First, calculate the concentration of D and L in the solution. Since 1 mole of a compound in 1000 mL of solution gives a 0.01 M concentration, you can calculate the concentration of D and L by dividing the number of moles by the volume in liters. Once you have the concentrations, use the formula mentioned earlier to calculate the observed rotation for both D and L separately. Finally, add the observed rotations of D and L to find the total observed rotation of the solution.
Remember to use the given molar mass of the compound (130.0 g/mol) to convert between moles and grams if necessary.
I hope this step-by-step explanation helps you understand how to solve these questions. If you have any further questions, feel free to ask!
To solve these questions, we need to use the concept of specific rotation, which is a measure of the optical activity of a chiral compound. The formula to calculate specific rotation is:
Specific rotation = observed rotation / (concentration * path length)
Where:
- Observed rotation is the angle of rotation observed in degrees.
- Concentration is the concentration of the chiral compound in moles per liter.
- Path length is the length of the sample container in decimeters.
Now let's solve the questions step-by-step:
(b) To calculate the observed rotation when the D solution is mixed with an equal volume of the enantiomer L, we can use the formula:
Observed rotation (mixture) = ([D] * αD + [L] * αL) / ([D] + [L])
Where:
- [D] is the concentration of D.
- [L] is the concentration of L.
- αD is the specific rotation of D.
- αL is the specific rotation of L.
Since the volume of the solutions is equal and they have the same concentration, the equation becomes:
Observed rotation (mixture) = (2 * [D] * αD) / (2 * [D]) = αD
So, the observed rotation when the D solution is mixed with an equal volume of the L solution will be the same as the specific rotation of D.
(c) When the solution of D is diluted with an equal volume of solvent, the concentration of D will be halved. Therefore, the observed rotation will also be halved. Therefore,
Observed rotation after dilution = Observed rotation (original solution) / 2
(d) The specific rotation after dilution can be calculated using the formula:
Specific rotation (after dilution) = Observed rotation (after dilution) / (concentration (after dilution) * path length)
Since we halved the concentration in part (c), the concentration after dilution will be half of the original concentration. Therefore,
Specific rotation (after dilution) = (Observed rotation (original solution) / 2) / (0.5 * concentration * path length)
(e) The specific rotation of L after the dilution described in part (c) will be the same as the specific rotation of D since they are enantiomers and have the same specific rotation.
(f) To calculate the observed rotation of 100 mL of the solution containing 0.01 mole of D and 0.005 mole of L, we need to determine the concentrations of D and L.
Concentration of D = (moles of D / total volume in liters) = (0.01 mol / 0.2 L) = 0.05 M
Concentration of L = (moles of L / total volume in liters) = (0.005 mol / 0.2 L) = 0.025 M
Using the formula for observed rotation:
Observed rotation = concentration * specific rotation * path length
Observed rotation = (0.05 M * αD * 1 dm) + (0.025 M * αL * 1 dm)
Plug in the values for αD and αL to find the observed rotation.
I hope this helps! Let me know if you have any further questions.
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