Final answer:
The specific rotation of a chiral compound can be calculated using the formula [a] = observed rotation / (concentration * path length). The observed rotation if the solution is mixed with an equal volume of the enantiomer of the compound will decrease by half. The specific rotation after dilution can be calculated using the same formula.
Step-by-step explanation:
The specific rotation ([a]) is a characteristic physical property of chiral compounds. It is defined as the observed rotation of the plane of plane-polarized light when the concentration is fixed to 1 g/mL and the path length is 1 dm. In the given question, the observed rotation of a 0.110 m solution of the chiral compound is +0.24° in a 1-dm sample container. The molar mass of the compound is 120.0 g/mol.
To calculate the specific rotation, we use the formula:
[a] = observed rotation / (concentration * path length)
Substituting the given values:
[a] = (+0.24°) / (0.110 m * 1 dm)
[a] = +2.18°/(dm*g/mL)
The observed rotation if this solution is mixed with an equal volume of a solution that is 0.150 M in the enantiomer of the compound can be calculated by considering that the concentration of the chiral compound will be halved. Therefore, the observed rotation will also decrease by half. Thus, the observed rotation will be +0.12°.
The observed rotation if the solution of the chiral compound is diluted with an equal volume of solvent will be zero. As the concentration of the chiral compound becomes negligible, there will be no observed rotation.
The specific rotation of the chiral compound after the dilution can be calculated using the same formula:
[a] = observed rotation / (concentration * path length)
Substituting the values:
[a] = (+0.12°) / (0.055 m * 1 dm)
[a] = +2.18°/(dm*g/mL)
The specific rotation of the enantiomer of the compound after the dilution will also be the same as the specific rotation of the original compound, as they are enantiomers and have the same physical properties.