Ch. 4 - Isomers: The Arrangement of Atoms in Space

Bruice8th EditionOrganic ChemistryISBN: 9780135213711Non è quello che usi tu?Cambia libro di testo

Bruice 8th Edition

Ch. 4 - Isomers: The Arrangement of Atoms in Space

Problema 81

Capitolo 4, Problema 81

A solution of an unknown compound (3.0 g of the compound in 200 mL of solution), when placed in a polarimeter tube 2.0 dm long, was found to rotate the plane of polarized light 18° in a counterclockwise direction. What is the specific rotation of the compound?

Guida verificata passo dopo passo

Step 1: Recall the formula for specific rotation: \( [\alpha] = \frac{\alpha}{l \cdot c} \), where \( [\alpha] \) is the specific rotation, \( \alpha \) is the observed rotation, \( l \) is the path length in decimeters, and \( c \) is the concentration in g/mL.

Step 2: Identify the given values from the problem: \( \alpha = -18^{\circ} \) (negative because the rotation is counterclockwise), \( l = 2.0 \, \text{dm} \), and the concentration \( c \) can be calculated as \( c = \frac{\text{mass of compound}}{\text{volume of solution}} = \frac{3.0 \, \text{g}}{200 \, \text{mL}} \).

Step 3: Calculate the concentration \( c \) by dividing the mass of the compound (3.0 g) by the volume of the solution (200 mL). This will give the concentration in g/mL.

Step 4: Substitute the values of \( \alpha \), \( l \), and \( c \) into the formula \( [\alpha] = \frac{\alpha}{l \cdot c} \). Ensure the units are consistent (e.g., \( l \) in dm and \( c \) in g/mL).

Step 5: Simplify the expression to find the specific rotation \( [\alpha] \). Remember to include the negative sign in the final calculation since the rotation is counterclockwise.

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Specific Rotation

Specific rotation is a property of chiral compounds that quantifies their ability to rotate plane-polarized light. It is defined as the observed rotation of light (in degrees) divided by the concentration of the solution (in grams per milliliter) and the path length of the sample (in decimeters). The formula is [α] = α / (c × l), where [α] is the specific rotation, α is the observed rotation, c is the concentration, and l is the path length.

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Specific rotation vs. observed rotation.

Chirality

Chirality refers to the geometric property of a molecule that makes it non-superimposable on its mirror image, much like left and right hands. Chiral molecules often exist as enantiomers, which are pairs of molecules that are mirror images of each other. The ability of chiral compounds to rotate polarized light is a key characteristic that is utilized in determining their specific rotation.

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What is chirality?

Polarimetry

Polarimetry is an analytical technique used to measure the angle of rotation of polarized light as it passes through a sample. This technique is particularly useful for studying chiral substances, as the degree of rotation can provide insights into the concentration and specific rotation of the compound. The polarimeter consists of a light source, a polarizer, a sample tube, and an analyzer to measure the rotation.

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