Question

20 multiple choice 2 points (s)-2 - chloropentane has a specific rotation of +34.07°. (i) show the structure of (s)-2 - chloropentane. (ii) what is the specific rotation of (r)-2 - chloropentane. (iii) if a sample containing (r)- and (s)- 2 - chloropentane has a specific rotation of -12.47°, calculate the percentage composition of the sample. (i) (ii) -34.07° (iii) %r = 31.70%; %s = 68.30% (i) (ii) -34.07°

Explanation:

Step1: Structure of (S)-2 - chloropentane

Draw the structure with the correct stereochemistry at the second - carbon atom where the chlorine is attached.

Step2: Specific rotation of enantiomers

Enantiomers have equal but opposite specific rotations. Since (S)-2 - chloropentane has a specific rotation of + 34.07°, (R)-2 - chloropentane has a specific rotation of - 34.07°.

Step3: Calculate percentage composition

Let the fraction of (R) - isomer be \(x\), then the fraction of (S) - isomer is \(1 - x\). The observed specific rotation \(\alpha_{obs}=-12.47^{\circ}\), and \(\alpha_{S}= + 34.07^{\circ}\), \(\alpha_{R}=-34.07^{\circ}\). So \(\alpha_{obs}=\alpha_{R}x+\alpha_{S}(1 - x)\). Substitute the values: \(-12.47=-34.07x + 34.07(1 - x)\). Expand: \(-12.47=-34.07x+34.07 - 34.07x\). Combine like - terms: \(-12.47 = 34.07-68.14x\). Rearrange to solve for \(x\): \(68.14x=34.07 + 12.47=46.54\). Then \(x=\frac{46.54}{68.14}\approx0.683\) (fraction of (S) - isomer), and \(1 - x = 0.317\) (fraction of (R) - isomer). Convert to percentages: %R = 31.70% and %S = 68.30%.

Answer:

(i) [Appropriate 3 - D structure of (S)-2 - chloropentane as shown in the correct option]
(ii) - 34.07°
(iii) %R = 31.70%; %S = 68.30%