Question

37 multiple choice 2 points glucose has a specific rotation of +52.8°. predict the concentration of a glucose aqueous solution contained in a 10 cm long polarimetry tube if a rotation of +15.8° was observed. 0.0299 g/ml 0.299 g/ml 0.334 g/ml 3.34 g/ml previous next

Explanation:

Step1: Recall the formula for specific rotation

The formula for specific rotation \([\alpha]_D^T=\frac{\alpha}{l\times c}\), where \([\alpha]_D^T\) is the specific rotation, \(\alpha\) is the observed rotation, \(l\) is the path - length (in dm), and \(c\) is the concentration (in g/mL).
First, convert the path - length from cm to dm. Given \(l = 10\space cm=1\space dm\) (since \(1\space dm = 10\space cm\)).
We know that \([\alpha]_D^T = + 52.8^{\circ}\), \(\alpha=+15.8^{\circ}\), and \(l = 1\space dm\).

Step2: Rearrange the formula to solve for concentration \(c\)

From \([\alpha]_D^T=\frac{\alpha}{l\times c}\), we can solve for \(c\) as \(c=\frac{\alpha}{l\times[\alpha]_D^T}\).
Substitute the given values: \(c=\frac{15.8^{\circ}}{1\space dm\times52.8^{\circ}}\).

Step3: Calculate the concentration

\(c=\frac{15.8}{52.8}\space g/mL\approx0.299\space g/mL\)

Answer:

B. 0.299 g/mL