Specific Rotation Calculation: Polarimeter Demystified

Chapter 6, Problem 5-32

(choose chapter or problem)

QUESTION:

Calculate the specific rotations of the following samples taken at $$25^{\ \circ}\mathrm{C}$$ using the sodium D line.

(a) 1.00 g of sample is dissolved in 20.0 mL of ethanol. Then 5.00 mL of this solution is placed in a 20.0-cm polarimeter tube. The observed rotation is $$1.25^{\circ}$$ counterclockwise.

(b) 0.050 g of sample is dissolved in 2.0 mL of ethanol, and this solution is placed in a 2.0-cm polarimeter tube. The observed rotation is clockwise $$0.043^{\circ}$$.

QUESTION:

Calculate the specific rotations of the following samples taken at $$25^{\ \circ}\mathrm{C}$$ using the sodium D line.

(a) 1.00 g of sample is dissolved in 20.0 mL of ethanol. Then 5.00 mL of this solution is placed in a 20.0-cm polarimeter tube. The observed rotation is $$1.25^{\circ}$$ counterclockwise.

(b) 0.050 g of sample is dissolved in 2.0 mL of ethanol, and this solution is placed in a 2.0-cm polarimeter tube. The observed rotation is clockwise $$0.043^{\circ}$$.

Step 1 of 2

(a)

Mass of sample = 1.00gm

Volume of ethanol = 20.0mL

Volume of sample = 5mL

Width of polarimeter tube  = 20.0cm = 2dm

Counterclockwise rotation $$=-1.25^{\circ}$$

Specific rotation  can be calculated as follows:-

$$[\boldsymbol{\alpha}]_{\mathbf{l}}^{\mathbf{T}}=\boldsymbol{\alpha} / \mathbf{l} \mathbf{c}$$

Where:

$$[\alpha]_{1}^{\mathrm{T}}=$$ specific rotation in degrees. (The correct units are deg $$\mathrm{cm}^2\mathrm{\ g}^{-1}$$, but are usually just given as degrees).  l is the wavelength of light used for the observation (usually 589 nm, the D line of a sodium lamp unless otherwise specified.  This wavelength is responsible for the orange-yellow color of the common sodium vapor street light). T is the temperature in $${ }^{\circ} \mathrm{C}$$.

$$\alpha=$$ observed rotation in degrees.

$$l=$$ cell path length in decimeters. (1 decimeter = 1 dm = 10 cm. A standard polarimeter tube is 1.00 dm in length.)

$$C=$$ concentration in $$\mathrm{g}\mathrm{\ ml}^{-1}$$ for a pure liquid compound (i.e., the liquid's density), or $$g\ 100\mathrm{ml}^{-1}$$ for a solution.

Now we have to calculate the concentration of liquid (density) = mass/volume

Substituting the values of mass and volume the

density $$=1.00\mathrm{g}/20.0\mathrm{\ mL}=0.0500\mathrm{\ g}/\mathrm{mL}$$

Thus the specific rotation:-

$$\begin{array}{c} {[\alpha] \mathrm{D}^{25}=\frac{-1.25^{\circ} }{(0.0500)(2.00)}=-12.5^{\circ}} \end{array}$$

Hence the specific rotation of the samples $$=-12.5^{\circ}$$

Specific Rotation Calculation: Polarimeter Demystified

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Discover how to calculate specific rotations of samples using a polarimeter in this informative chemistry tutorial. Explore optical activity and learn step-by-step calculations for two real-world examples. Enhance your understanding of specific rotation and its application in chemical analysis.