Question

A 1.50 g sample of coniine, the toxic extract of poison hemlock, was dissolved in 10.0 mL of ethanol and placed in a sample cell with a 5.00 cm pathlength. The observed rotation at the sodium D line was 11.21°. Calculate ${\mathbf{\left[}\mathbf{\alpha }\mathbf{\right]}}_{\mathbf{D}}$ for coniine.

Short answer

${\left[\mathrm{\alpha }\right]}_{\mathrm{D}}=\text{+16.1}°$for coniine

Step-by-step solution

Optical activity

Optical activity is defined as the ability of a substance to rotate the plane of polarized light that is passed through it.

Specific rotation

In a polarimeter, the angle of rotation of the plane of polarization of a ray of monochromatic light passing through a tube 1 decimeter long containing the substance at a concentration of 1 gram per millimeter in solution is measured in degrees.

Specific rotation is denoted by ${\left[\mathrm{\alpha }\right]}_{\mathrm{D}}$and calculated by the below-given formula:

$\begin{array}{c}{\left[\mathrm{\alpha }\right]}_{\mathrm{D}}=\frac{\text{Obser}\mathrm{ved}\text{rotation(degree)}}{\mathrm{Pathlength},\mathrm{l}\left(\mathrm{dm}\right)\times \mathrm{Concentration},\mathrm{c}(\mathrm{g}/{\mathrm{cm}}^3)}\\ =\frac{\mathrm{\alpha }}{\mathrm{l}\times \mathrm{c}}\end{array}$

[α]D for coniine

Values of observed rotation, pathlength and concentration are given. For coniine ${\left[\mathrm{\alpha }\right]}_{\mathrm{D}}$can be calculated as follows:

$\begin{array}{c}{\left[\mathrm{\alpha }\right]}_{\mathrm{D}}=\frac{\text{Obser}\mathrm{ved}\text{rotation(degree)}}{\mathrm{Pathlength},\mathrm{l}\left(\mathrm{dm}\right)\times \mathrm{Concentration},\mathrm{c}(\mathrm{g}/{\mathrm{cm}}^3)}\\ =\frac{\mathrm{\alpha }}{\mathrm{l}\times \mathrm{c}}\\ =\frac{{1.21}^{°}}{\begin{array}{l}5\times {10}^{-1}\mathrm{dm}\times \frac{1.50}{10}\mathrm{g}/\mathrm{ml}\\ =\frac{{1.21}^{°}}{.5\mathrm{dm}\times 0.150\mathrm{g}/\mathrm{ml}}\\ =+{16.1}^{°}\end{array}}\end{array}$