# Question a3ca9

Aug 17, 2015

[alpha]_(lamda)^T = -0.66""^@

#### Explanation:

Specific rotation can be found from observed rotation by using the formula

$\textcolor{b l u e}{{\left[\alpha\right]}_{L a m \mathrm{da}}^{T} = \frac{\alpha}{l \cdot c}}$, where

$\alpha$ - the measured rotation;
$l$ - the path length;
$c$ - the concentration of either the pure liquid, or the solution - in your case, it will represent the concentration of the solution.

Now, path length is usually expressed in decimeters and concentration for solutions in grams per 100 mL.

Another important thing to mention here is that you didn't specify the wavelength of light used, $l a m \mathrm{da}$, and the temperature at which you made the measurement, $T$, so I assume them to be the standard values.

So, start by converting the concentration from $\text{g/mL}$ to $\text{g/100 mL}$ and the path length from $\text{cm}$ to $\text{dm}$.

$\text{0.120 g"/"30 mL" = "0.004 g/mL}$

$0.004 \text{g"/(1color(red)(cancel(color(black)("mL")))) * (100color(red)(cancel(color(black)("mL"))))/"100 mL" = "0.4 g/100 mL}$

and

5.0color(red)(cancel(color(black)("cm"))) * "1 dm"/(10color(red)(cancel(color(black)("cm")))) = "0.5 dm"#

This means that the specific rotation will be

${\left[\alpha\right]}_{L a m \mathrm{da}}^{T} = \left(- 0.132 {\text{^@)/("0.5 dm " * " 0.4 g/100 mL") = color(green)(-0.66}}^{\circ}\right)$