# How do I find the specific absorptivity from the following graph?

Apr 25, 2017

The mass percentage of cobalt in your sample is 22.1%
The molecular extinction coefficien is 0.929

#### Explanation:

The concentration of cobalt can be determined out of the graph. The graph you have provided in the picture is a calibration curve. This curve shows that with higher concentrations, the absorbance is higher.

Now, this curve is probably obtained by creating known concentrations and measuring the absorbance of those solutions. These are the 6 points in the table in your picture.
In the graph, we can see clearly that the function is linear and gives a nice line connecting all the points. The function of this line is showed in the picture which is:
$y = 1.0768 x + 0.0011$
with $y$= Absorbance and $x$=concentration

We can now fill in the measure absorbance of your sample, which gave the value of 0.405. We use the function of the straight line to calculate the concentration of the sample:

$y = 1.0768 \cdot 0.405 + 0.0011 = 0.437204$ 1g/100 ml

Now we have 100 mL solution in the flask, therefore we now know that the amount of cobalt in your solution is 0.437204 gram.

So the concentration of cobalt in your solution is
0.437204/1.975 xx100%=22.1%
This is the mass percentage of cobalt in your sample.

__________
Now on to the specifik absorptivity.
I am pretty sure you mean the molecular extinction coefficient as that one seems possible to calculate from your information.

For this calculation, we use the Law of Lambert-Beer.
$A = \varepsilon \cdot c \cdot l$
with
A=absoption
$\varepsilon$=molecular extinction coefficient
l=lenght the light travels through the cuvette (cm) of the machine.

In most cases, the length of the cuvette is 1 cm. The absorption and the concentrations are given for some points. We can rewrite it as
$\varepsilon = \frac{A}{c \cdot l}$
For calculations, I used the fourth point on your graph.
$\varepsilon = \frac{0.4054}{0.4362 \cdot 1} = 0.92939$

Note that I do not know for sure if this is what you meant with the specifik absorptivity.