Question

Beer’s law is used to measure the concentration of species in solutions, once a “standardization curve” has been prepared for that species. In one such experiment, per cent transmission was measured for a series of solutions with known concentrations and the results were as follows:

Plot these results to obtain the standardization curve. An unknown concentration of the same species, measured in the same transmission cell, transmitted 35% of the incoming light. Calculate the concentration of the unknown solution.

Short answer

The concentration of the unknown solution is calculated as 2.6μg mL^-1.

Step-by-step solution

Definitions of Absorption and Transmittance

Absorption: The amount of intensity of incident radiation gets absorbed in the solution is called as absorption. Absorption is also identified as optical density. The absorption is calculated using the Lambert-Beer law.

Transmittance: The amount of incident radiation transmitted through the solution is known as transmittance.

Explanation Absorption and Transmittance

According to Lambert-Beer law, the graph between Absorbance and concentration forms a uniform straight line. After plotting the graph, by putting the straight line at the absorbance of the unknown solution, the concentration can be determined by placing a vertical line.

Calculate the concentration of an unknown solution

Percentage transmission is given, so firstly the conversion of percent transmittance to absorbance needs to be done to plot the graph.

Use the Lamber-Beer law to calculate absorbance:

A= log(I˳/I) and (I˳/I) = 1/T, Now, (Per cent Transmittance)/100 = T,

Use above expressions to conclude,

A = log (100/ (Per cent Transmittance))

After absorbance plot graphs to calculate unknown concentration:

So,

Draw horizontal and vertical at the transmittance percent of 35% which is 0.4556 absorbance the concentration is determined. Therefore, the concentration at 35% transmittance is 2.6 μg mL^-1.