Draw a diagram which explains why it’s possible to measure the concentration of a solute using a spectrophotometer.

Answer 1

Thanks for your question Sally! The Beer-Lambert law (or Beer's law) illustrates the linear relationship between solute concentration and absorbance of light. That means, the higher the concentration, the higher the absorbance.

To diagram the relationship between concentration (the number of solute molecules in a solution) and the absorbance (the amount of light absorbed by those molecules) you need to draw what happens with light in the spectrophotometer tube. To determine concentration, you need to make a standard (calibration) curve.

Make a visual outline of what happens when light hits a cuvette tube holding the solution in a spectrophotometer. Draw a tube with some solute molecules in it. Label the width of the tube as l (path length). Draw an arrow pointing at the tube which represents light hitting the tube; label this arrow as I₀ (incident intensity).  Then, draw an arrow directed away from the tube on the other side. This represents the light which is transmitted; label this arrow I (transmitted intensity).  Transmitted light is the light that passes through the tube without being absorbed by the molecules of solute.

The absorbance is indirectly related to transmittance, meaning as absorbance goes up, transmittance goes down. This makes sense logically. If there are a lot of molecules in a solution (high concentration) and you shine a light on it, then a lot of the light will be absorbed by the molecules which will make less light available to be transmitted out of the tube. But if there are only a few molecules of solute (low concentration), then only a little light will be absorbed by the solute and more light will be transmitted, unabsorbed, out of the tube.  

Transmittance (T) is the amount of transmitted light (I) over the amount of incident, or initial light (I₀).  

T= I/I₀

Absorbance (A) is found by taking the negative log of T.

A= -log T

Beer’s law states absorbance (A) is equal to the molar absorption coefficient (ε), which is a measure of a specific molecule’s ability to absorb light, times the concentration (c), times the optical length (l), which is the width of the cuvette tube.

A = εcl

You can think of this as a linear equation in the form of y=mx+b. The y-axis is your absorbance. The x-axis is concentration and the slope (m) is the molar absorption coefficient (ε). The optical length (l) is always kept at 1 centimeter and can be ignored, because a number multiplied by 1 is that number. Theoretically, there is no y-intercept (b), because without any solute (c=0), there should be no absorbance (A=0).

 

If you measure the absorbance of different standard dilutions of known concentrations, you can construct a graph with the data and derive the equation (A= εcl) by plotting the points on a graph (x axis is concentration and y axis is absorbance). This graph is called a standard curve, also known as a calibration curve.

After you construct this graph, you can use it to determine the concentration solute in an unknown solution by measuring the absorbance of your unknown in a spectrophotometer, then plotting it on the graph you made with your known solutions and corresponding absorbance readings. This will give you your unknown concentration.  You cannot find the concentration of an unknown solution without first making a standard curve.