Let us learn about the relationship between concentration and light.
The seemingly obvious way of taking reading on a colorimeter is to measure % transmission and adjust the ‘blank’ to 100%.
For example, consider a situation where a blank is measured followed by three standard solution having concentration of 1, 2 and 3 units respectively. Ideally, a colorimeter should be giving concentration reading directly, but consider the above solutions when analysed.
The solution with a concentration of 1 unit reduces the light to 50% therefore, the solution with a concentration of 2 units will reduce the light to 25% and the solution with a concentration of 3 units will reduce the light to 12.5% Fig. 22.6.
Therefore if the colorimeter is calibrated using a transmission scale, the following graph is produced:
The calibration in %T has the drawbacks of being non-linear and readings, decreasing, with increasing concentration. Bonguer first investigated this type of relationship for changes in thickness of solid materials. His work was followed by Lambert and Beer in 1852, who extended the studies to solutions. All three investigators contributed what is universally known as the .The Beer-Lambert Law.
T = I/I0
where T = Transmittance, l0 is the intensity of incident radiation and I is the intensity of transmitted radiation.
This states that:
The light transmitted through a solution changes in an inverse logarithmic relationship to the sample concentration.
In order to take measurements both directly and linearly in terms of concentration, %T readings must be converted into an inverse logarithmic form which are called optical density units (OD or absorbance (A).
The formula is: = OD = log10100%T
Therefore, for the given example, the relationship of OD to concentration is shown in the table 22.2 below. A calibration curve of OD against concentration is linear and directly proportion (22.)
Optical density (absorbance) is used for colorimetric analysis so that readings relate directly to concentration (Fig. 22.7).
Similarly, optical density changes directly with sample path length. Thus we arrive at
Abs = Ex c x I
Abs = Absorbance
E = Extinction coefficient or molar absorptivity
c = Concentration
I = Path length
I is fixed by the path length of the cuvette (usually 10mm) and E is a constant for each chemical species hence Abs x C.