using a spectrophotometer what is the relationship between absorbance and the concentration of light absoring substance in a solution.

Absorbance is a term used by chemists. It is the log to base 10 of Io/I. where Io is the intensity of light (or infrare radiation) entering a sample and I is what comes out at a specific wavcelength. It is related to path length (cm), species concentation (moles/lieter) and a species-dependent absorption parameter in liters*mole^-1*cm^-1

As a physicist, I was taught to use the term absorptance, which is somewhat different, I/Io. If the absorptance is A for a light beam travelling through a sample of path length L,

A = 1 - e^(-kL), where
k is the absorption coefficient. k is what is proportional to the concentration of the light-absorbing substance.

In spectroscopy, the absorbance A is defined as

You will find a more complete answer to your question at

http://en.wikipedia.org/wiki/Absorbance

The relationship between absorbance and the concentration of a light-absorbing substance in a solution is described by the Beer-Lambert Law. This law states that the absorbance (A) of a solution is directly proportional to the concentration (c) of the light-absorbing substance and the path length (L) through which the light passes.

Mathematically, the Beer-Lambert Law is expressed as:

A = ε × c × L

where:
A is the absorbance of the solution,
ε (epsilon) is the molar absorptivity or extinction coefficient of the substance,
c is the concentration of the light-absorbing substance in moles per liter (M),
L is the path length of the light through the solution in centimeters (cm).

In simpler terms, this equation states that absorbance increases linearly with the concentration of the light-absorbing substance. It means that the more concentrated the substance is, the more light it will absorb.

To determine the relationship between absorbance and concentration using a spectrophotometer, you need to:
1. Prepare a set of solutions with known concentrations of the light-absorbing substance.
2. Measure the absorbance of each solution using a spectrophotometer.
3. Plot a graph of absorbance (y-axis) versus concentration (x-axis).
4. The resulting graph should be a straight line. The slope of this line represents the molar absorptivity (ε) of the substance, while the y-intercept represents the absorbance when the concentration is zero.

By comparing the absorbance of an unknown solution to the calibration curve, you can determine the concentration of the light-absorbing substance in the unknown solution.