# Spectrophotometry

## Beer's Law

What are the factors that affect the amount of light a sample absorbs?

Tartrazine is a yellow colored food dye. Suppose photons pass through a solution containing dissolved tartrazine. From time to time, a photon might encounter a tartrazine molecule, in which case there is a chance the photon will be absorbed by the tartrazine. Once absorbed, the photon is gone and the photon's energy is deposited into the tartrazine.

For a photon passing through the sample solution, what is the probability the photon is absorbed by a tartrazine molecule?

The experiment below explores two factors that strongly affect the likelihood a photon is absorbed: the molar concentration ( *C* ) of the tartrazine and the cell path length ( *L* ). The molar concentration is the moles of tartrazine dissolved in each liter of solution. The cell path length is the length a solution through which the light passes. In chemistry *L* is often expressed in centimeters.

**Beer's Law** is a mathematical equation relating the absorbance ( *A* ) of a solution to the molar concentration of the absorbing molecule and the cell path length. Use the virtual experiment below to explore the effects of molar concentration and cell path length on the absorbance of light.

Operation of the Spectrophotometer: Select the desired cell path length and tartrazine concentration. Then start the simulation. Once photons begin reaching the detector, start the Data Acquisition. The intensity of light (photons per second) reaching the detector will be displayed. Note that the simulation employs more photons than are shown on the screen.

For a blank (that is, a solution containing no tartrazine), the intensity is *I*_{0} = 150. photons/sec . Use the measured intensity and this value for *I*_{0} to calculate the transmittance ( *T* ) and the absorbance ( *A* ). Explore how *T* and *A* depend upon *C* and *L*.

*T*=

*I*

*I*

_{0}

*A*= - log

_{10}

*T*

**Questions**

- Why is Beer's Law formulated in terms of absorbance rather than transmittance?
- Can you write a mathematical equation for Beer's Law?
- Are there any factors other than concentration and cell path length that you expect to influence the value of the absorbance?

**Reminders**

*I*_{0}= 150. photons/sec- μM represents micromolar. 1 μM = 1 x 10
^{-6}mole/L - The simulation operates with 425 nm photons.

*BeersLaw.html version 3.0*

*© 2000, 2014, 2023 David N. Blauch*