Calorimetry
Beer’s law: It states that the amount of light absorbed by a substance is directly proportional to the concentration of solution.
- It states that when a monochromatic beam of radiation passes through the light absorbing medium the rate of decrease of intensity of light with respect to the thickness of the medium is directly proportional to the no. density of the light absorbing medium $$-\frac{dI}{dx}\propto c$$
Lambert’s law: It states that the amount of light absorbed by a substance is directly proportional to the path length.
- It states that when a beam of monochromatic radiation passes through light absorbing medium the rate of decrease in the intensity of light with respect to the thickness of medium is directly proportional to the intensity of Incident radiation $$-\frac{dI}{dx}\propto I$$
Deriving a relation #
$$ \begin{align} -\frac{dI}{dx}=k cI\\ -\frac{dI}{I}=k cdx\\ -\ln(\frac{I}{I_0})=k cl\\\ A=-log(T)=\epsilon_v cl\\ ;\\ T=I/I_0 \end{align} $$
- ϵ_v: molar extension coefficient, property of light absorbing medium and signifies the ability of the material to absorb light at a particular wavelength. Depends on frequency.
- Units: molarity ^-1 length^-1 = mol^-1 cm^-1
- A: absorbance, and is a unit less quantity.
- The ratio $T=I/I_0$ is known as transmittance.
Examples #
Q. On passing monochromatic light through a 0.05M solution in a 2cm thick cell, the intensity of the transmitted light was reduced to 40%. Calculate the molar extension coefficient
$$ \begin{align} -log(40/100)=\epsilon_v0.052\\ \epsilon_v=3.98\\ M^{-1}cm^{-1} \end{align} $$ #
Q2. What percentage of light will be absorbed by a cell having a dye concentration of 25gm/l , if the same cell transmits 50% of the same wavelength when the concentration of the dye solution is 10gm/L
Log(100/50) = e 10 l
Log(100/x) = e 10 l
What should be the cell thickness if 80% of the light is absorbed by the first solution?
Absorbance is an additive property