Question

How to get new concentration from percent transmittance?

Answer 1

Hint: As we already know that transmittance is the percent of the light passing through the sample. It is always expressed in terms of percentage. This question is based on Beer-Lambert law and a relation between transmittance and absorbance.

Complete answer:
Relation between transmittance and absorbance is as follows:
 $A=-\log (T)$
Also, absorbance can be expressed in terms of concentrations.
 $A=\epsilon bc$
Where, $A$ is the absorbance, $\epsilon$ is the molar absorptivity, $b$ is the optical path length and $c$ is the concentration of in terms of molarity. Also, $\epsilon$ and $b$ are constants for the same substances.
By combining the above two equations,
 $-\log (T_1)=\epsilon b{c}_1$ …( $1$ )
 $-\log (T_2)=\epsilon b{c}_2$ …( $2$ )
Dividing equation $2$ by equation $1$ .
We get,
 ${\displaystyle \frac{c_2}{c_1}}={\displaystyle \frac{\log (T_2)}{\log (T_1)}}$
Now, new concentration can be calculated as
 $c_2=c_1{\displaystyle \frac{\log (T_2)}{\log (T_1)}}$
The above equation shows that or we can say it indicates that if transmittance of light is more, then it absorbs less. It absorbs less if less particles are solutions that block the path of the incoming light.

Additional Information:
Beer –lambert law indicates a linear relationship between the absorbance and the concentration, molar absorption coefficient and optical coefficient of the substances. In other words, we can say it is a linear relationship between the concentration and absorbance of the solution. It enables the concentration of a solution to be calculated by measuring absorbance of solutions.
Mathematically, it can be expressed as:
 $A=\epsilon bc$

Note:
Transmittance of the light provides information for many applications. It is used for measuring concentration of chemicals in solutions, atmospheric haze and water clarity. It is also used in testing window tint films, glass testing etc.