# GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/25

###### Question 25 (Textile Technology & Fibre Science)

Assuming Beer-Lambert law is applicable for dilute solutions, if the molar concentration of dye in the solution is doubled then the percentage increase in absorbance would be __100__.

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Formula-
A=bc ,
Where, A is absorbance
is molar absorbancy
b is length of light
c is molar concentration of dye in the solution
Here,
A is directly proportional to c ,
A1/A2=c1\c2 ,
As given in the question c2=2*c1 ,
By putting the value –
A1/A2=c1\c2 ,
A1/A2=c1\2*c1 ,
A1/A2=1/2 ,
A2/A1=2 ,
By substracting 1 both side ,
(A2/A1)-1=2-1 ,
A2-A1/A1=1 ,
A/A1=1 ,
(A/A1)*100=1*100
So,
Percentage increase in absorbance=100 (Answer)

### Explain Beer-Lambert law ?

The Beer-Lambert law, also known as the Beer-Lambert-Bouguer law, is a fundamental principle of spectroscopy that relates the amount of light absorbed by a material to the concentration of the absorbing species and the distance the light travels through the material.
The law states that the absorbance of a sample is directly proportional to its concentration and the path length of the light through the sample. Mathematically, the law is expressed as:
A = εcl
Where: A = absorbance
ε = molar absorptivity or extinction coefficient (a constant for a given substance and wavelength of light)
c = concentration of the absorbing species in moles per liter l = path length of the light through the sample in centimeters

The Beer-Lambert law is widely used in analytical chemistry and spectroscopy to quantitatively determine the concentration of a substance in a sample by measuring the amount of light absorbed by the sample at a particular wavelength. It is commonly used in various applications, such as measuring the concentration of a solute in a solution, determining the concentration of impurities in a sample, and analyzing the properties of various compounds in fields such as environmental science, biochemistry, and materials science.

### How do you find molar concentration ?

Molar concentration, also known as molarity, is a measure of the amount of solute in a solution, expressed as the number of moles of solute per liter of solution. You can calculate the molar concentration using the following formula:
Molarity = moles of solute / volume of solution (in liters)
To find the molar concentration of a solution, you need to know the amount of solute present in the solution, usually expressed in grams, and the volume of the solution, usually expressed in milliliters or liters. You will also need to know the molecular weight of the solute, which is the sum of the atomic weights of all the atoms in the molecule.
The steps to find the molar concentration are as follows:

Weigh the amount of solute using a balance, and record the mass in grams.
Calculate the number of moles of solute by dividing the mass of the solute by its molecular weight.
Measure the volume of the solution in liters or convert the volume to liters if it is given in milliliters.
Divide the number of moles of solute by the volume of the solution to get the molar concentration in moles per liter.

For example, if you have a solution containing 5 grams of sodium chloride (NaCl) dissolved in 1 liter of water, and the molecular weight of NaCl is 58.44 g/mol, the molar concentration can be calculated as follows:
Number of moles of NaCl = 5 g / 58.44 g/mol = 0.0854 mol
Volume of solution = 1 L
Molarity = 0.0854 mol / 1 L = 0.0854 M
Therefore, the molar concentration of the NaCl solution is 0.0854 M.