sir please give me all steps for doing numericals on these 3 topics ...

Molarity:

It is defined as the number of moles of the solute dissolved per litre of solution.It is denoted by ‘M’.

Mathematically, M = Number of moles of solute

Volume of the solution in litres

M can be calculated from the strength as: M = Strength in grams per litre

Molar mass of solute in gmol^-1

If ‘w’ gram of the solute are present in V cm3 of a given solution, then M = w X 1000

Molar mass V

Molality:

It is defined as the number of moles of the solute dissolved in 1000 grams of the solvent.It is denoted by ‘m’.

Mathematically, m = Number of moles of solute

Mass of the solvent in kg

If ‘a’ gram of the solute are dissolved in’b’gram of the solvent, then m = a X 1000

Molar mass of solute b

Mole fraction:

It is the fraction obtained by dividing number of moles of that constituent by the total nuimber of moles of all the constituents present in the solvent. It is denoted by ‘x’.

If n₁ and n₂ are the number of moles of solvent and solute respectively in a solution, then

Mole fraction of solvent in the solution, x₁ = n₁

n ₁ + n₂

Mole fraction of solute in the solution, x₂ = n₂

n ₁ + n₂

If a solution contains 4 moles of alcohol and 6 moles of water, then

Mole fraction of alcohol = 4 = 0.4

4 + 6

Mole fraction of water = 6 = 0.6

4 + 6

The sum of mole fractions of all the constituents of a solution is always equal to unity.

x ₁ + x₂ + x₃ + ......... = 1

It may be noted that mole fraction is a dimensionless quantity.