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Mole fraction:

It is the ratio of number of moles of a particular component of a solution to the total number of moles of the solution.
If a substance ‘A’ dissolves in substance ‘B’ and their number of moles are nA and nB , repsectively, then the mole fraction of A and B are given as :

$$Mole \ fraction \ of \ A=\frac{ No.\ of \ moles\ of\ A}{ No.\ of\ moles\ of\ solution}$$

$$n_A\over n_A+n_ B$$

$$Mole \ fraction \ of \ B = \frac{Number \ of \ moles \ of\ B}{ Number\ of\ moles\ of\ solution}$$

$$n_B\over n_A+n_ B$$

Molarity:

Molarity is defined as the number of moles of the solute present in 1 litre of the solution. It is the most widely used unit and is denoted by M. Molarity is expressed as follows:

$$Molarity \ (M) =\frac{ Number\ of\ moles\ of\ solute}{ Volume \ of\ solution\ in \ litres}$$

Molality:

Molality the number of moles of solute present in 1 kg of solvent. It is denoted by m. Molality is expressed as follows:

$$Molality \ (m) = \frac{Number\ of\ moles\ of\ solute }{Mass \ of \ solvent \ in \ kilograms}$$

by Expert (10.9k points)