Define molarity, molality, normality, mole-fraction.

Molarity (M): 

Molarity is defined as the number of moles of solute per litter of solution. That is,

Here,
     W = weight of solute.
     M = molecular mass of solute
     V = volume of solution

Molality (m):  

It is defined as the number of moles of solute per kg of solvent. That is,

Here,
     b = weight of solvent

Normality (N): 

It is defined as the number of gram equivalents of the solute dissolved per litter of the solution at a specific temperature.

Mole-fraction (x): 

Mole fraction is the ratio of the number of moles of solute and the total number of moles of solute and solvent. The mole fraction of any constituent of a solution is defined as the number of moles of that constituent per mole of the solution. If the solution contained moles  of A and  moles of B, then

and