### Solutions

**Mole fraction (x)**

The mole fraction of A and B will be as follows, if the number of moles of A and B are n_{A} and n_{B} respectively:
$$ x_{\,A} = \frac {n_{\,A}} {{n_{\,A}} + {n_{\,B}}} \text{ , and } x_{\,B} = \frac {n_{\,B}}{{n_{\,A}} + {n_{\,B}}} $$
n_{A} + n_{B} = 1

** Molarity (M) **

$$ \text {Molarity (M) } = \frac { \text{Moles of solute}} { \text{Volume of solution in liters}} $$

** Molarity (m) **

$$ \text {Molarity (m) } = \frac { \text{Moles of solute}} { \text{Mass of solvent in kilograms}} $$

** Parts per million (ppm)**

$$ \text { PPM} = \frac { \text{Number of parts of the component }} {\text{ Total number of parts of all components of the solution}} \times 10^{5} $$

** Raoult’s law for a solution of volatile solute in volatile solvent **

p_{A} = p_{A°} x_{A}

p_{B} = p_{B°} x_{B}

Where p_{A} and p_{B} are partial vapour pressures of component A and
component B in solution respectively. _{A°} and _{B°} are vapour pressures of pure
components A and B respectively.

** Raoults law for a solution of non-volatile solute and volatile
solvent **
$$ \frac {p _{\,A°} - p _{\,A}}{ p _{\,A°}} = ix _{\,B} $$
$$ = i \frac {n_{\,B}}{ N_{\,A}} = i \frac {W_{\,B} \times M_{\,A}}{M_{\,b} \times W_{\,A}} $$
Where x_{B} is mole fraction of solute, i is van’t Hoff factor and

$$ \frac {p _{\,A°} - p _{\,A}}{ p _{\,A°}} \text{is relative lowering of vapour pressure.} $$

** Osmotic pressure (π) of a solution **

πV = *i*nRT or

π = *i* CRT

where = π osmotic pressure in bar or atm, V is volume in liters, i = Van't Hoff factor, c = molar concentration in moles per liters, n = number of moles, T = Temperature on Kelvin Scale, R = 0.083 L bar mol^{–1} K^{–1}
and R = 0.0821 L atm mol^{–1} K^{–1}