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 nA and nB respectively:
$$ x_{\,A} = \frac {n_{\,A}} {{n_{\,A}} + {n_{\,B}}} \text{ , and } x_{\,B} = \frac {n_{\,B}}{{n_{\,A}} + {n_{\,B}}} $$
nA + nB = 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
pA = pA° xA
pB = pB° xB
Where pA and pB 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 xB 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 = inRT 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