IMPORTANT FORMULAE of SOLUTIONS

IMPORTANT FORMULAE of SOLUTIONS

In the formulae given below A represents solvent and B represents solute, also

MA = Molar mass of solvent MB = Molar mass of solute

WA = Mass of solvent VB = volume of solute

V = Volume of solution d = density of solution.

1(a). Mass of percentage (w/w) = $\displaystyle \frac{{{{W}_{A}}}}{{{{W}_{A}}+{{W}_{B}}}}\times 100$

(b). Volume percentage (v/v) = $\displaystyle \frac{{{{V}_{A}}}}{{{{V}_{A}}+{{V}_{B}}}}\times 100$

(c). Mass by volume percentage (W/v) = $\displaystyle \frac{{{{W}_{B}}\times 100}}{{V\left( {mL} \right)}}$

(d). Parts per million (ppm) = $\displaystyle \frac{{{{W}_{B}}}}{{{{W}_{A}}+{{W}_{B}}}}\times {{10}^{6}}$

2. Mole fraction of A, XA = $\displaystyle \frac{{{{n}_{A}}}}{{{{n}_{A}}+{{n}_{B}}}}$

mole fraction of B, XB = $\displaystyle \frac{{{{n}_{B}}}}{{{{n}_{A}}+{{n}_{B}}}}$

XA + XB = 1

3. Molarity (M) = $\displaystyle \frac{{\text{Moles of solute}}}{{\text{Volume of solution in litre}}}$ = $\displaystyle \frac{{{{n}_{B}}}}{{{{V}_{{\left( L \right)}}}}}$ = $\displaystyle \frac{{{{W}_{B}}}}{{{{M}_{B}}\times {{V}_{{\left( L \right)}}}}}$

4. Molality (m) = $\displaystyle \frac{{\text{Moles of solute}}}{{\text{Moles of solvent in kg}}}$ = $\displaystyle \frac{{{{n}_{B}}}}{{{{W}_{A}}}}\times 1000$ = $\displaystyle \frac{{{{W}_{B}}\times 1000}}{{{{M}_{B}}\times {{W}_{A}}}}$

5. Normality (N) = $\displaystyle \frac{{\text{Gram Equivalents of solute}}}{{\text{Volume of solution in litre}}}$ = $\displaystyle \frac{{{{W}_{B}}}}{{\text{Gram Equivalent Mass of solute }\times {{\text{V}}_{{\left( L \right)}}}}}$

6. Relationship between Molarity and Normality

The normality (N) and molarity (M) of a solution are related as follows :

Normality × Equivalent. mass (solute) = Molarity × Molar mass (solute)

7. Relationship between Molarity and Mass percentage (p)

If p is the mass percentage and d is the density of the solution then

Molarity = $\displaystyle \frac{{p\times d\times 10}}{{\text{Mol}\text{. mass }\left( {Solute} \right)}}$

Normality = $\displaystyle \frac{{p\times d\times 10}}{{\text{Eq}\text{. mass }\left( {Solute} \right)}}$

8. Dilution formula: If the solution of some substance is diluted by adding solvent from volume V1 to volume V2, then

M1V1 = M2V2 Similarly, N1V1 = N2V2

9. Raoult’s law for volatile solute

p_A = p_A⁰ x_A and p_B⁰ x_B

where p_A and p_B are partial vapour pressures of component ‘A’ and component ‘B’ in the solution.

P_A⁰ and p_B⁰ are vapour pressures of pure components ‘A’ and ‘B’ respectively.

Total vapour pressure = p = p_A + p_B = p_A⁰ x_A + p_B⁰ x_B

10. Raoult’s law for non-volatile solute

$\displaystyle \frac{{P_{A}^{0}-P}}{{P_{A}^{0}}}$ = X_B = $\displaystyle \frac{{{{n}_{B}}}}{{{{n}_{A}}+{{n}_{B}}}}$ (For a dilute solution n_B << n_A)