2. Expressing concentration of solutions

Expressing concentration of solutions 

Concentration Terms :

% Concentration

Mass percentage. :It is the amount of solute in grams dissolved per 100 g of solution. e.g., 10% solution of sodium chloride means 10 g of solid sodium chloride present in 100 g of solution

% w/w =  × 100

Ex.     10% w/w urea solution = 10 g of urea is present in 100 g of solution.

= 10 g of urea is present in 90 g of water.

Mass by volume percentage (% w/v) : It is defined as mass of solute dissolved per 100 ml of solution. It is commonly used in medicine and pharmacy.

% wt/vol. (w/v)

% w/v = wt. of solute/100 mL of solution

 % w/v =

Ex. 

10%  (w/v) urea solution. = 10 g of urea is present in 100 mL of solution.

 But not 10 g of urea present in 90 ml of water  for dilute solution  :  volume solution = volume solvent.

Volume percentage (% v/v) : It is defined as volume of a solute dissolved per 100 ml of solution.

% v/v =  × 100

Strength of solution in g/L : Weight of solute (in gram) per litre (1000 mL) of solution.

Ex.  

10%  (w/v) sucrose solution, then specify its concentration in g/L

100 mL .......... 10 g

1000 mL ....... = 100 g/L

Molarity (M) : It is expressed as the number of moles of solute per litre of solution.

Molarity = No. of moles of solute per litre of solution.

Let     n =  No. of moles of solute ; N = No. of moles of solvent ;  V = volume of solution

no. of moles of solute = molarity x volume ( in L)

no. of m. moles of solute = molarity x volume ( in mL)

If V₁ mL of C₁ molarity solution is mixed with V₂ mL of C₂ molarity solution (same substance or solute)

C_f (V₁+V₂) = C₁V₁ + C₂V₂

 C_f =  =  where C_f = molarity of final solution

Molality (m) : It is defined as number of moles of solute per 1000 g or 1 kg of solvent.

Molality = No. of moles of solute per kg(1000 g) of solvent.

Let w gram of solute (Molar mass = Mg/mole) is dissolved in 'W' gram of solvent.

molality =   molality =

Molality not depends on temperature.

Normality : It is defined as number of gram equivalents of solute dissolved per litre of solution.

No. of equivalents per litre of solution =  = n-factor molarity

No. of equivalents = normality × volume (in L)

Equivalent mass =

No. of equivalent= =

'n' - factor

(i) For oxidizing/reducing agents : no. of e^– involved in oxidation/reduction half reaction per mole of oxidising agent /reducing agent.

e.g.  : 5e^– + 8H⁺ + MnO₄^– =Mn²⁺ + H₂O         n- factor  = 5

(ii) For acid/ base reactions : no. of H⁺ ions displaced/ OH^– ions displaced per mole of acid/ base.

e.g.  : NaOH    n - factor = 1        H₂SO₄      n - factor = 2

(iii) For salt :   n = Total charge on cations.

or                                                          

total charge on anions              

 e.g.  : Al₂(SO₄)₃                    n - factor = charge on the cation = 2 x 3 = 6

Mole-fraction (x) : It is the ratio of number of moles of a particular component to the total number of moles of all the components. e.g., mole-fraction of component A, x_A = , where n_A is the number of moles of component 'A' and n_B is the number of moles of component 'B'.

For binary mixture.

X_solute =  = ; X_Solvent  =  =

X_solute  + X_Solvent = 1

 Parts per million (ppm) : The number of parts of solute present in 1 million parts of solution are called its ppm. When a solute is present in small quantities (very minute amounts), it is easier to express the concentration in parts per million.

(a) ppm (w/w) =  × 10⁶

(b) ppm (w/v) =  × 10⁶

(c) ppm (moles/moles) =  × 10⁶

Table : 1

 Note : All volume related concentration terms are temperature dependent.