6. DALTON’S ATOMIC THEORY

DALTON’S ATOMIC THEORY

In 1808, Dalton published ‘A New System of Chemical Philosophy’ in which he proposed the following:

1. Matter consists of indivisible atoms.

2. All the atoms of a given element have identical properties including identical mass. Atoms of different elements differ in mass.

3. Compounds are formed when atoms of different elements combine in a fixed ratio.

4. Chemical reactions involve reorganisation of atoms. These are neither created nor destroyed in a chemical reaction.

​DALTON LAW OF PARTIAL PRESSURE

At a given temperature, the total pressure exerted by two or more non-reacting gases occupying a definite volume is equal to the sum of the partial pressures of the component gases. Mathematically,

P = p_A + p_B + p_C + …..

when P is the total pressure and p_A, p_B, p_C, ….. are the partial pressures of the component gases A, B, C, ….. respectively. The pressure that a component gas of  the gaseous mixture would exert if it were only present in the volume under consideration at a given temperature, is the partial pressure of the component.

Derivation of Dalton’s Law

Let n₁ and n₂ be the no. of moles of two non-reacting gases ‘A’ and ‘B’ filled in a vessel of volume ‘V’ at temperature T.

Total pressure in the vessel ‘P’ may be calculated as

PV = (n₁ + n₂)RT      …….(i)         

Individual or partial pressure may be calculated as,

_pAV = n₁RT     …….(ii)

_pBV = n₂RT      …….(iii)

Adding (ii) and (iii), we get      

(p_A + p_B)V = (n₁ + n₂)RT     …….(iv)

Comparing equations (i) and (iv), we get      

P = p_A + p_B    (Dalton’ expression)       

Dividing equation (ii) by (i), we get    

 = x_A

p_A = x_A ´ P 

where x_A = mole fraction of ‘A’. Similarly, dividing (iii) by (i), we get

p_B = x_B ´ P

i.e., Partial pressure of a component = Mole fraction ´ total pressure

Relationship between total pressure and individual pressures (before mixing) of the constituent  gases at constant temperature

At constant temperature, let V₁ volume of a gas A at a pressure p₁ be mixed with V₂ volume of gas B at a pressure p₂. Both these gases do not react chemically.

Total volume = V₁ + V₂  

Let the total pressure be P and partial pressures of A and B be p_A and p_B respectively. Applying Boyle’s law,

P_A(V₁ + V₂) = p₁V₁        …….(i)       

and   p_B(V₁ + V₂) = p₂V₂      …….(ii)                    

Adding (i) and (ii)

p_A + p_B =         

or   P =     

Dalton’s Law fails in those gases which react chemically so not applicable to the following mixtures.

(i) NH₃+HCl

(ii) NO +O₂

(iii) H₂+F₂  

(iv) H₂+Cl₂

(v) SO₂+ Cl₂

Applications

(i) In the determination of pressure of dry gas :   When a gas is called over water, then it is moist , water also vaporizes simultaneously and exerts its own partial pressure. Partial pressure of water is called its aqueous tension. It depends upon temperature.

 If P and P¢ are the pressure of the dry gas and the moist gas respectively at t°C and p is the aqueous tension at that temperature, then by Dalton’s Law of Partial Pressures

P = P¢ - p

(ii) In the calculation of partial pressures : In a mixture of non-reacting gases A, B, C etc., if each gas is considered to be an ideal gas, then applying PV = nRT 

P_A = n_A , p_B = n_B  p_C = n_C

And so on.    

By Dalton’s law of partial pressures,

Total pressure, P = p_A + p_B + p_C + …  =  (n_A + n_B + n_C + …)

      (mole fraction of  A)

or       p_A = x_A ´ P 

Similarly, p_B = x_B ´ P and so on. Thus

Partial pressure of A = Mole fraction of A ´ Total pressure 

Amagat Law of Partial volume

Total volume of a mixture of gases which do not react at constant temperature and pressure is equal to sum of individual volumes (partial volumes) of constituent  gases.

V = åV_i = V₁ + V₂ + V₃ + ….. + V_n ​