Ostwald Dilution Law

Ostwald applied law of mass action to the equation and Ostwald dilution law. It has different mathematical form. By law of mass action:

MA ⇌ M⁺ + A^-

Rate of forward reactions Rf = kf [MA]

Rate of backward reaction Rb = kb [M⁺] [A^-]

where kf and kb are rate constants. At Equilibrium Rf = Rb so,

kf [MA] = kb [M⁺] [A^-]

Here

So,

Let Concentration of electrolytes is “c” moles /L.

Weak electrolytes are partially ionized and dissociated ions = α

Fraction of dissociated electrolytes = 1-α

Now for the reaction MA ⇌ M⁺ + A^-

Initial concentration c 0 0

At equilibrium (1-α)c αc αc

e.q.8.1

Ostwald Dilution Law in Terms of Concentration

For very weak electrolytes degree of dissociation is very low. α is very small as compared to 1 so, 1-α ≈ 1. E.q.8.1 becomes

Kα = α²c e.q.8.2

Ostwald Dilution Law in Terms of Volume

We know that V= 1/c is the volume which contains one mole of electrolytes. It can also be written as c=1/V. Putting value of c in e.q.8.1 we got

e.q.8.3

Here V is volume of dissociation.

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Ostwald Dilution Law in Terms of Equivalent Conductance

We know that α = Λ ／Λο. Putting this value of α in e.q.8.1 we got

e.q.8.4

Debye Huckel Theory

Variation of conductance with concentration or dilution of solution was well explained by Debye. Conductance depends on:

i. number of ions cations / anions

ii. Speed of ions

Conductance, equivalent conductance or molar conductance decreases with increase in concentration or increases increase in dilution. Conductance is related to concentration. Koherausch proposed law of independent migration. He proposed that, “each ion contributes a definite amount of conductance to the total conductance of an electrolyte, irrespective of other ion. He proposed an empirical equation

Here negative sign indicates inverse dilution, Ʌo is conductance at infinite dilution and k is empirical constant.

Weak Electrolytes

Decrease in conductance with increase in concentration can be explained in terms of degree of ionization (ratio of dissociated ions/ total no. of ions).

· α will decrease with increase in concentration

· α will increase with increase in dilution

Weak electrolytes are partially ionized. Suppose in 100mL water 200 molecules dissolves out of 1000 molecules so,

α = 0.2

if we increase concentration of molecules to 2000 then α = 0.1. Thus α decrease with increase in concentration. If 400 molecules will dissolve out of 1000 molecules, then α = 0.4. Thus α increases with increase in dilution. The no. of ions per unit volume decreases with increase in concentration or decrease in dilution. As a result, conductance decreases.

Strong Electrolytes

Unlike weak electrolytes all the molecules will be ionized. By the theory of strong electrolytes, conductance decrease with increase in concentration. It cannot be explained on the basis of degree of ionization. Debye and Huckel explained this behaviour on the basis of inter-ionic effect or on the basis of attraction between oppositely charged ions. This theory is called theory of strong electrolytes or theory of inter-ionic effect or more commonly “Debye Huckel theory” They proposed that two factors are involved:

1. Asymmetric effect:

Also called relaxation effect. They proposed that solution as a whole neutral. Each ion surrounded by a number of oppositely charged ions (ionic -atmosphere). In the absence of any field this ionic atmosphere is spherical and symmetrical. For conductance, electrodes are inserted, electric field is applied and ionic atmosphere is distorted. Ions start moving towards respective electrodes. Positive ions move towards negative electrode and vice versa

As a result, symmetry is distorted and there is no net effect on the movement of ions. Conductance is due to movement of ions. Negative sphere is attracted towards the electrode but, negative sphere cannot go towards the positive electrode due to attraction of positive ions. This effect is called retardation effect on speed of ions. Increase in concentration results in increase in ionic atmosphere which increases the retardation effect on each ion and thus decreases the speed and hence conductance.

Figure 8.1: Asymmetric effect

2) Electrophoretic effect:

As ions move in solvent, each ion is surrounded by solid molecule as well (solvation). Ions are solvated. Solvent molecules moves along the ions. Molecules of solvent are in counter flow. This decreases the speed of ions. Increase in concentration increases electrophoretic effect and decreases conductance.