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### Derive the relationship between degree of dissociation of an electrolyte and van’t Hoff factor. - Chemistry

Exercise | Q 4 | Page 46

# Derive the relationship between the degree of dissociation of an electrolyte and van’t Hoff factor.

### Solution:

1. The weak electrolytes involve the concept of degree of dissociation (α) that changes the van’t Hoff factor.

2. Consider an electrolyte AxBy that dissociates in aqueous solution as

 AxBy        ⇌      xAy+    +    yBx- Initially 1 mol                 0               0 At equilibrium (1 - α) mol      (x α mol)    (yα mol)

3. If α is the degree of dissociation of electrolyte, then the moles of cations are xα and those of anions are yα equilibrium. We have dissolved just 1 mol of electrolyte initially. α mol of electrolyte dissociates and (1 – α) mol remains undissociated at equilibrium.

Total moles after dissociation = (1 – α) + (xα) + (yα)

= 1 + α (x + y - 1)

= 1 + α (n - 1)

where, n = x + y = moles of ions obtained from dissociation of 1 mole of electrolyte.

4. The van’t Hoff factor given as

i = $\frac{\text{actual moles of particles insolution after dissociation}}{\text{moles of formula units dissoved in solution}}$

$=\frac{1+\alpha \left(\text{n - 1}\right)}{1}$

Hence, i = 1 + α(n - 1) or α = $\frac{\text{i}+1}{\text{n}-1}$

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