Understanding the Relationship Between Degree of Dissociation and van't Hoff Factor

The degree of dissociation (α) represents the fraction of molecules that dissociate into ions. The van't Hoff factor (i) indicates the ratio of observed colligative property to the expected value for a non-dissociating solute.

Step 1: General Dissociation Equation

For a weak electrolyte A_xB_y, the dissociation is:

$A_x{B}_y\rightleftharpoons x{A}^{\mathrm{y+}}+y{B}^{\mathrm{x-}}$

Step 2: Calculate Total Particles After Dissociation

Initial moles: 1

Dissociated: α moles

Undissociated: (1-α) moles

Ions produced: α(x + y) moles

Total particles after dissociation: (1-α) + α(x + y) = 1 + α(x + y - 1)

Step 3: Relate to van't Hoff Factor

van't Hoff factor i = (total particles after dissociation)/(initial particles)

$i=\frac{1+\alpha (x+y-1)}{1}=1+\alpha (x+y-1)$

Step 4: Solve for α

$i-1=\alpha (x+y-1)$

$\alpha =\frac{i-1}{x+y-1}$

Final Answer

The correct expression is: $\alpha =\frac{i-1}{x+y-1}$

Related Topics

• Colligative Properties
• Electrolyte Solutions
• Osmotic Pressure
• Boiling Point Elevation
• Freezing Point Depression

Important Formulae

van't Hoff factor: $i=\frac{\text{observed colligative property}}{\text{calculated colligative property}}$

For dissociation: $i=1+\alpha (n-1)$ where n = total ions produced

Degree of dissociation: $\alpha =\frac{i-1}{n-1}$