Question

How does van’t Hoff factor modify the equation for the elevation of boiling point?

Answer 1

The ratio of the observed (experimental) value of a colligative property to the normal (calculated) value of the same property is termed as van't Hoff factor, i.

Mathematically,

`i = "(Observed (experimental) value of a colligative property)"/"(Normal (calculated) value of the same colligative property)"`

or `i = (Delta_"obs")/(Delta_"cal")`    ...(i)

where Δ_obs and Δ_cal respectively represent the observed and calculated values of a colligative property. Thus,

for elevation of boiling point, `i = ((Delta T_b)_"obs")/((Delta T_b)_"cal")`

Since, a colligative property is proportional to number of particles of solute, we have

Δ_obs ∝ No. of particles present in the solution

and, Δ_cal ∝ Normal number of particles.

Hence, Eq. (i) becomes

`i = Delta_"obs"/Delta_"cal" = "(Number of particles present in the solution)"/"Normal number of particles"`    ...(ii)

Further molecular mass of a solute determined on the basis of a colligative property is inversely proportional to the colligative property. Thus, we have

`Delta_"obs" prop 1/M_"obs"^'`

`Delta_"cal" prop 1/M_"cal"^'`

Where `M_"obs"^'` and `M_"cal"^'` represent the observed molecular mass and calculated (normal) molecular mass of the solute.

Hence, Eq. (ii) becomes

`i = Delta_"obs"/Delta_"cal" = M_"cal"^'/M_"obs"^' = "(Number of particles present in the solution)"/"Normal number of particles"`    ...(iii)

From equation (iii), van't Hoff factor may also be defined as the ratio of normal molecular mass of a solute to its observed molecular mass, i.e.,

`i = "Normal molecular mass"/"Observed molecular mass"`

or Normal molecular mass = i × Observed molecular mass

For relative lowering of vapour pressure,

`(P^circ - P)/P^circ = i * chi_"solute"`

For elevation of boiling point, ΔT_b = i · K_b · m