A 1.00 molal aqueous solution of trichloroacetic acid $(C C l_{3} C O O H)$ is heated to its boiling point. The solution has the boiling point of ${100.8}^{o} C$ . Determine the van 't Hoff factor for trichloroacetic acid. $(K_{b}$ for water 0.512 K kg $M o l^{- 1}$ )
OR
Define the following terms:
(i) Mole fraction
(ii) Isotonic solutions
(iii) Van 't Hoff factor
(iv) Ideal solution

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Solution

Molarity of solution $= m = 1.00 m$
Boiling point of solution $= T_{b} = {100.8}^{o} C = 373.8 K$
Boiling point of water $= T_{b}^{o} = {100.0}^{o} C = 373 K$
Observed elevation in boiling point $= 373.8 - 373 = 0.8 K$
$K_{b}$ for water $= 0.512 K k g M o l^{-}$
Calculated elevation in boiling point
$Δ T_{b} = K_{b} \times m = 0.512 \times 1 = 0.512 K$
Van't Hoff factor $i = \frac{O b s e r v e d c o l l i g a t i v e p r o p e r t y}{C a l c u l a t e d c o l l i g a t i v e p r o p e r t y}$
$\Rightarrow i = \frac{0.8}{0.512} = 1.56$

(i) Mole fraction= The ratio of the number of moles of a given component of a mixture to the total number of moles of all the components.
$Mole fraction=Number of moles of the componentTotal Number of moles of all the components$

(II) Isotonic solution= An isotonic solution refers to two solutions having the same osmotic pressure across a semipermeable membrane. This state allows for the free movement of water across the membrane without changing the concentration of solutes on either side.

(iii) The van 't Hoff factor is a measure of the effect of a solute upon colligative properties such as osmotic pressure, relative lowering in vapor pressure, elevation of boiling point and freezing point depression.
Van't Hoff factor $i = \frac{O b s e r v e d c o l l i g a t i v e p r o p e r t y}{C a l c u l a t e d c o l l i g a t i v e p r o p e r t y}$

(iv) Ideal Solution= Ideal solution, homogeneous mixture of substances that has physical properties linearly related to the properties of the pure components. An ideal solution is a solution with thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero. The vapor pressure of the solution obeys Raoult's law, and the activity coefficient of each component is equal to one.

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