Question
Derive the mathematical expression between molar mass of a non-volatile solute and elevation of boiling point. State and explain van't Hoff-Avogadro's law.
✓
Answer
We know the formula of molality as,
molality, $m=\frac{\text { moles of solute }}{\text { mass of solvent in kg }}$
molality, $m=\frac{W_2 / M_2}{W_1 / 1000}=\frac{1000 W_2}{M_2 W_1}--1$
where $W_2=$ weight of solute
$M_2=$ molar mass of solute
$W_1=$ weight of solvent
Also, we have relation, $\Delta T_b=i \times k_b \times m$---- 2
From Eqn. 1 and 2 we get
$\Delta T_b=\frac{i \times k_b \times 1000 \times W_2}{M_2 \times W_1}$
So, $M_2=\frac{i \times k_b \times 1000 \times W_2}{\Delta T_b \times W_1}$
Van't Hoff-Avogadro's law:
At a given temperature, equal volumes of the solutions having the same osmotic pressure contain an equal number of solute particles. Therefore, the equal number of moles of the substances will contain an equal number of molecules.
Mathematically it is expressed as,
$\pi \propto n$
Osmotic pressure $\propto$ no. of molecules/amount of substance(moles).
"or"
$\frac{\pi_1}{n_1}=\frac{\pi_2}{n_2}-\cdots$1
$\pi_1 n_2=\pi_2 n_1$.
molality, $m=\frac{\text { moles of solute }}{\text { mass of solvent in kg }}$
molality, $m=\frac{W_2 / M_2}{W_1 / 1000}=\frac{1000 W_2}{M_2 W_1}--1$
where $W_2=$ weight of solute
$M_2=$ molar mass of solute
$W_1=$ weight of solvent
Also, we have relation, $\Delta T_b=i \times k_b \times m$---- 2
From Eqn. 1 and 2 we get
$\Delta T_b=\frac{i \times k_b \times 1000 \times W_2}{M_2 \times W_1}$
So, $M_2=\frac{i \times k_b \times 1000 \times W_2}{\Delta T_b \times W_1}$
Van't Hoff-Avogadro's law:
At a given temperature, equal volumes of the solutions having the same osmotic pressure contain an equal number of solute particles. Therefore, the equal number of moles of the substances will contain an equal number of molecules.
Mathematically it is expressed as,
$\pi \propto n$
Osmotic pressure $\propto$ no. of molecules/amount of substance(moles).
"or"
$\frac{\pi_1}{n_1}=\frac{\pi_2}{n_2}-\cdots$1
$\pi_1 n_2=\pi_2 n_1$.
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