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ELEVATION OF BOILING POINT (EBULLIOSCOPY) :
The boiling point of a liquid is the temperature at which its vapour pressure is equal to the atmospheric pressure. The vapour pressure of a liquid is lowered when a non-volatile solute is added to it. Hence, the temperature of the solution when its vapour pressure will be equal to atmospheric pressure will be higher than the temperature of the pure solvent. In other words, the boiling point of the solvent is elevated by the addition of non-volatile solute. The difference in the boiling point of the solution and the boiling point of the pure solvent is termed elevation of boiling point.
Elevation of boiling point,
(?T) = Boiling point of the solution – Boiling point of pure solvent
This can be better understood by plotting a graph of vapour pressure against temperature for a pure solvent and two solutions of different concentrations. The curves of the solutions always lie below the curve of the pure solvent. The line P0C represents the atmospheric pressure. T0, T1 and T2 represent the boiling points of pure solvent, solution I and solution II respectively. The vapour pressure of pure solvent, solution I and solution II at temperature T0 are P0, P1 and P2 respectively.
Assuming that the solutions are very dilute, these curves may be approximately taken as straight lines near the boiling point. Thus, ?ACE and ?ABD are similar.
Therefore, AC/AB = AE/AD
or T2–T0/T1–T0 = P0–P2/P0–P1
or ?T2/?T1 = ?P2/?P1
or ?T ∝ ?P
From Raoult’s law for dilute solution
p0–ps/p0 = wA/mA.mB/wB
(ps = vapour pressure of solution)
or p0–ps = wA/mA.mB/wB . p0
For the pure solvent, P0 (its vapour pressure at the boiling point) and mB (its molecular mass) are constant. Therefore,
p0 – ps ∝ wA/mAwB
or ?p ∝ ?T ∝ wA/mAwB
or ?T = K.wA/mAwB …(i)
where K is a constant, called as elevation constant.
When, wA/mA – 1 (one mole of solute) and wB = 1 g, then
?T = K
Thus, boiling point constant is equal to the elevation in boiling point which would be theoretically produced when 1 mole of a non-volatile solute is dissolved in 1 g of the solvent.
If wA/mA = 1 and wB = 100 g,
?T = K/100 = K'
K’ is called molecular elevation constant. It is defined as the elevation in boiling point produced when 1 mole of the solute is dissolved in 100 g of the solvent.
Thus, K = 100K’
Putting this value in Eq. (i),
?T = 100 K' wA/mAwB …(ii)
If wA/mA and wB = 1000 g.
?T = K/1000 = Kb
Kb is called molal elevation constant. It is defined as the elevation in boiling point produced when 1 mole of the solute is dissolved in 1000 g of the solvent.
Thus, K = 1000 Kb
Putting this value in Eq. (i),
?T* = 1000KbwA/mAwB …(iii)
or ?T = Molality × Kb
(since wA/mA×wB × 1000 = molality).
The elevation in boiling point of a solution of non-electrolyte is proportional to its molality and equimolal solutions of all the substances in the same solvent will show equal elevation in boiling points. There are known as Raoult’s laws of elevation of boiling point.