Arrange the following solutions in order of their increasing boiling points. (i) $10^{-4} \mathrm{M~}…
Arrange the following solutions in order of their increasing boiling points.
(i) $10^{-4} \mathrm{M~} \mathrm{NaCl}$
(ii) $10^{-4} \mathrm{M~}$ Urea
(iii) $10^{-3} \mathrm{M~} \mathrm{NaCl}$
(iv) $10^{-2} \mathrm{M~} \mathrm{NaCl}$
(i) < (ii) < (iii) < (iv)
(iv) < (iii) < (i) < (ii)
(ii) < (i$) \equiv($iii) < (iv)
(ii) < (i) < (iii) < (iv)
Solution
Boiling Point Elevation Calculation
The elevation in boiling point (\(\Delta T_{b}\)) is a colligative property and is directly proportional to the molality of the solution and the van't Hoff factor (\(i\)).
The formula is given by: \(\Delta T_{b}=i\cdot K_{b}\cdot m\) where \(K_{b}\) is the ebullioscopic constant of the solvent and \(m\) is the molality of the solution. Since the solvent is assumed to be the same for all solutions, \(K_{b}\) is constant. For dilute solutions, molarity can be approximated as molality. Therefore, the boiling point elevation primarily depends on the product of the van't Hoff factor (\(i\)) and the molarity (\(M\)).
The boiling point elevation is directly proportional to the \(i\cdot M\) value. Therefore, the solutions are arranged in increasing order of their boiling points by arranging them in increasing order of their calculated \(i\cdot M\) values. Compare the \(i\cdot M\) values: (ii) \(1\times 10^{-4}\) (i) \(2\times 10^{-4}\) (iii) \(2\times 10^{-3}\) (iv) \(2\times 10^{-2}\)