Question

A solution containing $30 g$ of non-volatile solute exactly in $90 g$ of water has a vapour pressure of $2.8 kPa$ at $298 K$ . Further, $18 g$ of water is then added to the solution and the new vapour pressure becomes $2.9 kPa$ at $298 K$ . Calculate the vapour pressure at $298 K$ .

Accepted Answer

Moles of solute $(n_{2}) = \frac{Mass of solute}{Molar mass of solute} = \frac{30 g}{M_{2} {gmol}^{- 1}} = \frac{30}{M_{2}}$

Moles of solvent $(n_{1}) = \frac{Mass of solvent}{Molar mass of solvent} = \frac{90 g}{18 {gmol}^{- 1}} = 5$

$\frac{{P_{1}}^{0} - P_{1}}{{P_{1}}^{0}} = \frac{n_{2}}{n_{1} + n_{2}} \frac{{P_{1}}^{0} - 2.8}{{P_{1}}^{0}} = \frac{30 / M_{2}}{5 + 30 / M_{2}} 1 - \frac{2.8}{{P_{1}}^{0}} = \frac{30}{(5 M_{2} + 30)} 1 - \frac{30}{5 M_{2} + 30} = \frac{2.8}{{P_{1}}^{0}} 1 - \frac{6}{M_{2} + 6} = \frac{2.8}{{P_{1}}^{0}} \frac{M_{2} + 6 - 6}{M_{2} + 6} = \frac{2.8}{{P_{1}}^{0}} \frac{{P_{1}}^{0}}{2.8} = 1 + \frac{6}{M_{2}} - - - - (1)$

Further, if we add $18 g$ of water then the moles of water is $\frac{90 + 18}{18} = \frac{108}{18} = 6$

$P_{1} = 2.9 kPa \frac{{P_{1}}^{0} - P_{1}}{{P_{1}}^{0}} = \frac{30 M_{2}}{M_{2} (6 M_{2} + 30)} = \frac{5}{M_{2} + 5} 1 - \frac{2.9}{{P_{1}}^{0}} = \frac{5}{M_{2} + 5} \frac{{P_{1}}^{0}}{2.9} = \frac{M_{2} + 5}{M_{2}} = 1 + \frac{5}{M_{2}} \frac{{P_{1}}^{0}}{2.9} = 1 + \frac{5}{M_{2}} - - - (2)$

Divide equation $(1)$ by $(2)$ we get;

$\frac{2.9}{2.8} = \frac{1 + 6 / M_{2}}{1 + 5 / M_{2}} \frac{2.9}{2.8} = \frac{1 + 6 / M_{2}}{1 + 5 / M_{2}} 2.9 (1 + \frac{5}{M_{2}}) = 2.8 (1 + \frac{6}{M_{2}}) 2.9 + \frac{14.5}{M_{2}} = 2.8 + \frac{16.8}{M_{2}} M_{2} = 23$

The molar mass of solute $= 23 g {mol}^{- 1}$

Putting the value of molar mass in the equation $(1)$

$\frac{{P_{1}}^{0}}{2.8} = 1 + \frac{6}{23} = \frac{29}{23} {P_{1}}^{0} = 3.53 kPa$

The vapour pressure of water $= 3.53 kPa$

Telangana Board Solutions for Chapter: Solutions, Exercise 5: Questions

Telangana Board Chemistry Solutions for Exercise - Telangana Board Solutions for Chapter: Solutions, Exercise 5: Questions

Questions from Telangana Board Solutions for Chapter: Solutions, Exercise 5: Questions with Hints & Solutions

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