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Question: What is the vapour pressure at \( 100{}^\circ C \) of a solution containing \( 18\text{ }g \) of wat...

What is the vapour pressure at 100∘C100{}^\circ C of a solution containing 18 g18\text{ }g of water and 12.96 g12.96\text{ }g of sucrose.

Explanation

Solution

We know that when a substance is put in a container that is constantly heated, the molecules of the substance are shown to travel in various directions at different speeds, which is attributed to the various levels of kinetic energy exhibited by the molecules of the liquid.

Complete answer:
As we know that the liquids have weak intermolecular forces. Heating the molecules of the liquid can help to break these forces and convert them to the vapour phase and thus increase the vapour pressure of the liquid. For e.g., acetone, benzene and sucrose have a higher vapour pressure than water at a given temperature.
As we supply heat to a liquid, its kinetic energy increases, resulting in an increase in the overall temperature. At the boiling point, the latent heat is used by the molecules to overcome the intermolecular forces of attraction in the liquid and to convert to the gaseous state, instead of increasing the temperature. Also, we know, vapour pressure of a solution is the product of mole fraction of that compound in the solution and vapour pressure of pure compound. Here we have;
Xsucrose=(1.68348)(1.68342)+(1.5618)=5×10−30.872=5.734×10−3{{X}_{sucrose}}=\dfrac{\left( \dfrac{1.68}{348} \right)}{\left( \dfrac{1.68}{342} \right)+\left( \dfrac{1.56}{18} \right)}=\dfrac{5\times {{10}^{-3}}}{0.872}=5.734\times {{10}^{-3}} thus, at 100∘C100{}^\circ C the PSolvent0=760torr.P_{Solvent}^{0}=760torr.
So, PSolvent0−PSolutionPSolvent0=5.734×10−3\dfrac{P_{Solvent}^{0}-{{P}_{Solution}}}{P_{Solvent}^{0}}=5.734\times {{10}^{-3}} on substitution we get PSolution=760−760×5.7×10−3=755.6torr{{P}_{Solution}}=760-760\times 5.7\times {{10}^{-3}}=755.6torr
Now, we got PSolution=755.6torr=755.56mm{{P}_{Solution}}=755.6torr=755.56mm of Hg [since 1torr=1mm1torr=1mm of Hg].

Note:
Remember molar mass of water is 18g/mol.18g/mol. Number of moles is the ratio of weight taken of a compound to the molar mass of that compound. Mole fraction of a component is the ratio of the number of moles of that component to the total number of moles of all the components present in the solution.