Question

The vapour pressure of a dilute aqueous solution of glucose is 750mm of Hg at 373K. Calculate the molality.

Answer 1

For this problem, we have to use the formula of relative vapour pressure through which we can calculate the mole fraction. And then we have to use the formula of molality in terms of mole fraction.

Complete step by step solution:
-In the given question, we have to calculate the molarity of a solution by using the vapour pressure of an aqueous solution.
-Now, as we know that vapour pressure of any substance is defined as the pressure that is exerted by the vapours on the liquid.
-Whereas molality is generally defined as the ratio of the number of moles of solute to the mass of the solvent in kilograms.
-Now, here the vapour pressure of a solution is given that is 750 mm of Hg so we have to use the molality formula in terms of mole fraction i.e.
$\dfrac{\text{P}{}^\circ \text{ - }{{\text{P}}_{\text{s}}}}{\text{P}{}^\circ }\ \text{= Mole fraction of solute}$
-Here, $\text{P}{}^\circ$ is the vapour pressure of the pure water, ${{\text{P}}_{\text{s}}}$ is the vapour pressure of solution so the value of mole fraction will be:
$\text{Mole fraction of solute, }{{\text{x}}_{\text{B}}}\text{ }\,\text{= }\dfrac{\text{760 - 750}}{760}\ =\text{ 0}\text{.013}$
-So, the mole fraction of solvent, ${{\text{x}}_{\text{A}}}$ will be $\text{1 - 0}\text{.013 = 0}\text{.987}$.
-Now, we will apply the formula of molality that is:
$\text{Molality = }\dfrac{{{\text{x}}_{\text{B}}}\text{ }\times \text{ 1000}}{{{\text{x}}_{\text{A}}}\text{ }\times \text{ Mass of solvent}}$
-Here, the mass of solvent i.e. ${{\text{H}}_{2}}\text{O}$is 18 g ($16\text{ + }2\text{ }\times \text{ 1 = 18}$).
$\text{Molality = }\dfrac{\text{0}\text{.013 }\times \text{ 1000}}{\text{0}\text{.987 }\times \text{ 18}}\text{ = 0}\text{.741m}$

Therefore, the molality of the solution is 0.741 m.

Note: Here, the mole fraction is the method that is used for determining the number of moles of a substance in a mixture. Moreover, the value of the vapour pressure of pure water is 760 mm because it is the standard value.