Question

18 g glucose is added to 178.2 g of water. The water vapour pressure of water for this aqueous solution at \[100^\circ C\] is:
A.704 torr
B.759 torr
C.7.6 torr
D.None of these

Answer 1

Hint: To solve this question, we must first calculate the mole fractions of both the solute and the solvent. Then we must calculate the mole fraction of the solvent. Finally, we must substitute all these values in the formula for vapour pressure, and then find the answer.

Formula used: \[{P_{solution}} = {X_{solvent}}.{P^0}_{solvent}\]

Complete Step-by-Step Answer:

Before we move forward with the solution of the given question, let us first understand some important basic concepts.
Mole fraction can be understood as the reaction of the total number of moles of a substance present in a compound, to the total number of moles of all the constituents of the compound. The mathematical formula for calculating mole fraction can be given as:
  \[x{}_1 = \dfrac{{n{}_1}}{{n{}_1 + n{}_2}}\] , where \[n{}_1\] is the number of moles of the substance under consideration while \[n{}_2\] is the number of moles of the other constituent present in the compound.
According to Raoult’s Law, the partial vapour pressure of a solvent in a solution is equivalent to the vapour pressure of the pure solvent multiplied by its own mole fraction in the solution. This can be mathematically represented as:
 \[{P_{solution}} = {X_{solvent}}.{P^0}_{solvent}\]
Moving back to the question, let us first calculate the number of moles of the solute and solvent.
1.Molar mass of water = 18 g
Number of moles of water \[ = \dfrac{{mass\,\,of\,\,the\,\,given\,\,sample}}{{molecular\,\,mass\,\,of\,\,the\,\,subs\tan ce}}\] \[ = \dfrac{{178.2}}{{18}}\] = 9.9 moles
2.Molar mass of glucose = 180 g
Number of moles of glucose \[ = \dfrac{{mass\,\,of\,\,the\,\,given\,\,sample}}{{molecular\,\,mass\,\,of\,\,the\,\,subs\tan ce}}\] \[ = \dfrac{{18}}{{180}}\] = 0.1 moles
Now, let us calculate the mole fraction of the solvent, i.e. water:
 \[x{}_{water} = \dfrac{{n{}_{water}}}{{n{}_{water} + n{}_{glu\cos e}}}\] \[ = \dfrac{{9.9}}{{9.9 + 0.1}}\] =0.99
Hence, the vapour pressure for this solution can be calculated as:
 \[{P_{solution}} = {X_{solvent}}.{P^0}_{solvent}\] = (0.99) (760 torr) … since the base vapour pressure of water is 760 mm of Hg, which is equivalent to 760 torr.
 \[{P_{solution}}\] = 752.4 torr

Hence, Option D is the correct option

Note: The given question did not have any ionic solids as the solute. In case we use an ionic solid, we need to introduce a correction factor known as Van’t Hoff factor to rectify the anomaly caused by the dissociation of the ions and thus increasing the number of particles in the solution.