Question

The vapour pressure of pure water is $ 23.8{\text{ }}mm $ $ Hg $ at $ {25^o}C $ . What is the vapour pressure of $ 2.50{\text{ }}molal $ $ {C_6}{H_{12}}{O_6} $ .

Answer 1

Hint :Vapour pressure is actually a measure of the tendency of a substance to change into a gaseous or a vapour state, and to be noted that it increases with temperature.

Complete Step By Step Answer:
According to Raoult's law, the vapour pressure of a component at a given temperature equals the mole fraction of that component times the vapour pressure of that component in a pure state.
 $ {P_{solution}} = {X_{solvent}}.P_{solvent}^o $
 $ {P_{solution}} $ =Vapour pressure of solution (Here, solution is $ {C_6}{H_{12}}{O_6} $ )
 $ {X_{solvent}} $ =mole fraction of solvent (Here, solvent is water)
 $ {P^o}_{solvent} $ =Vapour pressure of pure solvent (Here solvent is water)
(And, mole fraction refers to the ratio of the number of moles linked to one component in a solution or mixture to the total number of moles).
In the question we are given with the following information:
 $ P_{water}^o = 23.88mmHg $
 $ Molarity{\text{ }}of{\text{ }}solution = 2.5{\text{ }}molal $
Number of mole of $ {C_6}{H_{12}}{O_6} = 2.50 $
Let us assume amount of water $ = 1kg $
 $ M.W{\text{ }}of{\text{ }}water = 2 + 16 = 18 $
Thus number of moles i.e. n can be calculated as:
 $ n = \dfrac{m}{M} $ where, m is the given mass
Using this formula, we will calculate the number of moles of water as $ \dfrac{{1000}}{{18}} $
So, total number of moles = $ \dfrac{{1000}}{{18}} + 2.5 $
Now, $ {X_{water}} = \dfrac{{\dfrac{{1000}}{{18}}}}{{\dfrac{{1000}}{{18}} + 2.5}} = \dfrac{{1000}}{{1045}} $
Now, substituting the values, we will calculate the vapour pressure of $ 2.50{\text{ }}molal $ $ {C_6}{H_{12}}{O_6} $ as stated below:
 $ {P_{{C_6}{H_{12}}{O_6}}} = \dfrac{{1000}}{{1045}} \times 23.8 = 22.775{\text{ }}mmHg $
Hence, the vapour pressure of $ 2.50{\text{ }}molal $ $ {C_6}{H_{12}}{O_6} $ is $ 22.775{\text{ }}mmHg $ .

Note :
Molality, a measure of concentration, is especially used when we have to study the characteristics of solutions that are related to vapor pressure as well as alterations in temperature. In such cases, molality is preferred because its value does not vary with alteration in temperature. As in other measures of concentration, volume of solution is used which depends slightly upon temperature.