Question

Mole fraction of $ A $ in $ {H_2}O $ is $ 0.2 $ . The molality of $ A $ in $ {H_2}O $ is:
(A) $ 13.8 $
(B) $ 15.5 $
(C) $ 14.5 $
(D) $ 16.8 $

Answer 1

Hint: To calculate molality we first calculate number of moles using mole fraction formula then we put the values in molality formula. And the molality $ = $ moles of solute divided by mass of solvent in kilograms m $ = $ $ n $ (solute) divided by mass(solvent in kilogram).

Complete answer:
Molality is a measure of the number of moles of solute in a solution corresponding to $ 1Kg $ or $ 1000g $ of solvent. The SI unit for molality is $ \dfrac{{mol}}{{Kg}} $
 $ \Rightarrow m = \dfrac{{mol}}{{kg}} $
Where, $ m = $ molality
 $ mol = $ Moles of solute
 $ kg = $ kilogram of solvent.
Mole fraction of $ A $ is $ 0.2 $ , which means that $ 0.2 $ moles of $ A $ is present in the $ 1 $ mole of solution.
Mole fraction of $ B $ $ ({H_2}O) $ $ = 1 - {x_A} = 1 - 0.2 = 0.8 $
This means that $ 0.8 $ moles of $ B $ is present in $ 1 $ mole of solution.
To calculate the mass of water, we use the equation:
Number of moles $ = \dfrac{{given\;mass}}{{molar\;mass}} $
Moles of water $ = 0.8mol $
Molar mass of water $ = 18\dfrac{g}{{mol}} $
Putting values in above equation, we get:
 $ \Rightarrow 0.8 = \dfrac{{mass\;of\;water}}{{18\dfrac{g}{{mol}}}} $
Mass of water $ = 14.4g $
Now, we calculate the molality, by using the above molality formula:
We are given the mass of solute $ (A) = 0.2mol $ , mass of solvent(water) $ = 14.2g = 0.0144kg $
Putting the values in the formula, we get:
Molality $ = \dfrac{{0.2mol}}{{0.0144kg}} = 13.88\dfrac{{mol}}{{kg}} $
So, the correct answer is (A) $ 13.8 $ .

Additional Information:
The advantage of using molality as a measure of concentration is that molality only depends on the masses of solute and solvent, which are unaffected by variations in temperature and pressure. In contrast, solutions prepared volumetrically are likely to change as temperature and pressure change. In many applications, this is a significant advantage because the mass, or the amount, of a substance is often more important than its volume

Note:
The difference between the molality and molarity is that the molality of a solution is equal to the moles of solute divided by the mass of solvent in kilograms, while the molarity of a solution is equal to the moles of solute divided by the volume of solution in liters.