Question

What is the mole fraction of the solute in 1.00 m aqueous solution?
(A) 0.0354
(B) 0.018
(C) 0.177
(D) 1.770

Answer 1

Hint The addition of mole fractions of all the components in the solution is unity. Also, the molality comprises the weight of solvent (in Kgs) used; unlike molarity which uses volume of solution (in litres).

Complete step by step solution:
Knowing some basic mole-concept we can solve the given question easily. Let us see some of the definitions.
Molality- The ratio of moles of solute to a kilogram of solvent is molality. Its SI unit is moles per kilogram of solvent.
- Solute is the substance which is added in small amounts to the solvent to create a solution.
- Solvent is the substance present in excess which can add solute into it till saturation.
Mole fraction- Mole fraction represents the number of molecules of a particular component in a mixture divided by the total number of moles in the given mixture.
For given word problem,
1 molal aqueous solution means 1 mole of solute in 1 Kg of solvent i.e. water.
The molecular weight of water is 18 gm/mole
Thus,
The number of moles of the water = ($\dfrac{1000gm}{18gm/mole}$) = 55.56 mole.
Now, the mole fraction of water = $\dfrac{55.56}{(55.56+1)}$ = 0.982
As,
Mole fraction of solute + mole fraction of solvent = 1
Therefore,
Mole fraction of solute = (1 - 0.982) = 0.018

Hence, option (B) 0.018 is correct.

Note: Do note that mole fraction is the fraction of similar unit quantities so that will be unitless and also always less than unity. So, option (D) can never be the answer. Thus, we can ignore that option from the start.
Do have a proper balance in units and dimensions while solving the problem. Especially, when we calculate molality, do note that it has a weight of solvent in Kg and not in gm; in the empirical formula. Do not get confused between the two measuring quantities i.e. molality and molarity.