Question

A 5.2 molal aqueous solution of methyl alcohol, ${ CH }_{ 3 }$OH is supplied. What is the mole fraction of methyl alcohol in the solution?
(A.) 0.05
(B.) 0.10
(C.) 0.18
(D.) 0.086

Answer 1

Hint: First, try to simplify the data given in this question. 5.2 molal means there are 5.2 moles of methyl alcohol (solute) in 1000 kg of water (solvent). Now just calculate moles of water and then the mole fraction of methyl alcohol.

Complete step by step solution:
The first thing we need to know is that 5.2 molal means the molality of a solution is 5.2 m.
 A 5.2 molal aqueous solution of methyl alcohol means that 1 kg ( or 1000 g) of water (solvent) contains 5.2 moles of methyl alcohol (solute).

For the calculation of mole fraction of methyl alcohol, we need the following data -
Moles of methyl alcohol, which we already have = 5,2 moles
Total number of moles in the solution = moles of methyl alcohol + moles of water

Let’s calculate moles of water,
The molecular weight of water is 18 g/mol.
The mass of water is 1000 g
The number of moles of water = $\dfrac { mass\quad of\quad water\quad molecular }{ weight\quad of\quad water } \quad =\dfrac { 1000g }{ 18g/mol }$
The number of moles of water = 55.56 mol

Now,
The mole fraction of methyl alcohol = $\dfrac { moles\quad of\quad methyl\quad alcohol }{ Total\quad moles\quad in\quad solution } \quad =\dfrac { 5.2 }{ 5.2+55.56 }$
The mole fraction of methyl alcohol = 0.082

Therefore, we can conclude that the correct answer to this question is option D.

Note: We should not confuse us between the terms molal and molar. The molar is used to represent the molarity of the solution and Molal is used for the representation of molality, we have discussed it already.