Question

5.2 moles of aqueous solution of 1L of methyl alcohol, $C{{H}_{3}}OH$ is supplied. What is the mole fraction of methyl alcohol in the solution?
[A] 0.100
[B] 0.190
[C] 0.086
[D] 0.050

Answer 1

Hint:You should know that mole fraction is a concentration term. To solve this firstly identify the number of moles of solute in the given solution. After that you need to find out the number of moles of water in 1L. After that you can find the required answer by dividing the number of moles of solute by the sum of the number of moles of all the constituents in the solution.

Complete step by step solution:
In the question, it is given to us that 5.2 moles of methyl alcohol is present in 1L of the solution. We know that 1L is equal to 1kg.
So, here we have that 5.2 moles of the solute that is methyl alcohol is present in 1kg of solution. From the definition of molality we know that it is the number of moles of solute per litre of the solvent. Now, we need to find out the number of moles water in the solution. We can easily find out the number of moles of water present in 1 Kg of solution from its molecular weight.
We know that the molecular weight of water is 18 g/mol.
And, the number of moles is equal to weight upon molecular weight.
Here, we have 1 Kg of solution and we know 1 Kg = 1000 grams.
Therefore, we can write that number of moles of water = $\dfrac{1000g}{18g/mol}$ = 55.56 moles.Now we know that mole fraction is the fraction of molecules of solute (can be one or more) in a solution. We can find the mole fraction of a solute by dividing its number of moles in the solution by the total number of moles present in the solution.
Now let us calculate the mole fraction of methyl alcohol.
In the solution we have 55.56 moles of water and 5.2 moles of methyl alcohol.
Therefore, total number of molecules in the solution = 55.56 + 5.2 = 60.76 moles.
Therefore, mole fraction of methyl alcohol = $\dfrac{5.2}{60.76}$ = 0.08556 $\simeq $ 0.086.

Therefore, the correct answer is option [C] 0.086

Note: Mole fraction is basically a term to define the concentration of a solution. There are other concentration terms too like molarity, molality and normality. Molarity is the number of moles of solute per litre of solvent. Normality of a solution is the gram equivalent of solute per litre of the solvent and we’ve already discussed molality above, which is the number of moles of solute per kilogram of solvent.