Question

Calculate mole fraction of urea in 11.11 molal aqueous solution?
(A) 0.1
(B) 0.17
(C) 0.2
(D) 0.37

Answer 1

Hint: Approach this question with the help of mole concept. “Molality is defined as the number of moles of solute in per kilogram of solvent and mole fraction is defined as the number of moles of a component divided by total number of moles of the mixture or solution”.
Formula used:
We will require the following formulas in this solution:-
Molality: $m=\dfrac{n}{\text{w (in kg)}}$
Mole fraction: ${{x}_{i}}=\dfrac{{{n}_{i}}}{{{n}_{T}}}$
where,
n = number of moles of solute
w = mass of solvent in kilogram
${{n}_{T}}$ = total number of moles in the mixture

Complete answer:
As we know that molality is defined as number of moles of solute in per kilogram of solvent and mole fraction is defined as the number of moles of a component divided by total number of moles of the mixture or solution.
-Calculation of number of moles of urea from molarity:-
$m=\dfrac{n}{\text{w (in kg)}}$
$11.11=\dfrac{n}{\text{1 (in kg)}}$
As it is given that the molality of solution is 11.11 m which means 11.11 moles of urea are present in 1 kg of solvent that is 1000g of solvent. Since, we aren’t provided any information regarding the solvent so we will consider it as water. (Molecular mass of water = 18g)
Number of moles of water: $\dfrac{1000g}{18g/mol}=55.55moles$
-Calculation of mole fraction of urea:-
Mole fraction ${{x}_{urea}}=\dfrac{{{n}_{urea}}}{{{n}_{T}}}$
$\begin{align}
  & \Rightarrow {{x}_{urea}}=\dfrac{11.11}{11.11+55.55} \\
 & \Rightarrow {{x}_{urea}}=\dfrac{11.11}{66.66} \\
 & \Rightarrow {{x}_{urea}}=1.666\simeq 1.7 \\
\end{align}$
-Hence, the mole fraction of urea is = (B) 0.17

Note:
-Kindly remember to convert units as per requirement and use them in the formula to get the accurate result.
-If any solvent is not mentioned in the question specifically, then use water as a solvent.