Question

If 6g of solute is dissolved in 90g of water. The mole fraction of the solute is?
A. $\dfrac{1}{5}$
B. $\dfrac{1}{50}$
C. $\dfrac{1}{51}$
D. $\dfrac{1}{501}$

Answer 1

The mole fraction of the solute is the number of moles of urea divided by the total number of moles. Hence, first we have to find the number of moles of urea and water using the given mass and the molar mass of these compounds. Dividing the number of moles of urea with the sum of the number of moles of water and urea will give us the answer.

Formulas used: $n = \dfrac{W}{M}$
Where $n$ is the number of moles, $W$ is the given mass and $M$ is the molar mass.
${x_B} = \dfrac{{{n_B}}}{{{n_A} + {n_B}}}$
Where ${x_B}$ is the mole fraction of the solute and ${n_A},{n_B}$ represent the number of moles of the solvent and solute respectively.

Complete step by step answer:
Let us first find the number of moles of each component given:
$n = \dfrac{W}{M}$
Where $n$ is the number of moles, $W$ is the given mass and $M$ is the molar mass.
For urea ($N{H_2}(CO)N{H_2}$), molar mass of each element is: $N = 14g,H = 1g,C = 12g,O = 16g$. Hence, its molar mass is: $14 + (1 \times 2) + 12 + 16 + 14 + (1 \times 2) = 60g$
And the given mass is $W = 6g$. Substituting these values, we get:
${n_B} = \dfrac{6}{{60}} = \dfrac{1}{{10}} = 0.1mol$
Now let us find the number of moles of water
The molar mass of water (${H_2}O$) is $(1 \times 2) + 16 = 18g$
And the given mass is $W = 90g$. Substituting these values, we get:
${n_A} = \dfrac{{90}}{{18}} = 5mol$
Mole fraction of the solute is given by the formula:
${x_B} = \dfrac{{{n_B}}}{{{n_A} + {n_B}}}$
Where ${x_B}$ is the mole fraction of the solute and ${n_A},{n_B}$ represent the number of moles of the solvent and solute respectively.
Substituting the values we got, ${n_B} = 0.1mol$ and ${n_A} = 5mol$, we get:
$\Rightarrow {x_B} = \dfrac{{0.1}}{{5 + 0.1}} = \dfrac{{0.1}}{{5.1}}$
On solving this, we get the mole fraction as:
${x_B} = \dfrac{1}{{51}}$

So, the correct answer is Option C .

Note: Mole fraction is one of the methods of expressing the concentration of a component in a mixture. Other methods include molarity, molality, parts per million etc.
Since the number of moles do not change with temperature, mole fraction is a good concentration indicator in temperature dependent reactions.