Question

A solution of urea is 6% by mass. Calculate the mole fractions of urea and water in the solution. (Molecular mass of urea = 60).

Hint:

When given a percentage by mass, assume \(100\,\text{g}\) of solution to simplify calculation. Then convert grams to moles and calculate mole fraction by dividing each mole value by the total moles.

Answer 1

Assume \(100\,\text{g}\) of solution \(\Rightarrow\) \(6\,\text{g}\) urea and \(94\,\text{g}\) water.
Moles of urea \(=\dfrac{6}{60}=0.10\ \text{mol}\).
Moles of water \(=\dfrac{94}{18}=5.222\ \text{mol}\).
Total moles \(=0.10+5.222=5.322\ \text{mol}\).
Mole fraction of urea \(x_{\text{urea}}=\dfrac{0.10}{5.322}=0.0188\).
Mole fraction of water \(x_{\text{water}}=\dfrac{5.222}{5.322}=0.9812\).
\[ \boxed{x_{\text{urea}}\approx 0.0188, x_{\text{water}}\approx 0.9812} \]