Question

Determine mole fraction of water in an aqueous solution of urea having \(10\%\) w/w urea.

• A. \(0.967\)
• B. \(0.086\)
• C. \(0.323\)
• D. \(0.867\)

Answer 1

The Correct Option is A

Concept:
Weight percent composition can be converted to mole fraction by first determining the moles of each component using their molar masses and then applying the mole fraction formula: \[ x_i = \frac{\text{moles of component}}{\text{total moles of solution}} \] Step 1: Assume \(100\,\text{g\) of solution.} Since the solution contains \(10\%\) w/w urea: \[ \text{Mass of urea} = 10\,\text{g} \] \[ \text{Mass of water} = 90\,\text{g} \] Step 2: Calculate moles of each component. Molar mass of urea \(=60\,\text{g mol}^{-1}\) \[ n_{\text{urea}}=\frac{10}{60}=\frac{1}{6} \] Molar mass of water \(=18\,\text{g mol}^{-1}\) \[ n_{\text{water}}=\frac{90}{18}=5 \] Step 3: Find mole fraction of water. \[ x_{H_2O}=\frac{n_{\text{water}}}{n_{\text{water}}+n_{\text{urea}}} \] \[ x_{H_2O}=\frac{5}{5+\frac{1}{6}} \] \[ x_{H_2O}=\frac{30}{31}=0.967 \] \[ \boxed{x_{H_2O}=0.967} \]