34) What is the mole fraction of phosphoric acid in a 20.5% (by mass) aqueous solution? A) 0.0474 B) 0.0905 C) 0.0453

To find the mole fraction of phosphoric acid in a 20.5% (by mass) aqueous solution, we need to follow these steps:<br /><br />1. **Determine the masses of each component in the solution:**<br /> - Let's assume we have 100 g of the solution.<br /> - The mass of phosphoric acid (H₃PO₄) is 20.5 g.<br /> - The mass of water (H₂O) is 79.5 g.<br /><br />2. **Calculate the number of moles of each component:**<br /> - Molar mass of H₃PO₄ = 3(1.01) + 31.00 + 4(16.00) = 97.99 g/mol<br /> - Molar mass of H₂O = 2(1.01) + 16.00 = 18.02 g/mol<br /><br /> Number of moles of H₃PO₄:<br /> \[<br /> \text{Moles of H₃PO₄} = \frac{20.5 \text{ g}}{97.99 \text{ g/mol}} \approx 0.209 \text{ moles}<br /> \]<br /><br /> Number of moles of H₂O:<br /> \[<br /> \text{Moles of H₂O} = \frac{79.5 \text{ g}}{18.02 \text{ g/mol}} \approx 4.42 \text{ moles}<br /> \]<br /><br />3. **Calculate the mole fraction of phosphoric acid:**<br /> \[<br /> \text{Mole fraction of H₃PO₄} = \frac{\text{Moles of H₃PO₄}}{\text{Moles of H₃PO₄} + \text{Moles of H₂O}}<br /> \]<br /> \[<br /> \text{Mole fraction of H₃PO₄} = \frac{0.209}{0.209 + 4.42} \approx \frac{0.209}{4.629} \approx 0.0453<br /> \]<br /><br />Therefore, the mole fraction of phosphoric acid in the solution is approximately 0.0453.<br /><br />The correct answer is:<br />C) 0.0453