A pharmacist makes rubbing alcohol from 70 mL of ethanol (46 g/mol, density 0.789 g/mL) and 30 mL…

Step 1. Masses. Ethanol: $70 \times 0.789 = 55.23\ \text{g}$. Water: $30 \times 1.00 = 30\ \text{g}$.

Step 2. Mass percent. $\dfrac{55.23}{55.23 + 30} \times 100 = 64.8\ \%$.

Step 3. Moles. Ethanol: $\dfrac{55.23}{46} = 1.201\ \text{mol}$. Water: $\dfrac{30}{18} = 1.667\ \text{mol}$.

Step 4. Mole fraction. $x = \dfrac{1.201}{1.201 + 1.667} = 0.419$.