A laboratory mixes 40.0 mL of ethanol with 60.0 mL of water…

Step 1. Masses. Ethanol: $40.0 \times 0.789 = 31.56\ \text{g}$. Water: $60.0 \times 0.998 = 59.88\ \text{g}$.

Step 2. Mass percentage. $\dfrac{31.56}{31.56 + 59.88} \times 100 = 34.5\ \%$.

Step 3. Moles. Ethanol: $\dfrac{31.56}{46.069} = 0.685\ \text{mol}$. Water: $\dfrac{59.88}{18.015} = 3.324\ \text{mol}$.

Step 4. Mole fraction. $\dfrac{0.685}{0.685 + 3.324} = 0.171$.