To find the mole fraction of water in the solution containing equal numbers of moles of water (H₂O) and ethanol (C₂H₅OH), follow these steps:
1. Identify the number of moles of each component:
- Moles of water (H₂O): 1 mole
- Moles of ethanol (C₂H₅OH): 1 mole
2. Determine the total number of moles in the solution:
- Total moles = moles of water + moles of ethanol
- Total moles = 1 mole (H₂O) + 1 mole (C₂H₅OH)
- Total moles = 2 moles
3. Calculate the mole fraction of water:
- Mole fraction of water (X_water) is the ratio of the moles of water to the total moles in the solution.
- [tex]\( X_{\text{water}} = \frac{\text{moles of water}}{\text{total moles}} \)[/tex]
- [tex]\( X_{\text{water}} = \frac{1 \text{ mole (H}_2\text{O)}}{2 \text{ moles}} \)[/tex]
- [tex]\( X_{\text{water}} = 0.5 \)[/tex]
Thus, the mole fraction of water in the solution is 0.5.
