Final answer:
To find the mole fractions of zinc chloride and water, we calculate the moles of each, sum them for the total moles in solution, and then divide the moles of each substance by the total moles. The mole fraction of zinc chloride is approximately 0.00237, and the mole fraction of water is approximately 0.99763.
Step-by-step explanation:
To determine the mole fraction of zinc chloride (ZnCl₂) and water in a solution, we need to calculate the moles of both substances. First, we find the number of moles of zinc chloride by dividing its mass by its molar mass. The molar mass of zinc chloride is approximately 136.30 g/mol (65.38 for Zn and 2 x 35.45 for each Cl), so for 2.25 g of ZnCl₂:
Moles of ZnCl₂ = 2.25 g / 136.30 g/mol ≈ 0.0165 mol.
Then, we consider the mass of water. Since the density of water is approximately 1 g/mL, 125 mL of water has a mass of 125 g or 0.125 kg. The molar mass of water is approximately 18.015 g/mol, so the number of moles of water is:
Moles of H₂O = 125 g / 18.015 g/mol ≈ 6.938 mol.
The total number of moles in the solution is the sum of the moles of ZnCl₂ and water:
Total moles = moles of ZnCl₂ + moles of H₂O ≈ 0.0165 mol + 6.938 mol = 6.9545 mol.
Finally, the mole fraction for each substance is calculated by dividing the moles of that substance by the total moles:
- Mole fraction of ZnCl₂ = moles of ZnCl₂ / total moles ≈ 0.0165 mol / 6.9545 mol ≈ 0.00237.
- Mole fraction of H₂O = moles of H₂O / total moles ≈ 6.938 mol / 6.9545 mol ≈ 0.99763.
The mole fraction of zinc chloride in the solution is approximately 0.00237, and the mole fraction of water is approximately 0.99763.