Final answer:
The vapor pressure of a solution with 19 grams of NaCl in 0.315 kg water can be calculated using Raoult's Law. First, determine the moles of NaCl and water, then find the mole fraction of water. Apply Raoult's Law to find the solution's vapor pressure, which is approximately 22.92 mmHg at 25 °C.
Step-by-step explanation:
To calculate the vapor pressure of a solution containing NaCl in water, we use Raoult's Law. This law states that the vapor pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution. We can determine the mole fraction of the solvent, water, by first calculating the number of moles of NaCl and then the number of moles of water. Because NaCl dissociates into two ions, each mole of NaCl will produce two moles of solute particles.
First, calculate the moles of NaCl:
Number of moles = Mass (g) / Molar mass (g/mol)
Number of moles of NaCl = 19 g / 58.44 g/mol
≈ 0.325 mol
Since NaCl produces two moles of particles:
Total solute particles = 0.325 mol × 2
= 0.65 mol
Next, calculate the moles of water:
Number of moles of water = Mass (kg) × (1000 g/kg) / Molar mass of water (g/mol)
Number of moles of water = 0.315 kg × 1000 g/kg / 18.015 g/mol
≈ 17.48 mol
Now, calculate the mole fraction of water:
Mole fraction of water = Moles of water / (Moles of water + Moles of solute particles)
Mole fraction of water = 17.48 mol / (17.48 mol + 0.65 mol)
≈ 0.964
Finally, apply Raoult's Law to find the vapor pressure of the solution:
Vapor pressure of solution = Mole fraction of water × Vapor pressure of pure water
Vapor pressure of solution = 0.964 × 23.8 mmHg
= 22.92 mmHg