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If the vapor pressure of pure water is 23.8 mmHg at 25°C, what is the vapor pres

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Question: If the vapor pressure of pure water is 23.8 mmHg at 25°C, what is the vapor pressure of a solution containing 1 mole of NaCl in 1 kg of water?

Options:

  1. 20.0 mmHg
  2. 22.0 mmHg
  3. 23.0 mmHg
  4. 23.8 mmHg

Correct Answer: 22.0 mmHg

Solution: 

Using Raoult\'s law, the vapor pressure lowering is calculated considering the van \'t Hoff factor for NaCl.

If the vapor pressure of pure water is 23.8 mmHg at 25°C, what is the vapor pres

Practice Questions

Q1
If the vapor pressure of pure water is 23.8 mmHg at 25°C, what is the vapor pressure of a solution containing 1 mole of NaCl in 1 kg of water?
  1. 20.0 mmHg
  2. 22.0 mmHg
  3. 23.0 mmHg
  4. 23.8 mmHg

Questions & Step-by-Step Solutions

If the vapor pressure of pure water is 23.8 mmHg at 25°C, what is the vapor pressure of a solution containing 1 mole of NaCl in 1 kg of water?
  • Step 1: Understand that vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature.
  • Step 2: Know that pure water has a vapor pressure of 23.8 mmHg at 25°C.
  • Step 3: Recognize that when a solute (like NaCl) is added to a solvent (like water), the vapor pressure of the solution decreases.
  • Step 4: Use Raoult's law, which states that the vapor pressure of a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution.
  • Step 5: Calculate the number of moles of water in 1 kg. The molar mass of water is about 18 g/mol, so 1 kg (1000 g) of water is approximately 55.56 moles.
  • Step 6: Determine the van 't Hoff factor (i) for NaCl, which is 2 because NaCl dissociates into two ions: Na+ and Cl-.
  • Step 7: Calculate the total number of moles in the solution: 1 mole of NaCl + 55.56 moles of water = 56.56 moles total.
  • Step 8: Calculate the mole fraction of water in the solution: mole fraction of water = moles of water / total moles = 55.56 / 56.56.
  • Step 9: Calculate the vapor pressure of the solution using Raoult's law: vapor pressure of solution = vapor pressure of pure water * mole fraction of water.
  • Step 10: Substitute the values to find the new vapor pressure of the solution.
  • Raoult's Law – Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the solution.
  • Van 't Hoff Factor – The van 't Hoff factor (i) accounts for the number of particles a solute dissociates into in solution; for NaCl, i = 2 since it dissociates into Na+ and Cl-.
  • Vapor Pressure Lowering – The decrease in vapor pressure of a solvent when a non-volatile solute is added, calculated using the formula ΔP = i * X_solute * P°_solvent.
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