How many grams of NaCl must be added to 225.0 g
of H2O at 45 °C to lower the vapor pressure of water
by 2.21 mmHg? The vapor pressure of pure water is
71.93 mmHg at 45 °C.
vp lowering = Xsolute*PoH2O
Solve for Xsolute
mols H2O = grams/molar mass
XNaCl = mols NaCl/(mols NaCl + mols H2O)
You know XNaCl and mols H2O, solve for mols NaCl, then
mols NaCl = grams/molr mass NaCl. You know mols and molar mass NaCl; solve for grams NaCl.
Then remember NaCl has i = 2 for the van't Hoff factor so divide the final mols by 2.
To calculate the number of grams of NaCl that must be added to lower the vapor pressure of water by a certain amount, we need to use the concept of the vapor pressure lowering known as Raoult's law.
Raoult's law states that the partial pressure of a solvent (in this case, water) above a solution is directly proportional to the mole fraction of the solvent in the solution.
Mathematically, it can be expressed as:
P = Xsolvent * Psolvent
Where:
P is the partial pressure of the solvent above the solution
Xsolvent is the mole fraction of the solvent in the solution
Psolvent is the vapor pressure of the pure solvent
To calculate the mole fraction of the solvent, we need to determine the number of moles of the solute (NaCl) and the solvent (water).
1. Calculate the mole fraction of the solute (NaCl):
- Convert the given mass of NaCl to moles using the molar mass of NaCl (58.44 g/mol).
2. Calculate the mole fraction of the solvent (water):
- Convert the given mass of water to moles using the molar mass of water (18.015 g/mol).
3. Calculate the initial partial pressure of the solvent (water):
- Use Raoult's law by substituting the mole fraction of the solvent and the vapor pressure of pure water at that temperature.
4. Calculate the final partial pressure of the solvent:
- The final partial pressure is the initial partial pressure minus the vapor pressure lowering (2.21 mmHg).
5. Determine the mole fraction of the solvent in the final solution:
- Rearrange the equation P = Xsolvent * Psolvent to solve for Xsolvent.
6. Calculate the final mole fraction of the solute (NaCl):
- The final mole fraction of the solute can be calculated by subtracting the mole fraction of the solvent from 1.
7. Calculate the moles of the solute (NaCl) needed:
- Multiply the final mole fraction of the solute by the total moles of the solution.
8. Finally, calculate the mass of NaCl needed:
- Convert the moles of NaCl to grams using the molar mass of NaCl.
Following these steps, we can find the answer to the question.