The vapor pressure of water at 45.0 °C is 71.93 mmHg. What is the vapor pressure of water over a solution prepared from 75.0 g of citric acid (C6H8O7) in 0.420 kg of water at this temperature?
those closing tags are a pain, right? :-(
PH2O> = XH2O>*o</supH2O
mols H2O = g/molar mass = 420/18 = ?
mols C6H8O7 = g/molar mass = 75.0/192 = ?
Total mols = mols H2O + mols C6H8O7 = ?
XH2O</sub = mols H2O/total mols
Calculate mols H2O, mols C6H8O7, total mols, then XH2O
Substitute into equation 1 and solve.
Post your work if you get stuck.
Let me try again. I tried to type in subscripts and superscripts and that didn't work well because I didn't do it right. I think you can interpret this OK. If not let me know.
PH2O = XoH2O
mols H2O = g/molar mass = 420/18 = ?
mols C6H8O7 = g/molar mass = 75.0/192 = ?
Total mols = mols H2O + mols C6H8O7 = ?
XH2O = mols H2O/total mols
Calculate mols H2O, mols C6H8O7, total mols, then XH2O
Substitute into equation 1 and solve.
Post your work if you get stuck.
Sorry again. Replace equation 1 with the following:
PH2O = XH2O*Psup>oH2O
A REAL pain.
To find the vapor pressure of water over a solution prepared from citric acid and water, we need to consider the vapor pressure lowering due to the presence of the solute.
The vapor pressure lowering can be calculated using Raoult's law, which states that the partial pressure of a component in a solution is proportional to its mole fraction. The vapor pressure lowering (∆P) can be calculated using the formula:
∆P = P°solvent × Xsolvent
Where:
- ∆P is the vapor pressure lowering
- P°solvent is the vapor pressure of the pure solvent (water in this case)
- Xsolvent is the mole fraction of the solvent (water in this case)
First, we need to calculate the mole fraction of water (Xsolvent):
- The molecular weight of water (H2O) is 18.015 g/mol.
- The molecular weight of citric acid (C6H8O7) is 192.13 g/mol.
- We can calculate the moles of water and citric acid:
Moles of water = Mass of water / Molecular weight of water
Moles of water = 0.420 kg / 18.015 g/mol
Moles of water = 23.31 mol
Moles of citric acid = Mass of citric acid / Molecular weight of citric acid
Moles of citric acid = 75.0 g / 192.13 g/mol
Moles of citric acid = 0.390 mol
Now we can calculate the mole fraction of water:
Xsolvent = Moles of water / (Moles of water + Moles of citric acid)
Xsolvent = 23.31 mol / (23.31 mol + 0.390 mol)
Xsolvent = 0.983
Next, we need to find the vapor pressure of pure water at 45.0 °C (P°solvent). We can refer to a vapor pressure table or use an equation to find this value. For this example, we will assume that the vapor pressure of water is 71.93 mmHg.
Finally, we can calculate the vapor pressure of water over the solution:
Vapor pressure of water = P°solvent × Xsolvent
Vapor pressure of water = 71.93 mmHg × 0.983
Vapor pressure of water = 70.71 mmHg
Therefore, the vapor pressure of water over the solution is approximately 70.71 mmHg.