Given that the vapor pressure of water is 17.54 Torr at 20 °C, calculate the vapor-pressure lowering of aqueous solutions that are 1.90 m in (a) sucrose, C12H22O11, and (b) aluminum chloride. Assume 100% dissociation for electrolytes.
I got .5799 Torr for sucrose, but I can't figure out what to multiply that by to get the answer for aluminum chloride. I just need that factor to complete this problem.
The factor to which you refer is i, the van't Hoff factor. It is 4 for AlCl3.
To calculate the vapor-pressure lowering, also known as the Raoult's law equation, you need to use the formula:
ΔP = Xsolvent × Psolvent
Where:
- ΔP is the vapor-pressure lowering
- Xsolvent is the mole fraction of the solvent
- Psolvent is the vapor pressure of the solvent
For the case of sucrose (C12H22O11), you can assume that it does not dissociate, so it will remain as a solute molecule. To calculate Xsolvent for sucrose, you need to use the formula:
Xsolvent = moles of the solvent / total moles of the solution
Given that the sucrose solution is 1.90 m, which stands for moles per liter, you can calculate the moles of sucrose (C12H22O11) using the molarity and the volume of the solution:
moles of C12H22O11 = molarity × volume
Then, calculate the total moles of the solution by adding the moles of sucrose to the moles of water (solvent). Since water has a molarity of 55.5 M and the volume is not given, we will assume 1.00 L for simplicity:
moles of water = molarity × volume
Now that you have the moles of the solvent and the total moles of the solution, you can calculate Xsolvent using the formula mentioned above. Then, substitute Xsolvent and the vapor pressure of water (17.54 Torr) into the Raoult's law equation to calculate the vapor-pressure lowering (ΔP) of the sucrose solution.
To determine the factor for aluminum chloride (AlCl3), it is important to know if it dissociates in water. Assuming complete dissociation as stated in the question, aluminum chloride will dissociate into Al3+ and 3 Cl- ions. Since ΔP is directly proportional to the mole fraction of solute particles, you can calculate the number of solute particles by considering the dissociation.
For every mole of AlCl3, you get 4 total particles (1 Al3+ ion and 3 Cl- ions). Hence, to calculate the mole fraction of the solute, divide the moles of AlCl3 by the total moles of the solution (including water). Repeat the same process as for sucrose to calculate Xsolvent for aluminum chloride. Finally, substitute Xsolvent and the vapor pressure of water into the Raoult's law equation to calculate the vapor-pressure lowering (ΔP) of the aluminum chloride solution.