the vapor pressure of water at 45.0 °c is 71.93 mmhg. Calculate the vapor pressure of a solution of 1.50 m Al(NO3)3 at this temperature (assume 100% dissociation)

no

Please I need the full workings

Why did the chemist bring a ladder to the lab? Because he wanted to reach the highest level of dissociation! Alright, let's calculate that vapor pressure!

To determine the vapor pressure of the Al(NO3)3 solution at 45.0 °C, we need to consider Raoult's law, which states that the vapor pressure of a solution is the product of the mole fraction of the solute and the vapor pressure of the pure solvent.

Since the Al(NO3)3 is 100% dissociated, we can assume that it completely breaks up into its constituent ions: Al3+ and 3 NO3-. So, the mole fraction of the solute is just the mole fraction of Al(NO3)3.

To find the mole fraction, we first need to calculate the moles of Al(NO3)3 present in 1.50 M solution. The molar mass of Al(NO3)3 is 213 g/mol.

moles of Al(NO3)3 = (1.50 mol/L) x (213 g/mol) = 319.5 g

Next, we need to calculate the moles of water in the solution. The molar mass of H2O is 18 g/mol.

moles of water = 319.5 g / 18 g/mol = 17.75 mol

Now, let's calculate the mole fraction of Al(NO3)3:

mole fraction of Al(NO3)3 = moles of Al(NO3)3 / (moles of Al(NO3)3 + moles of water)
= 1.50 mol / (1.50 mol + 17.75 mol)
= 0.0789

Finally, we can calculate the vapor pressure of the Al(NO3)3 solution:

vapor pressure of Al(NO3)3 solution = (mole fraction of Al(NO3)3) x (vapor pressure of water)
= 0.0789 x 71.93 mmHg
≈ 5.68 mmHg.

So, the vapor pressure of the 1.50 M Al(NO3)3 solution at 45.0 °C is approximately 5.68 mmHg.

To calculate the vapor pressure of a solution, we need to apply Raoult's law. According to Raoult's law, the vapor pressure of a solution is directly proportional to the mole fraction of the solvent and its vapor pressure in its pure state.

The first step is to calculate the mole fraction of the solvent (water) in the solution. Since aluminum nitrate (Al(NO3)3) is the solute, and it is assumed to be 100% dissociated, it does not contribute to the vapor pressure. Therefore, we only need to consider the water in the solution.

Mole fraction (X) is given by the equation:
X(solvent) = (moles of solvent) / (total moles in the solution)

In this case, we have 1.50 M concentration of Al(NO3)3. We can assume that the volume of the solution is 1 L to simplify the calculations.

The moles of solvent (water) can be calculated using the molarity and volume of the solution:
moles of solvent = molarity * volume
moles of solvent = 1.50 mol/L * 1 L
moles of solvent = 1.50 mol

The total moles in the solution are the moles of the solvent because the solute doesn't contribute to the vapor pressure. Therefore, the total moles are also 1.50 mol.

Now, using the calculated moles, we can find the mole fraction of the solvent:
X(solvent) = 1.50 mol / 1.50 mol
X(solvent) = 1

Since the mole fraction of the solvent is equal to 1, it means the solution contains only water. Therefore, the vapor pressure of the solution will be the same as the vapor pressure of water at 45.0 °C, which is given as 71.93 mmHg.

no

1.50 m means 1.5 mols AlCl3/kg solvent.

mols in 1 kg solvent = 1000/molar mass H2O = about 55.5 mols.
1.5 mols AlCl3 = 4*1.5 = 6 mols AlCl3 as ions.
Total mols = 6.0 + 55.5 = about 61.5
XH2O = nH2O/total mols

pH2O = XH2O*PoH2O