When a 2.5 mol of sugar (C12H22O11) are added to a certain amount of water the boiling point is raised by 1 Celsius degree. If 2.5 mol of aluminum nitrate is added to the same amount of water, by how much will the boiling point be changed?

For sugar:

delta T = Kb*m
Substitute and solve for m = molality.

Then m = mols kg solvent. You know mols and m, solve for kg solvent

Using that kg solvent, convert 2.5 mol Al(NO3)3 to m

Then plug m and Kb into
delta T = i*Kb*m
You know Kb and m. The van't Hoff factor for Al(NO3)3 is 4.

To find the change in boiling point when 2.5 mol of aluminum nitrate (Al(NO3)3) is added to the same amount of water, we can use the concept of molality and the cryoscopic constant.

The change in boiling point (ΔTb) is directly proportional to the molality of the solute. The molality (m) is defined as the moles of solute per kilogram of solvent.

First, let's determine the molality of sugar in the solution. Since 2.5 mol of sugar (C12H22O11) is added to a certain amount of water, we need to know the mass of water to calculate the molality. Let's assume the mass of water is 1 kg for simplicity.

The molality (m) can be calculated using the formula:

m = (moles of solute) / (mass of solvent in kg)

Given that we have 2.5 mol of sugar and assume 1 kg of water, the molality of sugar in the solution is:

m_sugar = 2.5 mol / 1 kg = 2.5 mol/kg

Now, to find the change in boiling point due to aluminum nitrate, we need to compare the molality of sugar with the molality of aluminum nitrate.

Since the amount of water is the same, we can assume that the boiling point change is only dependent on the molality of the solute.

If we assume the cryoscopic constant (Kb) for water is 0.512 °C/m, then the change in boiling point due to sugar can be calculated as:

ΔTb_sugar = Kb * m_sugar

However, in this case, we are interested in finding the change in boiling point due to aluminum nitrate. Let's denote this as ΔTb_aluminum nitrate.

Since the change in boiling point is directly proportional to the molality, we can write the following relationship:

ΔTb_aluminum nitrate / ΔTb_sugar = m_aluminum nitrate / m_sugar

Since we know the change in boiling point for sugar (1 °C) and the molality of sugar (2.5 mol/kg), we can rearrange the equation and solve for ΔTb_aluminum nitrate:

ΔTb_aluminum nitrate = (ΔTb_sugar * m_aluminum nitrate) / m_sugar

Substituting the values we know:

ΔTb_aluminum nitrate = (1 °C * m_aluminum nitrate) / (2.5 mol/kg)

Therefore, to find the change in boiling point when 2.5 mol of aluminum nitrate is added to the same amount of water, you need to know the molality of aluminum nitrate in the solution.