The boiling point of an aqueous 1.83 m salt solution is 102.5°C. Determine the value of the van't Hoff factor for this solute if the Kb for water is 0.512°C/m.

delta T = i*Kb*m

Substitute and solve for i.

To determine the value of the van't Hoff factor for the solute in the salt solution, we can use the formula:

ΔTb = i * Kb * m

where:
ΔTb is the boiling point elevation,
i is the van't Hoff factor,
Kb is the molal boiling point elevation constant for the solvent, in this case, water,
and m is the molality of the solute.

We are given:
ΔTb = 102.5°C,
Kb = 0.512°C/m.

To find the molality (m) of the solute, we need to use the formula for molality:

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

However, we are not given the mass of the solvent. Fortunately, we can use the molarity (M) and the density (d) to find the mass of the solvent. The formula for molarity is:

M = moles of solute / liters of solution

And the formula for density is:

density = mass / volume

So, we can rearrange the density formula to solve for mass:

mass = density * volume

Since we are given the concentration (molarity), we can find the volume using the formula:

volume = moles of solute / M

Now we have all the necessary information to calculate the van't Hoff factor (i).

1. Calculate the molality (m) of the solute:
- Convert the molarity (1.83 m) to moles of solute per liter of solution.
- Calculate the mass of the solvent using the density of water.
- Calculate the volume of the solvent using the formula for volume.
- Use the mass and volume to calculate the molality (m) of the solute.

2. Calculate the van't Hoff factor (i) using the boiling point elevation (ΔTb), molality (m), and the molal boiling point elevation constant (Kb).

Let's perform the calculations step by step:

1. Calculate the molality (m) of the solute:
Given:
- Molarity (M) = 1.83 m
- Kb for water = 0.512 °C/m

a. Convert molarity to moles per liter:
The molarity (M) of 1.83 m means there are 1.83 moles of solute in 1 liter of solution.

b. Calculate the mass of the solvent (water):
The density of water is approximately 1 g/mL or 1000 kg/m³.
We will assume 1 liter of solution has a mass of 1000 grams and convert it to kilograms:
mass = 1000 g = 1 kg

c. Calculate the volume of the solvent:
Using the formula:
volume = moles of solute / M

volume = 1.83 moles / 1.83 M = 1 liter (since the molality and molarity are the same)

d. Calculate the molality (m):
m = moles of solute / mass of solvent (in kg)
m = 1.83 moles / 1 kg = 1.83 m

So, the molality (m) of the solute is 1.83 m.

2. Calculate the van't Hoff factor (i):
Given:
- ΔTb = 102.5 °C
- Kb for water = 0.512 °C/m
- Molality (m) = 1.83 m

We can rearrange the formula as follows:
i = ΔTb / (Kb * m)

i = 102.5 °C / (0.512 °C/m * 1.83 m) = 112

So, the value of the van't Hoff factor for the solute in the salt solution is 112.