an aqueous solution of calcium chloride boils at 101.3 degrees Celsius. How many kilograms of calcium chloride were dissolved in 1000.0 g of the solvent??

We need to determine the boiling point elevation due to the presence of solutes in the solution, and then use this to find the molality of the solution, which will then allow us to find the mass of solute.

The boiling point elevation formula is:
ΔTb = Kb * molality, where ΔTb is the boiling point elevation, Kb is the ebullioscopic constant of the solvent, and molality (m) is the molality of the solution.

For water, Kb = 0.512 K kg/mol.

We are given that an aqueous solution of calcium chloride boils at 101.3°C. The boiling point of pure water is 100°C. Therefore, the boiling point elevation ΔTb due to the presence of solutes is (101.3 - 100) °C = 1.3°C.

Now we can find the molality of the solution:
1.3°C = 0.512 K kg/mol * molality
molality = 1.3 / 0.512 = 2.5390625 mol/kg

Now we need to find the mass of the calcium chloride solute. Calcium chloride has a molar mass of approximately 110.98 g/mol.

mass of calcium chloride = molality * 1000.0 g solvent * Molar mass CaCl2
mass of calcium chloride = 2.5390625 mol/kg * 1.0 kg * 110.98 g/mol = 281.72 g

Therefore, 281.72 g (or 0.2817 kg) of calcium chloride were dissolved in 1000.0 g of the solvent.

To determine the mass of calcium chloride dissolved in the solvent, we need to use the boiling point elevation equation. The equation is as follows:

ΔTb = Kbm

where:
ΔTb = boiling point elevation
Kb = molal boiling point constant
m = molality of the solution

We can rearrange the equation to solve for the molality (m):

m = ΔTb / Kb

However, we need the boiling point elevation (ΔTb) and the molal boiling point constant (Kb) for the solvent.

For water (the solvent), the molal boiling point constant (Kb) is 0.512 °C/m. The boiling point elevation (∆Tb) can be calculated by subtracting the boiling point of pure water (100 °C) from the boiling point of the calcium chloride solution (101.3 °C):

ΔTb = 101.3 °C - 100 °C = 1.3 °C

Now, we can substitute the values into the equation to find the molality (m):

m = 1.3 °C / 0.512 °C/m = 2.54 m

The molality (m) is 2.54 m, which means there are 2.54 moles of calcium chloride per kilogram of solvent.

Since we have 1000.0 g of solvent, we can convert it to kilograms:

1000.0 g / 1000 = 1.0 kg

Now, we can calculate the mass of calcium chloride:

mass of calcium chloride = molarity x molar mass x mass of solvent

The molarity can be calculated by multiplying the molality by the density of water:

molarity = molality x density of water = 2.54 m x 1000 g/L = 2540 g/L

The molar mass of calcium chloride (CaCl2) is 111 g/mol.

mass of calcium chloride = 2540 g/L x 111 g/mol x 1.0 kg = 281,940 g

Therefore, 281,940 grams (or 281.94 kg) of calcium chloride were dissolved in 1000.0 g of solvent.

To determine the amount of calcium chloride dissolved in the solvent, we can use the concept of boiling point elevation.

Boiling point elevation is directly proportional to the concentration of dissolved particles in a solution. The equation for boiling point elevation is given by:

ΔTb = Kbm

Where:
ΔTb is the boiling point elevation,
Kb is the molal boiling point constant of the solvent, and
m is the molality of the solute (calcium chloride in this case).

First, we need to find the molal boiling point constant for the solvent, which is water in this case. The molal boiling point constant for water is approximately 0.512 °C/m.

Given:
ΔTb = 101.3 °C
Kb = 0.512 °C/m
m = ?

Let's substitute these values into the equation:

101.3 = 0.512 * m

Now, we can solve for m (the molality of the solute):

m = 101.3 / 0.512
m ≈ 197.85 mol/kg

This means that there are approximately 197.85 moles of calcium chloride dissolved per kilogram of water.

Now, we have to find the amount of calcium chloride dissolved in 1000.0 g (1 kg) of the solvent. To do this, we need to convert the molality into the mass of calcium chloride using its molar mass.

The molar mass of calcium chloride (CaCl2) is approximately 110.98 g/mol.

Let's calculate the amount of calcium chloride by multiplying the molality by its molar mass:

Amount of calcium chloride = m * molar mass
Amount of calcium chloride = 197.85 mol/kg * 110.98 g/mol

Calculating this, the amount of calcium chloride dissolved in 1 kg of the solvent is approximately:

Amount of calcium chloride = 21942.507 g ≈ 21.942 kg

Therefore, approximately 21.942 kg of calcium chloride were dissolved in 1000.0 g (1 kg) of the solvent.