What is the boiling point of a solution made using 731g of sucrose, C12H22O11, in 0.250kg of water,h2o ?

To determine the boiling point of a solution, you need to use the concept of colligative properties, specifically boiling point elevation. The boiling point elevation for a solution is given by the formula:

ΔTb = Kbm

Where:
ΔTb is the change in boiling point,
Kb is the molal boiling point elevation constant which depends on the solvent,
m is the molality of the solution, and
b is the overall constant (in this case, it is equal to the boiling point elevation constant for water, which is approximately 0.512 °C/m).

To calculate the molality (m), you need to determine the number of moles of sucrose and the mass of the water in kilograms.

1. Calculate the molar mass of sucrose (C12H22O11):
The molar mass of carbon (C) is 12.01 g/mol, the molar mass of hydrogen (H) is 1.008 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol. Multiply the molar mass of each element by its respective subscript in the formula, then sum them up:
(12.01 g/mol * 12) + (1.008 g/mol * 22) + (16.00 g/mol * 11) = 342.34 g/mol

2. Calculate the number of moles of sucrose:
Divide the mass of sucrose by its molar mass:
731 g / 342.34 g/mol = 2.135 mol

3. Calculate the mass of water in kilograms:
Divide the mass of water by 1000 to convert it to kilograms:
0.250 kg

4. Calculate the molality (m):
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
m = moles of solute / mass of solvent (in kg)
m = 2.135 mol / 0.250 kg = 8.54 mol/kg

5. Calculate the change in boiling point (ΔTb):
Using the equation ΔTb = Kbm:
ΔTb = (0.512 °C/m) * (8.54 mol/kg)

6. Calculate the boiling point of the solution:
The boiling point elevation is added to the boiling point of the pure solvent (water). The boiling point of water is approximately 100 °C.
Boiling Point of Solution = 100 °C + ΔTb

Substitute the calculated value of ΔTb into the equation:
Boiling Point of Solution = 100 °C + (0.512 °C/m * 8.54 mol/kg)

Calculating this expression will give you the boiling point of the solution made using 731g of sucrose in 0.250kg of water.