you make a solution by dissolving 25.0g of sodium chloride in 100.0 mL of water. What is the boiling point of the solution?
mols NaCl = grams/molar mass
Solve for mols.
molality NaCl = mols NaCl/kg solvent
Solve for m.
delta T = i*Kb*m
i = 2 for NaCl. Solve for delta T, then add to 100 to find the new boiling point.
To determine the boiling point of the solution, we need to consider the effect of adding a solute (sodium chloride) to a solvent (water) on the boiling point of the solution. This effect is known as boiling point elevation.
Boiling point elevation occurs because the solute particles disrupt the normal boiling process by lowering the vapor pressure of the solution. As a result, the boiling point of the solution is higher than the boiling point of the pure solvent.
To calculate the boiling point elevation, we can use the following formula:
ΔTb = K{b} × m
where:
ΔTb is the boiling point elevation (difference between the boiling point of the solution and the boiling point of the pure solvent)
Kb is the molal boiling point elevation constant for the solvent (water)
m is the molality of the solute in the solution
The molality (m) is calculated by dividing the moles of solute by the mass of the solvent (water) in kilograms. However, in this case, we are given the mass of sodium chloride and the volume of water, so we need to convert them to the appropriate units first.
Given:
Mass of sodium chloride (solute) = 25.0 g
Volume of water (solvent) = 100.0 mL
Step 1: Convert the volume of water to mass in kilograms.
Since the density of water is 1 g/mL, the mass of water is 100.0 g (100.0 mL) = 100.0 g.
Converting to kilograms:
Mass of water = 100.0 g ÷ 1000 = 0.100 kg
Step 2: Calculate the molality (m) of the sodium chloride solution.
Molality (m) = moles of solute ÷ mass of solvent (in kg)
To determine the moles of sodium chloride, we need to divide the given mass by its molar mass. The molar mass of sodium chloride is 58.44 g/mol.
Moles of sodium chloride = 25.0 g ÷ 58.44 g/mol = 0.428 mol
Molality (m) = 0.428 mol ÷ 0.100 kg = 4.28 mol/kg
Step 3: Determine the boiling point elevation (ΔTb).
The molal boiling point elevation constant (Kb) for water is 0.512 °C/m.
ΔTb = Kb × m = 0.512 °C/m × 4.28 mol/kg = 2.19 °C
Step 4: Calculate the boiling point of the solution.
The boiling point elevation is the difference between the boiling point of the solution and the boiling point of the pure solvent.
Boiling point of the solution = Boiling point of pure solvent (water) + ΔTb
The boiling point of pure water is 100 °C (elevation of 0 °C).
Boiling point of the solution = 100 °C + 2.19 °C = 102.19 °C
Therefore, the boiling point of the solution is 102.19 °C.