Glycerol (a non-electrolyte that can be used
as antifreeze and coolant in a car radiator)
has a density of 1.261 g/mL and a molecular
weight of 92 g/mol. If 111 mL of glycerol
are mixed with 5.1 kg of water, by how much
would the boiling point of the solution be
raised above that of pure water? Kb for water
= 0.512◦C/m.
Answer in units of ◦C.
mass glycerol = mL x density = ? grams.
mols glycerol = grams /molecular weight
molality = m = mols slycerol/kg water
delta T = Kb*molality
new boiling point = delta T + 100 C = ?
Post your work if you get stuck.
To determine how much the boiling point of the solution would be raised above that of pure water, we need to use the formula for boiling point elevation:
ΔTb = Kb * m
where ΔTb is the change in boiling point, Kb is the boiling point elevation constant, and m is the molality of the solution.
First, we need to calculate the molality (m) of the solution, which is the number of moles of solute (glycerol) per kilogram of solvent (water).
Step 1: Calculate the mass of glycerol in grams.
mass = density * volume
mass = 1.261 g/mL * 111 mL
mass = 140.271 g
Step 2: Convert the mass of glycerol to moles.
moles = mass / molecular weight
moles = 140.271 g / 92 g/mol
moles = 1.526 mol
Step 3: Calculate the total mass of the solution.
mass of water = 5.1 kg = 5100 g
total mass of solution = mass of glycerol + mass of water
total mass of solution = 140.271 g + 5100 g
total mass of solution = 5240.271 g
Step 4: Calculate the molality.
molality = moles of solute / mass of solvent (in kilograms)
molality = 1.526 mol / 5.1 kg
molality = 0.299 m
Now we have the molality of the solution (m = 0.299). Next, we can calculate the change in boiling point (ΔTb) using the given boiling point elevation constant (Kb = 0.512°C/m).
ΔTb = Kb * m
ΔTb = 0.512°C/m * 0.299 m
Finally, we can substitute the values into the equation and calculate the change in boiling point:
ΔTb = 0.512°C/m * 0.299 m
ΔTb ≈ 0.153°C
Therefore, the boiling point of the solution would be raised by approximately 0.153°C above that of pure water.