A 50/50 blend of engine coolant and water (by volume) is usually used in an automobile\'s engine cooling system. If your car\'s cooling system holds 4.00 gallons, what is the boiling point of the solution? Make the following assumptions in your calculation; at normal filling conditions, the densities of engine coolant and water are 1.11 g/mL and 0.998 g/mL respectively. Assume that the engine coolant is pure ethylene glycol (HOCH2CH2OH), which is non-ionizing and non-volatile, and that the pressure remains constant at 1.00 atm. Also, you\'ll need to look up the boiling-point elevation constant for water.
Convert 2 gallons ethylene glycol to mL then use density to calculate the mass.
Convert 2 gallons H2O to mL and use density to calculate the mass.
mols ethylene glycol = grams/molar mass
molality of the soln then is moles ethylene glycol/kg H2O
delta T = 1*Kb*molality.
You can look up Kb but I think it is 0.52. You should confirm that. Solve for delta T and add to 100 C to find new boiling point.
A 50/50 blend of engine coolant and water (by volume) is usually used in an automobile\'s engine cooling system. If your car\'s cooling system holds 4.10 gallons, what is the boiling point of the solution? Make the following assumptions in your calculation: at normal filling conditions, the densities of engine coolant and water are 1.11 g/mL and 0.998 g/mL respectively. Assume that the engine coolant is pure ethylene glycol (HOCH2CH2OH), which is non-ionizing and non-volatile, and that the pressure remains constant at 1.00 atm. Also, you\'ll need to look up the boiling-point elevation constant for water.
To find the boiling point of the solution, we need to use the boiling point elevation formula:
ΔTb = Kb * m
Where:
ΔTb = boiling point elevation
Kb = boiling point elevation constant for water
m = molality of the solution
First, let's calculate the molality (m) of the solution:
Molality (m) = moles solute / mass of solvent (in kg)
Since the solution is a 50/50 blend of coolant and water by volume, the total volume of the solution is 4.00 gallons.
First, we need to convert the volume to a mass:
Mass of solution = volume * density
Volume of solution = 4.00 gallons
Using the given densities, we can calculate the mass of the coolant and water:
Mass coolant = (volume coolant / total volume) * mass of solution
Mass water = (volume water / total volume) * mass of solution
Now, we can calculate the mass of the water and coolant components:
Mass coolant = (0.50 * 4.00 gallons) * (1.11 g/mL)
Mass water = (0.50 * 4.00 gallons) * (0.998 g/mL)
Next, let's convert the masses to moles:
Moles coolant = mass coolant / molar mass coolant
Moles water = mass water / molar mass water
The molar mass of ethylene glycol (HOCH2CH2OH) is 62.07 g/mol, and the molar mass of water (H2O) is 18.02 g/mol.
Now, we can calculate the molality of the solution:
Molality (m) = (moles coolant + moles water) / mass of water (converted to kg)
Finally, we can calculate the boiling point elevation:
ΔTb = Kb * m
By looking up the boiling-point elevation constant (Kb) for water, we can substitute the values and calculate the boiling point elevation.
The boiling point of the solution will be the boiling point of pure water (100°C) plus the boiling point elevation (ΔTb).
Note: Since the values needed for the calculation are not provided, you will need to look up the boiling-point elevation constant (Kb) for water to complete the calculation.
To find the boiling point of a 50/50 blend of engine coolant and water, we'll need to consider the boiling point elevation caused by adding solute (engine coolant) to the solvent (water).
The boiling-point elevation is given by the equation: ΔTb = Kbp * molality,
where ΔTb is the boiling point elevation, Kbp is the boiling-point elevation constant, and molality is the molal concentration of the solution.
To calculate the molality of the solution, we first need to determine the mass of engine coolant and water required to fill the cooling system.
Given:
Volume of the cooling system = 4.00 gallons
Density of engine coolant = 1.11 g/mL
Density of water = 0.998 g/mL
To convert gallons to mL:
1 gallon = 3785.41 mL
Therefore, the volume of the cooling system in mL is:
4.00 gallons * 3785.41 mL/gallon = 15141.64 mL
Since the blend is 50/50 by volume, we'll have half of the volume for each component.
The volume of engine coolant = 15141.64 mL / 2 = 7570.82 mL
The volume of water = 15141.64 mL / 2 = 7570.82 mL
Next, we can calculate the mass of engine coolant and water:
Mass = volume * density
Mass of engine coolant = 7570.82 mL * 1.11 g/mL = 8403.38 g
Mass of water = 7570.82 mL * 0.998 g/mL = 7558.84 g
Now, we can determine the molality of the solution:
Molality (m) = moles of solute / mass of solvent
Since the engine coolant is non-ionizing, we can assume it does not dissociate into ions, and its moles are equal to its mass divided by its molar mass.
The molar mass of ethylene glycol (HOCH2CH2OH) can be found using the periodic table. It is:
2 * (1.01 g/mol for hydrogen) + 2 * (12.01 g/mol for carbon) + 6 * (16.00 g/mol for oxygen) = 62.07 g/mol
Moles of engine coolant = mass of engine coolant / molar mass
Moles of engine coolant = 8403.38 g / 62.07 g/mol = 135.43 mol
Now, we can calculate the molality:
Molality = moles of solute / mass of solvent
Molality = 135.43 mol / 7558.84 g = 0.0179 mol/g
With the molality calculated, we can now determine the boiling point elevation using the boiling-point elevation constant for water.
Unfortunately, the boiling-point elevation constant for water, Kbp, is not provided in the question. You'll need to look up this value in a reliable source, such as a chemistry handbook or online database.
Once you have the value of Kbp, you can calculate the boiling-point elevation:
ΔTb = Kbp * molality
Finally, add the boiling point elevation to the normal boiling point of water (100°C or 212°F) to find the boiling point of the solution.