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 4.90 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.
Convert 4.90 gallons to liters.
1/2 of that will be glycol; 1/2 will be water.
Using density, convert L H2O to grams and L glycol to grams.
Convert grams glycol to moles. moles = grams/molar mass
Convert moles glycol to molality. m = moles/kg solvent
Then delta T= Kb*m
Solve for delta T and add to 100 C to find the new boiling point.
To calculate the boiling point of the solution, we need to consider the colligative properties of the solution. One of these properties is the boiling point elevation, which is determined by the concentration of the solute (in this case, the engine coolant). The boiling point elevation can be calculated using the formula:
ΔTb = Kb * m
Where:
ΔTb is the boiling point elevation
Kb is the molal boiling point elevation constant (a property of the solvent)
m is the molality of the solute (the amount of solute in moles per kilogram of solvent)
First, we need to calculate the molality of the engine coolant solution:
Moles of engine coolant = Volume of engine coolant * Density of engine coolant / Molar mass of engine coolant
Moles of engine coolant = (0.5 * 4.90 gallons) * (1 L / 3.78541 gallons) * (1.11 g/mL) * (1 kg / 1000 g) / (62.07 g/mol)
Next, we need to calculate the mass of the water:
Mass of water = Volume of engine coolant * Density of water
Mass of water = (0.5 * 4.90 gallons) * (1 L / 3.78541 gallons) * (0.998 g/mL) * (1 kg / 1000 g)
Now, we can calculate the molality:
m = Moles of engine coolant / (Mass of water + Mass of engine coolant)
Once we have the molality, we can calculate the boiling point elevation:
ΔTb = Kb * m
Lastly, we need to convert the boiling point elevation to the boiling point of the solution using the equation:
Boiling point of the solution = Boiling point of the pure solvent (water) + ΔTb
The boiling point of pure water at 1.00 atm is 100°C. By adding ΔTb to this, we can find the boiling point of the solution.