What is the boiling point of the water in your radiator if 2.00kg of antifreeze (ethylene glycol, C2H6O2) is added to 9.00x10^3 grams of water?
Convert 2.00 kg antifreeze to moles. moles = grams/molar mass.
molality = moles/kg solvent.
delta T = Kb*molality. Determine delta T and add that to 100 C.
To determine the boiling point of the water in your radiator after adding antifreeze, we need to use the concept of colligative properties and the equation known as the boiling point elevation.
The boiling point elevation is the difference between the boiling point of a pure solvent (in this case, water) and the boiling point of the solvent with a non-volatile solute (in this case, antifreeze) added to it.
The boiling point elevation can be calculated using the formula:
ΔTb = i * Kb * m
Where:
ΔTb: Boiling point elevation
i: Van't Hoff factor (number of particles into which the solute dissociates)
Kb: Boiling point elevation constant (a solvent-specific constant)
m: Molality of the solute (moles of solute divided by kilograms of solvent)
First, we need to calculate the moles of antifreeze added to water. You provided the mass of antifreeze, which is 2.00kg. To convert this to grams, multiply by 1000:
Mass of antifreeze = 2.00kg * 1000g/kg = 2000g
Next, we need to calculate the number of moles of antifreeze. To do this, we divide the mass of antifreeze by its molar mass, which can be found by looking up the atomic masses of the elements in the compound:
C2H6O2:
C (carbon) - atomic mass = 12.01 g/mol
H (hydrogen) - atomic mass = 1.01 g/mol
O (oxygen) - atomic mass = 16.00 g/mol
Molar mass of C2H6O2 = (2 * atomic mass of C) + (6 * atomic mass of H) + (2 * atomic mass of O)
= (2 * 12.01) + (6 * 1.01) + (2 * 16.00)
= 24.02 + 6.06 + 32.00
= 62.08 g/mol
Now we can calculate the number of moles:
moles of antifreeze = mass of antifreeze / molar mass of antifreeze
= 2000g / 62.08g/mol
Next, we need to calculate the molality of the antifreeze.
Molality (m) = moles of solute / mass of solvent in kg
You provided the mass of water as 9.00 x 10^3 grams. To convert this to kilograms, divide by 1000:
Mass of water = 9.00 x 10^3 g / 1000 = 9.00 kg
Now we can calculate the molality:
molality = moles of antifreeze / mass of water in kg
= moles of antifreeze / 9.00 kg
Finally, we need to calculate the boiling point elevation (ΔTb).
To find the boiling point elevation constant (Kb) for water, we can refer to a table or look it up. For water, Kb ≈ 0.512 °C/m.
ΔTb = i * Kb * m
The Van't Hoff factor (i) represents the number of particles a solute dissociates into in a solution. Since ethylene glycol (C2H6O2) does not dissociate into ions, its Van't Hoff factor is 1.
Now, we can substitute the values into the equation and solve for ΔTb:
ΔTb = 1 * 0.512 °C/m * molality
After finding ΔTb, we can add it to the boiling point of pure water, which is 100 °C at sea level, to determine the boiling point of the water in your radiator with the antifreeze added.
Boiling point of water in radiator = 100 °C + ΔTb
Once you have calculated the value of ΔTb, you can find the boiling point of the water in your radiator by adding it to 100 °C.