Question: if you added ethylene glycol to your car's radiator to lower the freezing point to -31.0 degree C, what would the corresponding boiling point of the coolant in your radiator. The freezing point and boiling point constants for water are 1.86 and .510 degree C/m
The correct answer for this problem is 108.5 degree C, but i don't get how they got that. Did they use the Delta Tf=Kf. How did they plug in the numbers to get that answer. Any help on doing the problem would be great?
It's done this way.
delta T = Kf*m
delta T you know is 31. You know Kf. Calculate m (molality or the concentration of the ethylene glycol).
Now go to the boiling point.
delta T = Kb*m
You want to calculate delta T, you know Kb and m is what you just calculated from the first part of the problem. The answer is, indeed, 108.5 although tha's too many significant figures to use. You have 3 s.f. in your numbers; therefore, the answer should be rounded to 108 (but follows your teacher's instructions).
To find the corresponding boiling point of the coolant in your car's radiator, we can use the colligative property known as boiling point elevation.
The formula for boiling point elevation is ΔTb = Kb * m, where ΔTb is the change in boiling point, Kb is the boiling point constant, and m is the molality of the solute.
In your case, ethylene glycol is the solute, and water is the solvent. Ethylene glycol is a non-volatile substance that dissolves in water to lower its freezing point and raise its boiling point.
First, we need to calculate the molality of the ethylene glycol solution. Molality is defined as the amount of solute (in moles) divided by the mass of the solvent (in kg).
Let's assume we add ethylene glycol in such a way that the concentration is 50% by mass. This means that you have 50 grams of ethylene glycol for every 50 grams of water, giving you a total mass of 100 grams.
Calculate the moles of ethylene glycol using its molar mass. The molar mass of ethylene glycol is approximately 62.07 g/mol.
Number of moles of ethylene glycol = Mass of ethylene glycol / Molar mass of ethylene glycol
Number of moles of ethylene glycol = 50 g / 62.07 g/mol ≈ 0.8056 mol
Now, calculate the molality of the solution using the moles of ethylene glycol and the mass of water (since water is the solvent).
Molality = Number of moles of solute / Mass of solvent (in kg)
Molality = 0.8056 mol / 0.1 kg = 8.056 mol/kg
Next, we can use the boiling point elevation formula ΔTb = Kb * m to calculate the change in boiling point. The boiling point constant Kb is given as 0.510 °C/m for water.
ΔTb = 0.510 °C/m * 8.056 mol/kg ≈ 4.11456 °C
Finally, to find the corresponding boiling point, we add the change in boiling point to the normal boiling point of water, which is 100 °C.
Corresponding boiling point = Normal boiling point of water + ΔTb
Corresponding boiling point = 100 °C + 4.11456 °C ≈ 104.11 °C
So, if you added ethylene glycol to your car's radiator to lower the freezing point to -31.0 °C, the corresponding boiling point of the coolant in your radiator would be approximately 104.11 °C.
Note: The answer you provided, 108.5 °C, might have been rounded to the nearest degree.