Some ethylene glycol, HOCH2CH2OH, is added to your car's cooling system along with 4.4 kg of water. If the freezing point of the water-glycol solution is -15.0°C, how many grams of HOCH2CH2OH must have been added?
I used the equation: 15 celcius = 1 x 1.86 celcius/moles per kg x molality and got 8.064 but I don't know the units and I don't know where to use 4.4kg of water.
To solve this problem, you can use the concept of molality and the freezing point depression equation. The freezing point depression is given by the equation:
ΔTf = Kf × m
where
ΔTf is the change in freezing point,
Kf is the cryoscopic constant for the solvent (water in this case), and
m is the molality of the solute (ethylene glycol in this case).
Firstly, let's solve for the molality (m) of the ethylene glycol in the solution. Molality is defined as the number of moles of solute per kilogram of solvent. Given that 4.4 kg of water is present, we can calculate the molality using the following equation:
molality (m) = moles of solute / kg of solvent
Now, we need to calculate the molality of ethylene glycol. To do that, you need to know the moles of ethylene glycol and the molecular weight of ethylene glycol.
The molecular weight of ethylene glycol (HOCH2CH2OH) can be calculated as follows:
molecular weight = (number of carbon atoms x atomic weight of carbon) + (number of hydrogen atoms x atomic weight of hydrogen) + (number of oxygen atoms x atomic weight of oxygen)
For ethylene glycol (HOCH2CH2OH):
C: 2 (atomic weight = 12.01 g/mol)
H: 6 (atomic weight = 1.01 g/mol)
O: 2 (atomic weight = 16.00 g/mol)
Now, calculate the moles of ethylene glycol by dividing the given mass by the molecular weight:
moles = mass / molecular weight
Once you determine the moles of ethylene glycol, you can calculate the molality using the equation stated earlier.
Now, substituting the known values into the freezing point depression equation:
ΔTf = Kf × m
Given that the freezing point depression (ΔTf) is -15.0°C, and assuming the cryoscopic constant (Kf) for water is 1.86 °C/m, you can solve for the molality (m) calculated earlier. Then, rearrange the equation to solve for the moles of ethylene glycol added.
moles of ethylene glycol = molar mass of ethylene glycol × molality × (kg of water)
Finally, multiply the moles of ethylene glycol by the molecular weight to obtain the mass of ethylene glycol that must have been added to the solution.
mass of ethylene glycol added (in grams) = moles of ethylene glycol × molecular weight