I've got a similar question as a previous student.
What is a minimum volume (in gallons) of ethylene glycol (CH2OHCH2OH, an antifreeze) that has to be added to 3.00 gal of water if you desire this engine cooling solution (for a auto radiator) NOT to be frozen below - 25.9 oC - a very cold Siberian or Canadian winter temperature?
The density of water and the antifreezer is 0.9975 g/mL and 1.141 g/mL respectively.
Hint: You must first calculate a minimum value of the required molality of the antifreezer first, then find the reqiuired volume based on it.
What is molar mass of ethylene glycol? g/mol
The required molality of ethylene glycol: m
The required volume of ethylene glycol: gal.
I've got the mass and I've got the molality but I can't get from there to the gallons of ethylene glycol would be needed. I'm missing the steps there so any help would be great. Thanks!
Here is my response to the problem on Sunday.
http://www.jiskha.com/display.cgi?id=1348448021
To solve this problem, we need to follow these steps:
Step 1: Convert the given temperature from Celsius to Kelvin.
- Subtract 25.9 from 273 to convert it to Kelvin: - 25.9 + 273 = 247.1 K.
Step 2: Calculate the freezing point depression.
- The equation to calculate the freezing point depression is ΔTf = Kfm, where ΔTf is the freezing point depression, Kf is the cryoscopic constant, and m is the molality of the solute.
- Here, our solute is ethylene glycol (CH2OHCH2OH), and we need to find the required molality (m).
Step 3: Calculate the molar mass of ethylene glycol.
- Given that the molar mass of ethylene glycol is needed, we can find this using the periodic table.
- The atomic masses of carbon (C), hydrogen (H), and oxygen (O) are 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively.
- Multiply the atomic masses of each element by the number of atoms present: (2 × C) + (6 × H) + (2 × O).
Step 4: Calculate the molality (m).
- Divide the mass of the ethylene glycol by its molar mass to find the number of moles.
- Molality (m) is given by the equation: m = (moles of solute) / (mass of solvent in kg).
- The mass of the solvent (water) is given as 3.00 gallons, and we need to convert it to kg.
Step 5: Calculate the required volume of ethylene glycol.
- The volume can be calculated using the equation: Volume = (moles of solute) / (molarity of solute).
- Since we have the moles of solute, divide it by the molarity.
Let's calculate each step:
Step 1: The temperature in Kelvin is 247.1 K.
Step 2: The freezing point depression can be calculated using the equation ΔTf = Kfm. However, the value of Kf (cryoscopic constant) is missing from the question. Once you have the value of Kf, you can substitute it into the equation along with the calculated value of m to find ΔTf.
Step 3: The molar mass of ethylene glycol can be calculated by adding the atomic masses of each element present in the compound: (2 × C) + (6 × H) + (2 × O).
Step 4: To calculate the molality (m), divide the moles of solute by the mass of the solvent in kg. Use the given densities of water and ethylene glycol to convert the given volumes to masses and then multiply by the molar mass to convert to moles.
Step 5: Once you have the value of m, you can calculate the required volume of ethylene glycol using the equation Volume = (moles of solute) / (molarity of solute). In this case, we need to convert the volume from liters to gallons.
Following these steps should help you determine the required volume of ethylene glycol (in gallons) that needs to be added to 3.00 gal of water to prevent freezing below - 25.9 oC.