Ok so reviewing my notes I also got 11,326.6 as the volume in ml. The density of water he wanted us to use was (0.9975) and I went from 1 gal of H2O = 3.785 liters = 3785 grams then multiplied by 3 giving me 11,355g H2O. The only other step I could come up with was using the molality of solute 15.48 mols/kg x 11.355 kg of solvent and working my way back from grams to gallons of ethylene glycol which gave me 0.260 gal. The computer did not like that answer. I'm a little confused on the g/lbs you mentioned in your previous answer.
I might point out that 3785 mL is not 3785 g but 3785*0.9975 = 3775 g.
Here is the problem as I worked it. I have rounded here and there but I think all of it is ok in general.
delta T = Kf*m
25.9 = 1.86m
m = 25.9/1.86 = 13.9
3 gallons H2O = 11.356 L
mass = v*d = 11,356 mL x 0.9975 = 11,329 grams = 11.329 kg.
m = mols/kg solvent
mols solute = m*kg solvent = 13.9*11.329 = 157.5 mols solute.
mols solute = grams solute/molar mass solute
g = mols x molar mass = 157.5 x 62.068 = 9787.5 g ethylene glycol.
m = v*d and v = m/d = 9787.5/1.141 = 8578 mL solute.
Convert that to gallons = 2.266 which I would round to 2.27 gallons. I hope this helps you find your trouble.
I apologize for the confusion. Let's go through the calculations step by step.
First, you correctly converted 1 gallon of water into metric units. 1 gallon is equal to 3.785 liters. Since the density of water is 0.9975 g/ml, you multiplied 3.785 liters by 0.9975 g/ml to get 3,775 grams of water.
Next, you multiplied the mass of water by 3 to account for the three-fold dilution. So, 3,775 grams of water multiplied by 3 equals 11,325 grams of water.
However, instead of converting grams to kilograms, you converted grams to gallons of ethylene glycol. This is where the error occurred. To find the volume of ethylene glycol needed, you need to use the molality of the solute (15.48 mol/kg) and the mass of the solvent (11,325 grams or 11.325 kg).
To find the moles of ethylene glycol, multiply the molality (15.48 mol/kg) by the mass of the solvent (11.325 kg). This gives you approximately 175.104 moles of ethylene glycol.
To convert moles to grams, multiply the moles of ethylene glycol by its molar mass. The molar mass of ethylene glycol is approximately 62.07 g/mol. By multiplying 175.104 moles by 62.07 g/mol, you get approximately 10,864.545 grams of ethylene glycol.
Now, to convert grams to gallons, divide the mass of ethylene glycol (10,864.545 grams) by the density of ethylene glycol, which is typically around 1.113 g/ml. This calculation would be: 10,864.545 grams / 1.113 g/ml = 9,768.619 ml.
Since 1 gallon is equal to 3.785 liters or 3,785 ml, divide the volume in ml (9,768.619 ml) by 3,785 ml/gallon to get the volume in gallons. This calculation gives you approximately 2.58 gallons of ethylene glycol.
So, the correct answer is approximately 2.58 gallons of ethylene glycol, not 0.260 gallons as previously calculated. I apologize for any confusion caused by the incorrect calculation before.