What volume ( L ) of the solute methanol should be mixed with 3.41 L of the solvent ethanol to make a solution that is 11.0 m methanol?
Am I supposed to use the molality eq'n?
yes.
m = mols solute/kg solvent
You will need the densities to convert grams to volume and volume to grams.
I converted ethanol using it's density, so I got mass=(.7893 kg/L)(3.41 L)=2.691513 g ethanol
then plugged it into m=#mols solute/kg mass solvent to solve for # mols of solute which I got to be #mols=(11 m)(2.691513 g ethanol)=29.6066
Now do I take this and multiply it with the molar mass of methanol, and then use the density relation to solve for volume?
I wouldn't go that way. What you have done so far is very good. I would then determine how much methanol was needed.
molality = moles CH3OH/0.269 kg solvent
moles CH3OH = 11 x 0.269 = ??
Then moles CH3OH x molar mass CH3OH = grams and convert that with density to volume CH3OH.
Hmm okay, I followed that and is the answer that you got 119.795 L?
Hang on a second. I've messed up in a couple of places. Let me get it straight an I will post back here.
I have been using the wrong molar masses (I thought I knew them by memory but I didn't). Also, I used the wrong volume of ethanol. So here goes the correct way.
3.41 L ethanol x 1000 = 3410 mL ethanol.
m = v x d
m = 3410 x 0.789 = 2960 grams or 2.96 kg ethanol.
How much solute do we need?
m = moles solute/kg solvent.
11 = moles solute/2.69
11 x 2.69 = 29.59 mols solute = 29.59 moles methanol.
20.59 moles methanol x molar mass (32) = 946.9 grams methanol.
m = v x d
946.9 = v x 0.792 g/mL
v = 1196 mL or 1.196 L.
You may get slightly different values if you use slightly different molar masses and/or slightly different densities.
Now let's check it to make sure we are right.
1.196 L methanol/3.41 L ethanol.
1.196 L methanol = 1196 mL
1196 mL x 0.792 g/mL = 947 grams methanol.
947/32 = 29.6 moles methanol.
3.41 L ethanol solvent = 3410 grams.
m = v*d
m = 3410 x 0.789 g/mL = 2690 g ethanol or 2.69 kg ethanol.
Then 29.6 mols solute/2.69 kg = 11.00 m.
I'm glad you wrote that Hmmm--it made me go back and check the problem and my numbers. I hope I haven't confused you.
To determine the volume of methanol required to make a solution of 11.0 m methanol, you need to use the molality equation.
Molality (m) is defined as the ratio of moles of solute to the mass of the solvent in kilograms:
molality (m) = moles of solute / mass of solvent (kg)
In this case, we know that the solvent is ethanol and we are trying to find the volume of the solute, methanol. Since the molarity of the solution is given, we can use the equation:
molarity (M) = moles of solute / volume of solution (L)
First, you need to find the moles of methanol:
moles of methanol = molarity (M) * volume of solution (L)
Since the molarity is given as 11.0 m and the volume of the solution is unknown, we can rewrite the equation as:
moles of methanol = 11.0 m * volume of solution (L)
Now, substitute the volume of the solution by adding the volume of the solvent, ethanol, with the volume of the solute, methanol:
moles of methanol = 11.0 m * (volume of ethanol (L) + volume of methanol (L))
We know that the volume of the ethanol is given as 3.41 L, so we can rearrange the equation to solve for the volume of methanol:
volume of methanol (L) = (moles of methanol / 11.0 m) - volume of ethanol (L)
To calculate the moles of methanol, we need to convert the molality (m) to moles using the formula:
moles of solute = molality (m) * mass of solvent (kg)
Since the mass of the solvent is not provided, we need additional information to determine the moles of methanol.