Something that will lower the freezing point of water to -3.7 degrees Celsius if one mole were placed in 1000 grams of water? To solve this I know I have to use the equation Tf= IKfm, Tf= 3.7, but how I go about the problem there if I don't know Kf or the the mole of solute (for molality)? Please show work, thank you!!
I think you must assume some things.
1. Since you know the solvent is water you can look up the Kf value of 1.86/mol.
2. You have your choice of solute so you can pick one that has an i = 1 or an i of some other value.
3. So 3.7 = iKm
if you chose i = 2 you could pick a solute of NaCl.
K is 1.86; therefore,
3.7 = 2*1.86m
m = about 0.99 but you need to confirm that and obtain a more accurate number if you wish.
m = mols/kg solvent or
mol = m*kg solvent = 0.99* 1 kg = 0.99 mols
mol = grams/molar mass or
grams = mols x molar mass
grams NaCl = mols NaCl (0.99) x molar mass = ?
That will get you grams NaCl to provide 3.7 delta T in 1 kg H2O.
Instead of NaCl, can I pick any other salt, as long as it has a Van't Hoff factor/ i value of 2?
Of course. van't Hoff factors are at best just good guesses; you might be closer to reality by picking something with i = 1; i.e., a complete non-electrolyte like ethyl alcohol or something like that.
How did you get .99 for the molality value?
To find the solution, we need to use the equation Tf = iKfm, where Tf is the freezing point depression, i is the van't Hoff factor, Kf is the molal freezing point depression constant, and m is the molality of the solute.
In this case, you want to lower the freezing point of water to -3.7 degrees Celsius. Let's assume that the van't Hoff factor (i) is 1, which is typical for non-electrolytes. Therefore, we can rewrite the equation as:
-3.7 = (1)(Kf)(m)
Now, we need to find the molal freezing point depression constant (Kf). Kf is a constant that depends on the solvent. For water, the value of Kf is approximately 1.86 °C·kg/mol.
Next, we need to find the molality (m) of the solute. Molality is defined as the number of moles of solute divided by the mass of the solvent in kilograms.
Since you don't know the number of moles of solute, we'll need to find that first. You mentioned that you have one mole of solute, so we can calculate the mass of the solute using the molar mass.
Finally, we can substitute the values into the equation to find the molality:
-3.7 = (1)(1.86)(m)
Solving for m, we get:
m = -3.7 / (1.86)
m ≈ -1.99 mol/kg
It's important to note that a negative molality value doesn't make physical sense. Molality is a positive value, so make sure to double-check the given information and calculations.
To recap, in order to find the molality of the solute, you need to know the values of the van't Hoff factor (i), the molal freezing point constant (Kf), and the number of moles of solute. If any of these values are missing, you won't be able to calculate the molality accurately.