Calculate the freezing point depression and osmotic pressure at 25 degrees C of an aqueous solution of 1.0 g/L of a protein (mol wt= 90,000) if the density of the solution is 1.0 g/mL.
I know how to calculate freezing point depression and osmotic pressure, but I'm having trouble calculating the molarity and molality to use in the equations. Any help would be appreciated. Also, with the way the information is given, does the 90,000 count for sig figs or is it a "known value"?
With the way 90,000 is listed (no period at the end), we REALLY don't know. Technically it has only one s.f.. It is a measured value.
molality = mols/kg solvent
mols=g/molar mass. I assume the concentration of the protein is 1.0g/L if I read the problem correctly.
Thus, the #mols = 1.0/90,000 = ??
So molarity = # mols/L = ??M
For such small concentrations AND with the density of the solution being 1.0 g/L, won't the molality and molarity be the same? Check my thinking.
To calculate the molality and molarity of the protein solution, we first need to determine the number of moles of protein in 1.0 g of the solution.
The molar mass of the protein is given as 90,000 g/mol. Since the concentration of the protein is 1.0 g/L, we can calculate the number of moles (mol) of protein in 1.0 g of the solution using the formula:
Number of moles = Mass of protein / Molar mass
Number of moles = 1.0 g / 90,000 g/mol
Calculating this, we find that the number of moles of protein in 1.0 g of the solution is approximately equal to 1.1 x 10^-5 mol.
Now, let's calculate the molality of the protein solution. Molality is defined as the number of moles of solute per kilogram of solvent (in this case, water). Since the density of the solution is given as 1.0 g/mL, we can assume that the density of water is also 1.0 g/mL. Therefore, 1.0 g of the solution is equal to 1.0 mL of the solution, which is equivalent to 1.0 x 10^-3 kg of water.
The molality (m) of the protein solution is given by the formula:
molality = Number of moles / Mass of solvent in kg
molality = (1.1 x 10^-5 mol) / (1.0 x 10^-3 kg)
Calculating this, we find that the molality of the protein solution is approximately equal to 1.1 x 10^-2 mol/kg.
Now, let's determine the molarity of the protein solution. Molarity is defined as the number of moles of solute per liter of solution. Since the concentration of the protein is given as 1.0 g/L, which is numerically equivalent to 1.0 x 10^-3 kg/L, we can calculate the molarity (M) using the formula:
molarity = Number of moles / Volume of solution in L
molarity = (1.1 x 10^-5 mol) / (1.0 x 10^-3 L)
Calculating this, we find that the molarity of the protein solution is approximately equal to 1.1 x 10^-2 mol/L.
Now, since the density of the solution is 1.0 g/mL and the concentration is 1.0 g/L, the molality and molarity values are indeed the same in this case.
I hope this explanation helps you calculate the molality and molarity of the protein solution.