35.0 g of an organic compound dissolved in 500. g of water have a freezing point of -3.72 degrees C. What is the molecular weight of the solute?
35*9.8
To find the molecular weight of the solute, you need to use the concept of freezing point depression.
Freezing point depression is a colligative property, which means it depends on the number of particles rather than the nature of those particles. The formula to calculate the freezing point depression is:
ΔT = Kf * m
where ΔT is the freezing point depression, Kf is the cryoscopic constant (a property specific to the solvent), and m is the molality of the solution (moles of solute per kilogram of solvent).
In this case, the freezing point depression (ΔT) is given as -3.72 degrees Celsius. The mass of the solute is 35.0 g, and the mass of the solvent (water) is 500.0 g.
First, calculate the molality (m):
m = n solute / m solvent
where n solute is the number of moles of the solute and m solvent is the mass of the solvent in kilograms.
m solvent = 500.0 g / 1000 = 0.500 kg
Next, calculate the number of moles of the solute (n solute) using the equation:
n solute = m solute / M solute
where m solute is the mass of the solute and M solute is the molecular weight of the solute.
m solute = 35.0 g
Now, rearrange the equation to solve for M solute:
M solute = m solute / n solute
Plugging in the given values:
M solute = 35.0 g / (m solute / M solute)
Simplify the equation:
M solute = (35.0 g * M solute) / m solute
Multiply both sides by m solute:
M solute * m solute = 35.0 g * M solute
Divide both sides by M solute:
m solute = 35.0 g
Finally, solve for M solute:
M solute = (35.0 g) / m solute
Substituting the given values:
M solute = (35.0 g) / 0.5 kg
M solute = 70 g/mol
Therefore, the molecular weight of the solute is 70 g/mol.