A solid nonelectrolyte with a mass of 11.32g is dissolved in 115.00g of water. The observed freezing point of the solution is-3.44 degrees C. Given Kf of water=1.86 degrees C/m, what is the molar mass of the unknown solid?
you have 3.44/1.86 moles.
molemass=11.32*3.44/1.86
To find the molar mass of the unknown solid, we need to use the formula for calculating the freezing point depression (ΔTf) of a solution:
ΔTf = Kf * m
Where:
ΔTf = freezing point depression
Kf = freezing point depression constant (provided as 1.86 degrees C/m for water)
m = molality of the solution
To find the molality (m), we need to calculate the number of moles of the solute and the mass of the solvent.
Step 1: Calculate the number of moles of the solute (unknown solid)
n = m/M
Where:
n = moles of solute
m = mass of solute
M = molar mass of solute (to be determined)
In the given data:
m = 11.32 g
Step 2: Calculate the mass of the solvent (water)
mass of solvent = mass of solution - mass of solute
mass of solvent = 115.00 g - 11.32 g
mass of solvent = 103.68 g
Step 3: Calculate the molality (m)
m = n/mass of solvent
Step 4: Calculate the freezing point depression (ΔTf)
ΔTf = Kf * m
Now we can substitute the values into the formula to find the molar mass (M):
ΔTf = (1.86 degrees C/m) * [n/(mass of solvent)]
Given that the observed freezing point depression is -3.44 degrees C:
-3.44 = (1.86 degrees C/m) * [n/(103.68 g)]
Now we can solve for n:
n = (-3.44 degrees C) * (103.68 g) / (1.86 degrees C/m)
n ≈ -191.85 g·mol
Since the molar mass cannot be negative, the negative sign is irrelevant. Therefore, the molar mass of the unknown solid is approximately 191.85 g/mol.