A solution that contains 55.0 g of ascorbic acid (Vitamin C) in 250. g of water freezes at −2.34°C. Calculate the molar mass (in units of g/mol) of the ascorbic acid. Kf of water is 1.86°C/m.
From the amount of freezing point lowering and the Kf value, you can calculate the molality of the solution.
It's called Ebbing's formula. See
http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/meltpt.html
It tells us the solution is 1.25 molal. Therefore 250 ml and should have 0.313 moles of ascorbic acid.
If 0.313 moles is 55 g, the molar mass is 55/0.313 = 176.
The correct value is 176.12
http://en.wikipedia.org/wiki/Ascorbic_acid
Well, isn't that a cool question! Let's break it down step by step.
First, we need to calculate the change in freezing point of the solution. The formula for that is:
ΔT = Kf * molality
Since we know the freezing point depression (ΔT) is -2.34°C and Kf of water is 1.86°C/m, we can rearrange the formula to solve for molality.
molality = ΔT / Kf
Plugging in the values, we have:
molality = (-2.34°C) / (1.86°C/m)
molality = -1.258 m
Next, we need to calculate the number of moles of ascorbic acid in 55.0 g.
moles = mass / molar mass
Since we want to find the molar mass of ascorbic acid, we can rearrange the formula:
molar mass = mass / moles
Plugging in the values, we have:
molar mass = 55.0 g / (moles of ascorbic acid)
Now, to find the moles of ascorbic acid, we need to multiply the molality by the mass of the solvent (water) in kilograms.
moles = molality * mass of solvent (in kg)
Since the mass of water is given as 250 g, we convert it to kg:
mass of water = 250 g = 0.250 kg
Finally, we can calculate the moles of ascorbic acid:
moles = -1.258 m * 0.250 kg
moles = -0.3145 mol
Now, let's plug that back into our molar mass formula:
molar mass = 55.0 g / (-0.3145 mol)
molar mass = -175.0 g/mol
Hmm, that seems a bit strange. A negative molar mass? That doesn't make sense. So it looks like there might be an error in the calculations or the given values. Better double-check your numbers and try again! Keep smiling and keep crunching those numbers!
To find the molar mass of ascorbic acid (Vitamin C), we can use the freezing point depression formula. The formula is given by:
ΔT = Kf * m
where:
ΔT = change in freezing point (in °C)
Kf = freezing point depression constant (in °C/m)
m = molality of the solution (in mol/kg)
First, let's calculate the change in freezing point (ΔT):
ΔT = freezing point of pure solvent - freezing point of solution
ΔT = 0°C - (-2.34°C)
ΔT = 2.34°C
Next, we need to find the molality of the solution:
molality (m) = moles of solute / mass of solvent (in kg)
Since we are given the mass of ascorbic acid and the mass of water, we can calculate the mass of solvent:
mass of solvent = mass of water / 1000
mass of solvent = 250. g / 1000
mass of solvent = 0.250 kg
Next, we need to find the moles of ascorbic acid:
moles of ascorbic acid = mass of ascorbic acid / molar mass
Let's assume the molar mass of ascorbic acid is M g/mol. By substituting the given values into the formula, we get:
2.34 = 1.86 * (mass of ascorbic acid / (0.250))
Simplifying the equation gives:
mass of ascorbic acid = (2.34 * 0.250) / 1.86
Now, we can calculate the moles of ascorbic acid:
moles of ascorbic acid = mass of ascorbic acid / M
Substituting the known values, we have:
55.0 g / M = (2.34 * 0.250) / 1.86
To solve for M, we can cross-multiply and rearrange the equation:
55.0 * 1.86 = 2.34 * 0.250 * M
M = (55.0 * 1.86) / (2.34 * 0.250)
Simplifying further gives:
M ≈ 176.78 g/mol
Therefore, the molar mass of ascorbic acid (Vitamin C) is approximately 176.78 g/mol.
To calculate the molar mass of ascorbic acid, we need to use the equation:
ΔT = Kf * m
where:
- ΔT is the freezing point depression, which is the difference between the freezing point of the pure solvent (water) and the freezing point of the solution.
- Kf is the cryoscopic constant for water, which is given as 1.86°C/m.
- m is the molality of the solution, which is the number of moles of solute per kilogram of solvent.
First, let's calculate the molality of the solution:
m = (mass of solute in kg) / (mass of solvent in kg)
Mass of solute (ascorbic acid) = 55.0 g
Mass of solvent (water) = 250. g = 0.250 kg
m = (55.0 g) / (0.250 kg) = 220 g/kg
Now, let's calculate the freezing point depression:
ΔT = Kf * m
ΔT = (1.86°C/m) * (220 g/kg) = 409.2°C.g/kg
The freezing point depression is given as -2.34°C, so:
-2.34°C = 409.2°C.g/kg
Now, we can solve for the molar mass of ascorbic acid using the equation:
molar mass = (mass of solute) / (moles of solute)
To find the moles of solute, we can use the equation:
moles of solute = (mass of solute) / (molar mass)
Let's assume the molar mass of ascorbic acid is M:
moles of solute = (55.0 g) / (M g/mol)
Setting this equal to the molality:
409.2°C.g/kg = (55.0 g) / (M g/mol)
Now, let's solve for M:
M = (55.0 g) / (409.2°C.g/kg)
M = 0.1343 g/mol
Therefore, the molar mass of ascorbic acid is approximately 0.1343 g/mol.