Vitamin K is involved in normal blood clotting. When 1.36 g of vitamin K is dissolved in 25.0 g of camphor, the freezing point of the solution is lowered by 4.56 °C. The freezing point and Kf constant for camphor can be found here. Calculate the molar mass of vitamin K.
delta T = Kf*m.
Substitute and solve for molality.
Then m = mols/kg solvent.
Sustitute and solve for mols.
Then mol = grams/molar mass. You know mol and grams, solve for molar mass.
Thanks Dr. Bob,
Can you solve this step-by-step so that I can understand how to do this. I am really confused and lost. Thanks.
To calculate the molar mass of vitamin K, we need to use the formula:
ΔT = Kf * m * i
Where:
ΔT = change in freezing point
Kf = freezing point depression constant (in this case, for camphor)
m = molality of the solution
i = van't Hoff factor
First, we need to find the molality of the solution:
Molality (m) can be calculated using the formula:
m = (moles of solute) / (mass of solvent in kg)
The mass of camphor can be calculated by subtracting the mass of vitamin K from the total mass of the solution:
Mass of camphor = mass of solution - mass of vitamin K
Mass of camphor = mass of solution - 1.36 g
Mass of camphor = 25.0 g - 1.36 g
Mass of camphor = 23.64 g
Next, we need to convert the mass of camphor to kg:
Mass of camphor (kg) = 23.64 g / 1000
Mass of camphor (kg) = 0.02364 kg
Now we can calculate the molality:
m = (moles of solute) / (mass of solvent in kg)
m = (moles of vitamin K) / (0.02364 kg)
Now we can rearrange the formula to find moles of vitamin K:
moles of vitamin K = m * (mass of solvent in kg)
moles of vitamin K = m * 0.02364 kg
Next, we need to convert the freezing point depression to Kelvins:
ΔT(K) = ΔT(°C) + 273.15
ΔT(K) = -4.56 °C + 273.15
ΔT(K) = 268.59 K
Now we can rearrange the formula and solve for the moles of vitamin K:
moles of vitamin K = ΔT(K) / (Kf * m)
moles of vitamin K = 268.59 K / (Kf * m)
Finally, we can calculate the molar mass of vitamin K using the formula:
molar mass (g/mol) = mass (g) / moles
molar mass (g/mol) = 1.36 g / moles of vitamin K
Now, substituting the values and solving for the molar mass:
molar mass (g/mol) = 1.36 g / (268.59 K / (Kf * m))
molar mass (g/mol) = 1.36 g / (268.59 K / (Kf * m))
Please provide the freezing point depression constant (Kf) for camphor to proceed with the calculation.
To calculate the molar mass of vitamin K, we need to use the freezing point depression equation and the given data.
The freezing point depression is given by the equation:
ΔTf = Kf * m
Where:
ΔTf = the change in freezing point (in this case, -4.56 °C)
Kf = the cryoscopic constant for camphor (-38.0 °C/m)
m = molality of the solution
First, let's calculate the molality (m) of the solution using the given data:
Mass of camphor = 25.0 g
Molar mass of camphor (C10H16O) = 152.23 g/mol
Using the formula for molality:
m = moles of solute / mass of solvent (in kg)
The moles of camphor can be calculated as:
moles = mass / molar mass
moles = 25.0 g / 152.23 g/mol
Now, convert the mass of camphor to kg:
mass of camphor in kg = 25.0 g / 1000
Once we have the moles of camphor and the mass of camphor in kg, we can calculate the molality:
m = moles of camphor / mass of camphor in kg
Next, let's calculate the moles of vitamin K using the freezing point depression equation:
ΔTf = Kf * m
Rearranging the equation to solve for m:
m = ΔTf / Kf
Now substituting the given values:
m = -4.56 °C / -38.0 °C/m
Finally, using Avogadro's number (6.022 × 10^23), we can calculate the moles of vitamin K:
moles of vitamin K = m * (moles of camphor / mass of camphor in kg)
Having found the moles of vitamin K, we can calculate the molar mass:
molar mass of vitamin K = mass of vitamin K / moles of vitamin K.