Vitamin K is involved in normal blood clotting. When 2.40 g of vitamin K is dissolved in 25.0 g of camphor, the freezing point of the solution is lowered by 8.05 °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 m
m = mols/kg solvent
Substitute and solve for mols
mols = grams/molar mass. You have mols and grams, solve for molar mass.
Why did the vitamin K go into business with the camphor? They wanted to help each other "freeze" in the cutthroat world of blood clotting!
But let's get to business. To find the molar mass of vitamin K, we can use the equation:
ΔT = Kf * m
Where ΔT is the change in freezing point temperature, Kf is the freezing point depression constant, and m is the molality of the solution.
We can rearrange the equation to solve for molar mass:
m = (ΔT / Kf) / (moles of solute / kilograms of solvent)
First, we need to find the moles of solute (vitamin K). We can use the grams and molar mass relationship:
moles of solute = grams of solute / molar mass of solute
Substituting the given values:
m = (8.05 °C / Kf) / (2.40 g / molar mass of vitamin K / 1000 g)
Now, we can calculate the molar mass of vitamin K:
molar mass of vitamin K = (8.05 °C / Kf) / (2.40 g / m)
Remember to substitute the value of Kf for camphor from the given data. Now you can solve the equation and find the molar mass of vitamin K!
To calculate the molar mass of vitamin K, we can use the formula:
ΔT = Kf × m × i
where:
ΔT = freezing point depression
Kf = cryoscopic constant (provided in the question)
m = molality of the solution
i = van't Hoff factor (number of particles formed when the substance dissolves)
First, we need to calculate the molality of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)
Given that 2.40 g of vitamin K is dissolved in 25.0 g of camphor, we need to convert the mass of camphor to kg:
mass of camphor (in kg) = 25.0 g / 1000 = 0.025 kg
Next, we need to calculate the moles of vitamin K:
moles of vitamin K = mass of vitamin K / molar mass of vitamin K
Since we are trying to find the molar mass, we'll rearrange the equation as:
molar mass of vitamin K = mass of vitamin K / moles of vitamin K
Now, for the freezing point depression, we plug in the given values:
ΔT = -8.05 °C
Kf = constant for camphor (provided in the question)
Now, we can rearrange the formula and solve for the molar mass of vitamin K:
molar mass of vitamin K = mass of vitamin K / (ΔT / (Kf × m × i))
Since we're assuming vitamin K is a non-electrolyte, the van't Hoff factor (i) is 1.
molar mass of vitamin K = mass of vitamin K / (ΔT / (Kf × m))
Now we can substitute the given values into the equation and solve for the molar mass of vitamin K.
To calculate the molar mass of vitamin K, we can use the colligative property of freezing point depression. The equation for freezing point depression is given as:
ΔT = Kf * m
where:
ΔT is the change in freezing point temperature,
Kf is the freezing-point depression constant, and
m is the molality of the solution, which is the ratio of moles of solute to the mass of solvent in kilograms.
In this case, we are given the change in freezing point (ΔT) for the solution of 2.40 g of vitamin K dissolved in 25.0 g of camphor, which is 8.05 °C. The Kf (freezing-point depression constant) for camphor can be found in a reference source.
First, let's calculate the molality (m) of the solution using the mass of vitamin K and the mass of camphor:
m = moles of solute / mass of solvent (in kg)
To find the moles of solute (vitamin K), we need to use its molar mass (M):
moles of solute = mass of solute / molar mass
Now, we can substitute this back into the equation ΔT = Kf * m and solve for the molar mass (M):
M = mass of solute / moles of solute
Let's calculate the molar mass of vitamin K step by step:
Step 1: Convert the given masses into grams:
mass of vitamin K = 2.40 g
mass of camphor = 25.0 g
Step 2: Calculate the molality (m):
m = moles of solute / mass of solvent (in kg)
= moles of vitamin K / mass of camphor (in kg)
Given that the mass of camphor is 25.0 g, we need to convert it into kilograms:
mass of camphor (in kg) = 25.0 g / 1000 (convert g to kg)
Step 3: Find the moles of solute (vitamin K):
moles of vitamin K = mass of vitamin K / molar mass
Step 4: Substitute the values into the freezing point depression equation:
ΔT = Kf * m
Solve for moles of solute (vitamin K):
moles of vitamin K = ΔT / (Kf * m)
Step 5: Calculate the molar mass of vitamin K:
M = mass of vitamin K / moles of vitamin K
Now, let's plug in the given values and solve the equation. However, without the values of the freezing point depression constant (Kf) and the molar mass of camphor, we cannot arrive at the exact solution. Please provide the values of Kf and the molar mass of camphor from the reference source you mentioned.