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. Calculate the molar mass of vitamin K. Kf value is 37.8 and the normal freezing point is 176 degrees C
I worked one like this last evening for you. Just follow the steps I provided then. I shall be happy to help you through this if you show your work and explain in detail what it is you don't understand.
To calculate the molar mass of vitamin K, we can use the formula:
ΔTf = Kf * m * i
Where:
ΔTf = Change in freezing point (in degrees Celsius)
Kf = Freezing point depression constant for the solvent (in °C kg/mol)
m = Molality of the solution (in mol solute/kg solvent)
i = Van't Hoff factor (number of particles into which the solute dissociates)
First, let's calculate the molality of the solution.
Molality (m) is defined as the number of moles of solute per kilogram of solvent. We need to find the moles of vitamin K and the mass of the solvent (camphor).
Moles of vitamin K:
Using the molar mass (M) formula:
Moles (n) = Mass (m) / Molar Mass (M)
Given that the mass of vitamin K (m) is 2.40 g, we need to convert this to moles by dividing the mass by the molar mass.
We need to find the molar mass of vitamin K:
Molar Mass (M) = Mass (m) / Moles (n)
Now we can calculate the molality (m):
m = Moles (n) / Mass of Solvent (in kg)
Given that the mass of camphor (solvent) is 25.0 g, we need to convert this to kg by dividing it by 1000.
Next, we can calculate the change in freezing point (ΔTf) using the given information.
ΔTf = Normal Freezing Point - Freezing Point of Solution
Given:
Normal Freezing Point = 176 °C
Freezing Point of Solution = Normal Freezing Point - Change in Freezing Point = 176 °C - 8.05 °C
Finally, we can rearrange the formula to find the molar mass (M):
Molar Mass (M) = Mass (m) / Moles (n)
Now, let's plug in the values and solve the equation step by step:
Given values:
Mass of vitamin K (m) = 2.40 g
Mass of solvent (camphor) = 25.0 g
Change in freezing point (ΔTf) = 8.05 °C
Kf value = 37.8 °C kg/mol
Normal Freezing Point = 176 °C
Step 1: Calculate the moles of vitamin K
Moles (n) = Mass (m) / Molar Mass (M)
Step 2: Calculate the molality of the solution
m = Moles (n) / Mass of Solvent (in kg)
Step 3: Calculate the change in freezing point (ΔTf)
ΔTf = Normal Freezing Point - Freezing Point of Solution
Step 4: Calculate the molar mass (M)
Molar Mass (M) = Mass (m) / Moles (n)
By following these steps and plugging in the given values, you can find the molar mass of vitamin K.