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.
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.
Can you solve this step-by-step so that I can understand how to do this. I am really confused and lost. Thanks.
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.
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.