A 7.85 g sample of a compound with the empirical formula C5H4 is dissolved in 301 g of benzene. The freezing point of the solution is 1.05C below that of pure benzene. what are the molar mass and molecular formula of this compound?
delta T = Kf*m
You know delta T and Kf, solve for molality.
Then molality = mols/kg solvent. You know m and kg solvent, solve for mols.
Then mols = grams/molar mass. You know mols and grams, solve for molar mass.
The empirical formula is C5H4. Calculate the empirical formula mass.
empirical formula mass x n = molar mass.
The molecular formula then is
(emprical formula)n
To find the molar mass and molecular formula of the compound, we need to use the colligative property known as freezing point depression.
The formula used to calculate freezing point depression is:
ΔT = Kf * m
Where:
ΔT = the change in temperature (in Celsius)
Kf = the molal freezing point depression constant (a property of the solvent)
m = the molality of the solution (the number of moles of solute per kilogram of solvent)
First, let's calculate the change in temperature, ΔT. We know that the freezing point of pure benzene is lowered by 1.05C. Therefore, ΔT = 1.05C.
Next, we need to calculate the molality, m. We can find the number of moles of solute by dividing the mass of the sample by its molar mass.
molar mass = (mass of sample) / (moles of sample)
Since we have the mass of the sample (7.85 g), we need to find the moles of the sample. The moles of the sample can be calculated using the formula:
moles of sample = (mass of sample) / (molar mass of empirical formula)
The empirical formula of the compound is C5H4, which has a total molar mass of (5 * molar mass of C) + (4 * molar mass of H). The molar mass of carbon (C) is approximately 12 g/mol, and the molar mass of hydrogen (H) is approximately 1 g/mol.
molar mass of empirical formula = (5 * 12 g/mol) + (4 * 1 g/mol) = 64 g/mol
moles of sample = 7.85 g / 64 g/mol
Now, we can calculate the molality, m:
m = (moles of sample) / (mass of benzene in kg)
The mass of benzene in kg can be calculated by dividing the mass of benzene by 1000 (since there are 1000 grams in a kilogram).
mass of benzene in kg = 301 g / 1000 = 0.301 kg
Finally, we can substitute the values into the freezing point depression equation:
1.05C = Kf * (moles of sample / mass of benzene in kg)
We can rearrange the equation to solve for Kf:
Kf = (1.05C) / (moles of sample / mass of benzene in kg)
Now that we know Kf, we can find the molar mass of the compound. The equation for molal freezing point depression constant is:
Kf = ΔT_f / m
Where ΔT_f is the freezing point depression for the solvent (benzene), and m is the molality of the solution. We know that the freezing point depression for benzene is 5.12 C/m (molal freezing point depression constant for benzene).
Thus,
5.12 C/m = (1.05C) / (moles of sample / mass of benzene in kg)
We can rearrange the equation to solve for moles of sample:
moles of sample = (1.05C) * (mass of benzene in kg) / 5.12 C/m
Now, substituting the known values:
moles of sample = (1.05C) * (0.301 kg) / 5.12 C/m
Finally, we can calculate the molar mass of the compound:
molar mass = (mass of sample) / (moles of sample)
Substituting the known values, the molar mass would be:
molar mass = 7.85 g / (moles of sample)
Once we have the molar mass, we can find the molecular formula by comparing it with the empirical formula. Divide the molar mass by the molar mass of the empirical formula and multiply each subscript in the empirical formula by the resulting number to get the molecular formula.
To find the molar mass and molecular formula of the compound, we need to use the freezing point depression equation and the concept of molality.
1. Calculate the freezing point depression (∆Tf):
∆Tf = Kf * m
where Kf is the freezing point depression constant for benzene (5.12 °C•kg/mol) and m is the molality of the solution.
2. Calculate the molality (m):
m = moles of solute / mass of solvent in kg
3. Calculate the moles of solute:
moles of solute = mass of solute / molar mass of solute
4. Calculate the molar mass of solute:
molar mass of solute = mass of solute / moles of solute
5. Calculate the empirical formula molar mass:
empirical formula molar mass = (molar mass of carbon x number of carbon atoms) + (molar mass of hydrogen x number of hydrogen atoms)
6. Find the molecular formula using the empirical formula molar mass and the expected molar mass of the compound.
Let's calculate each step:
Given data:
Mass of solute = 7.85 g
Mass of solvent (benzene) = 301 g
Freezing point depression constant (Kf) = 5.12 °C•kg/mol
Freezing point depression (∆Tf) = 1.05 °C
Molar mass of carbon = 12.01 g/mol
Molar mass of hydrogen = 1.008 g/mol
Step 1:
∆Tf = Kf * m
1.05 = 5.12 * m
Step 2:
m = moles of solute / mass of solvent in kg
Convert the mass of solvent to kg:
mass of solvent = 301 g = 0.301 kg
m = (moles of solute) / 0.301 kg
Step 3:
moles of solute = mass of solute / molar mass of solute
moles of solute = 7.85 g / molar mass of solute
Step 4:
molar mass of solute = mass of solute / moles of solute
Step 5:
empirical formula molar mass = (molar mass of carbon x number of carbon atoms) + (molar mass of hydrogen x number of hydrogen atoms)
Step 6:
To find the molecular formula, we need to compare the empirical formula molar mass with the expected molar mass of the compound.
Please provide the expected molar mass of the compound.