A solution of 2.50g of compound having the empirical formula C6H5P in 25.0g of benzene is observed to freeze at 4.3 degrees Celsius. Calculate the molar mass of the solute and its molecular formula.
To calculate the molar mass and molecular formula of the solute, we need to follow several steps:
Step 1: Calculate the moles of solvent (benzene) used.
Moles = mass / molar mass
Given that the mass of the benzene is 25.0g and the molar mass of benzene is 78.11 g/mol, we can calculate the moles of benzene:
Moles of benzene = 25.0g / 78.11 g/mol = 0.32 mol
Step 2: Calculate the freezing point depression (∆Tf) caused by the solute.
∆Tf = Kf * molality
In this case, we don't have the molality directly, but we can calculate it.
Step 3: Calculate the moles of solute using the empirical formula.
The empirical formula of the solute is C6H5P, which means it contains 6 carbon atoms, 5 hydrogen atoms, and 1 phosphorus atom.
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
Molar mass of phosphorus (P) = 30.97 g/mol
Molar mass of empirical formula = 6 * 12.01 g/mol + 5 * 1.01 g/mol + 1 * 30.97 g/mol = 100.14 g/mol
Moles of solute = mass of solute / molar mass of empirical formula
Given the mass of the solute is 2.50g:
Moles of solute = 2.50g / 100.14 g/mol = 0.025 mol
Step 4: Calculate the molality of the solute.
Molality (m) = moles of solute / kg of solvent
Given the mass of the solvent (benzene) is 25.0g, which is equivalent to 0.025 kg:
Molality (m) = 0.025 mol / 0.025 kg = 1.0 mol/kg
Step 5: Calculate the freezing point depression (∆Tf).
∆Tf = Kf * molality
For benzene, the freezing point depression constant (Kf) is 5.12 °C/m.
∆Tf = 5.12 °C/m * 1.0 mol/kg = 5.12 °C
Step 6: Calculate the molal freezing point depression constant (Kf') for the solute.
We know that ∆Tf = Kf' * molality
Since ∆Tf = 5.12 °C and m = 1.0 mol/kg, we can rearrange the equation to solve for Kf':
Kf' = ∆Tf / molality = 5.12 °C / 1.0 mol/kg = 5.12 °C⋅kg/mol
Step 7: Calculate the moles of solute absorbed by the solvent.
∆Tf = Kf' * moles of solute
Given that ∆Tf = 4.3 °C and Kf' = 5.12 °C⋅kg/mol:
4.3 °C = 5.12 °C⋅kg/mol * moles of solute
Solving for moles of solute:
moles of solute = 4.3 °C / 5.12 °C⋅kg/mol = 0.84 mol
Step 8: Calculate the molar mass of the solute.
Molar mass of solute = mass of solute / moles of solute
Given the mass of the solute is 2.50g and moles of solute is 0.84 mol:
Molar mass of solute = 2.50g / 0.84 mol = 2.98 g/mol
Step 9: Calculate the molecular formula of the solute.
To find the molecular formula, we divide the molar mass of the solute by the molar mass of the empirical formula.
Molecular formula = Molar mass of solute / Molar mass of empirical formula
Molecular formula = 2.98 g/mol / 100.14 g/mol = 0.030 mol
Since the empirical formula has 0.025 mol of solute, the molecular formula is obtained by multiplying the empirical formula by 0.030 moles:
Molecular formula = C6H5P * 0.030 = C0.18H0.15P0.03
To simplify the molecular formula, we need to round the fractional subscripts to whole numbers. In this case, we multiply the entire formula by 2 to eliminate the fractions:
Molecular formula = C6H10P2
So, the molar mass of the solute is 2.98 g/mol, and its molecular formula is C6H10P2.
To calculate the molar mass of the solute and its molecular formula, we need to follow these steps:
Step 1: Calculate the number of moles of the solute
First, we need to convert the mass of the compound to moles. The molar mass of C6H5P can be calculated as follows:
(6 x 12.01 g/mol) + (5 x 1.01 g/mol) + 31.00 g/mol = 94.11 g/mol
The number of moles can be calculated by dividing the mass of the compound by its molar mass:
Number of moles = 2.50 g ÷ 94.11 g/mol ≈ 0.0266 mol
Step 2: Calculate the number of moles of benzene
Next, we need to convert the mass of benzene to moles. The molar mass of benzene (C6H6) is:
(6 x 12.01 g/mol) + (6 x 1.01 g/mol) = 78.11 g/mol
The number of moles of benzene can be calculated by dividing its mass by its molar mass:
Number of moles = 25.0 g ÷ 78.11 g/mol ≈ 0.3202 mol
Step 3: Calculate the molality of the solution
The molality of a solution is the number of moles of solute divided by the mass of the solvent (in kg). In this case, we divide the number of moles of the solute by the mass of benzene in kg:
Molality (m) = 0.0266 mol ÷ 25.0 g ≈ 1.06 mol/kg
Note: We converted grams to kg by dividing by 1000.
Step 4: Calculate the freezing point depression constant (Kf)
The freezing point depression constant (Kf) for benzene is 5.12 °C/m.
Step 5: Calculate the change in freezing point
The change in freezing point (∆Tf) can be calculated using the following equation:
∆Tf = Kf x m
∆Tf = 5.12 °C/m x 1.06 mol/kg ≈ 5.43 °C
Step 6: Calculate the freezing point of the solution
The freezing point of the solution is the freezing point of the pure solvent minus the change in freezing point (∆Tf).
Freezing point of solution = 4.3 °C - 5.43 °C ≈ -1.13 °C
Step 7: Calculate the number of moles of solute particles
The freezing point depression is related to the number of moles of solute particles by the equation:
∆Tf = (Kf x m) x (number of particles)
For C6H5P, the number of particles is the same as the number of moles, so:
0.0266 mol = (5.12 °C/m x 1.06 mol/kg) x (number of particles)
Solving for the number of particles gives:
Number of particles ≈ (0.0266 mol) / (5.12 °C/m x 1.06 mol/kg) ≈ 0.0049 particles
Step 8: Determine the empirical formula ratio
The empirical formula represents the simplest whole-number ratio of atoms in a compound. To determine the empirical formula, divide the number of atoms in each element by the smallest number of atoms:
C6H5P divided by 0.0049 ≈ C1224H1005P204
Step 9: Determine the molecular formula
The molecular formula of the compound is a multiple of its empirical formula. To find the multiple, divide the molar mass of the compound by the molar mass determined earlier:
Molar mass of compound / molar mass determined earlier = x
Let x = Molar mass of the compound
x g/mol / 94.11 g/mol = 1.0 x 1224
x = 115496.64 g/mol
Therefore, the molar mass of the solute is approximately 115496.64 g/mol, and its molecular formula is C1224H1005P204.