A solutionof 2.50g of a compound having the empirical formula C7H6O2 in 25.0g of benzene is observed to freeze at 4.3 degree C.Calculate the molar mass of the solute and its Molecular formula
Look up normal freezing point benzene.
Look up freezing point constant for benzene (Kf = ?).
delta T = Kf*molality
Solve for molality.
molality = moles/kg solvent
Solve for moles
moles = grams/molar mass
Solve for molar mass.
Find the mass of the empirical formula.
(molar mass/empirical mass) = ?? and round to the nearest whole number and call that number n. The molecular formula is (empirical formula)n.
To determine the molar mass and molecular formula of the solute, we need to follow a step-by-step process.
Step 1: Calculate the moles of benzene (C6H6)
To calculate the moles of benzene, we use the formula:
moles = mass / molar mass
Given that the mass of benzene is 25.0g and its molar mass is 78.11 g/mol, we can calculate:
moles of benzene = 25.0g / 78.11 g/mol = 0.3203 mol
Step 2: Calculate the moles of the solute
To determine the moles of the solute, we need to calculate the freezing point depression using the formula:
ΔT = Kf * molality
Given that the freezing point depression (ΔT) is 4.3 °C and the cryoscopic constant (Kf) of benzene is 5.12 °C/molal, we can rearrange the formula to calculate the molality:
molality = ΔT / Kf = 4.3 °C / 5.12 °C/molal = 0.83984 mol/kg
Next, we'll calculate the moles of the solute by multiplying the molality by the mass of benzene in kilograms:
moles of solute = molality * mass of solvent (in kg)
mass of benzene in kg = 25.0g / 1000 = 0.025 kg
moles of solute = 0.83984 mol/kg * 0.025 kg = 0.020996 mol
Step 3: Calculate the empirical formula mass
To determine the empirical formula mass, we need to calculate the sum of the molar masses of the empirical formula elements (C, H, and O):
Empirical formula mass = (molar mass of C * number of C atoms) + (molar mass of H * number of H atoms) + (molar mass of O * number of O atoms)
Using the atomic masses of C = 12.01 g/mol, H = 1.01 g/mol, and O = 16.00 g/mol, along with the empirical formula C7H6O2, we can calculate:
Empirical formula mass = (12.01 g/mol * 7) + (1.01 g/mol * 6) + (16.00 g/mol * 2) = 104.14 g/mol
Step 4: Calculate the molar mass of the solute
To determine the molar mass of the solute, we divide the mass of the solute by the number of moles:
Molar mass of solute = mass of solute / moles of solute
Given that the mass of the solute is 2.50g and the moles of solute is 0.020996 mol, we can calculate:
Molar mass of solute = 2.50g / 0.020996 mol = 119.38 g/mol
Step 5: Determine the molecular formula
To find the molecular formula, we need to compare the molar mass of the solute to the empirical formula mass.
Molar mass of solute = n * empirical formula mass
We divide the molar mass of the solute by the empirical formula mass to find the value of n:
n = Molar mass of solute / empirical formula mass = 119.38 g/mol / 104.14 g/mol = 1.147
Since n is approximately 1, it suggests that the empirical formula is also the molecular formula.
Therefore, the molar mass of the solute is approximately 119.38 g/mol and the molecular formula of the solute is C7H6O2.