A7.85gsampleofacompoundwiththeempiricalformulaC5H4is dissolvedin301gofbenzene.Thefreezingpointofthesolutionis1.05 °Cbelowthatofpurebenzene.Whatarethemolarmassandmolecular formulaofthiscompound?

To find the molar mass and molecular formula of the compound, we need to use the freezing point depression equation:

ΔT = Kf * m

Where:
ΔT = change in freezing point
Kf = freezing point depression constant for benzene (5.12 °C/m)
m = molality of the solution (moles of solute per kg of solvent)

First, let's calculate the molality of the solution:

molality = moles of solute / kg of solvent

The moles of solute can be calculated using the empirical formula:

Empirical formula mass = (5 * atomic mass of carbon) + (4 * atomic mass of hydrogen)
Empirical formula mass = (5 * 12.01 g/mol) + (4 * 1.01 g/mol)
Empirical formula mass = 60.05 g/mol + 4.04 g/mol
Empirical formula mass = 64.09 g/mol

moles of solute = mass of solute / empirical formula mass
moles of solute = 7.85 g / 64.09 g/mol
moles of solute = 0.1224 mol

Now, let's calculate the molality:

molality = 0.1224 mol / 0.301 kg
molality = 0.406 mol/kg

Next, let's calculate the change in freezing point:

ΔT = 1.05 °C

Now, let's use the freezing point depression equation to find the molar mass:

ΔT = Kf * m
1.05 °C = 5.12 °C/m * 0.406 mol/kg

Solving for molar mass:

molar mass = ΔT / (Kf * m)
molar mass = 1.05 °C / (5.12 °C/m * 0.406 mol/kg)
molar mass = 5.12 m * 0.406 mol/kg / 1.05 °C
molar mass = 1.97 mol/kg

Finally, let's find the molecular formula:

The empirical formula mass is 64.09 g/mol.
The molar mass is 1.97 mol/kg.

The molecular formula mass is a whole number multiple of the empirical formula mass:

Molecular formula mass = (empirical formula mass) * n

Where n is the whole number multiple.

n = molar mass / empirical formula mass
n = 1.97 mol/kg / 64.09 g/mol
n = 0.0307 mol/g

Since n is less than 1, we need to multiply the empirical formula by a whole number to get the molecular formula. Let's multiply by 2:

Molecular formula mass = (empirical formula mass) * 2
Molecular formula mass = 64.09 g/mol * 2
Molecular formula mass = 128.18 g/mol

Therefore, the molar mass of the compound is 128.18 g/mol and the molecular formula is C10H8.