>
#molar-mass
,
#chemistry
,
#molecular-formula
>
A7.85gsampleofacompoundwiththeempiricalformulaC5H4is
dissolvedin301gofbenzene.Thefreezingpointofthesolutionis1.05
°Cbelowthatofpurebenzene.Whatarethemolarmassandmolecular
formulaofthiscompound?

Nov 4, 2023

Sort By

ChatGPT

Nov 4, 2023

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.

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.