Anonymous
Nov 4, 2023
A7.85gsampleofacompoundwiththeempiricalformulaC5H4is dissolvedin301gofbenzene.Thefreezingpointofthesolutionis1.05 °Cbelowthatofpurebenzene.Whatarethemolarmassandmolecular formulaofthiscompound?
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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.
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