a flask with a volume of 267.5 mL contains a few milliliters of a volatile hydrocarbon. after vaporizing the gas at 100 degrees C, the flask is weighed and found to contain 0.728 grams of hydrocarbon vapor at 755 mmHg. a separate combustion analysis experiment revealed that the empirical formula osf the hydrocarbon was CH2. What is the molecular formula?
To determine the molecular formula of the hydrocarbon, we need to use the ideal gas law and the empirical formula to find the molar mass, and then compare it to the actual molar mass.
Step 1: Convert the volume of the flask to liters.
- Volume = 267.5 mL = 267.5 / 1000 = 0.2675 L
Step 2: Use the ideal gas law equation to find the number of moles.
- PV = nRT
- P = 755 mmHg = 755 / 760 atm (since 1 atm = 760 mmHg)
- R = 0.0821 L·atm/K·mol (gas constant)
- T = 100 + 273.15 = 373.15 K (temperature in Kelvin)
Plugging in the values into the ideal gas law equation:
PV = nRT
(755/760) * 0.2675 = n * 0.0821 * 373.15
Solving for n:
n = ((755/760) * 0.2675) / (0.0821 * 373.15)
n ≈ 0.009197 moles
Step 3: Determine the molar mass of the empirical formula (CH2).
- Carbon (C) has a molar mass of 12 g/mol.
- Hydrogen (H) has a molar mass of 1 g/mol.
- CH2 has a molar mass of 12 + (2 * 1) = 14 g/mol.
Step 4: Calculate the empirical formula mass.
Empirical formula mass = molar mass of CH2 = 14 g/mol
Step 5: Calculate the actual molar mass of the hydrocarbon.
Actual molar mass = mass of hydrocarbon vapor / moles of hydrocarbon vapor
Actual molar mass = 0.728 g / 0.009197 moles ≈ 79.19 g/mol
Step 6: Determine the ratio of the actual molar mass to the empirical formula mass.
Molar mass ratio = Actual molar mass / Empirical formula mass
Molar mass ratio = 79.19 g/mol / 14 g/mol ≈ 5.657
Step 7: Find the whole number ratio of the atoms in the molecular formula.
Since the empirical formula CH2 has two hydrogen atoms, we need to multiply the subscripts by the molar mass ratio to get the molecular formula.
Molecular formula = C(H2) * Molar mass ratio
Molecular formula = C(H2) * 5.657
Simplifying the formula:
Molecular formula = C(11.314)H14.126
Rounding to nearest whole numbers:
Molecular formula = C11H14
Therefore, the molecular formula of the hydrocarbon is C11H14.