Gas Law Calculation: Determining Molecular Formula of Unknown Gas

Can we determine the molecular formula of an unknown gas based on its composition and physical properties?

Given data: An unknown gas is composed of 60.0% carbon and 40.0% hydrogen. A 5.00 g sample of the gas occupies a 3.50 L volume at 25.00°C and 130 kPa.

Yes, we can determine the molecular formula of the unknown gas based on the given data.

Let's find out the molecular formula of the unknown gas.

The molecular formula of a compound represents the number of atoms of each element in the compound. To find the molecular formula of the unknown gas, we first need to determine its empirical formula. The empirical formula is the simplest formula that shows the ratio of the number of atoms of each element in the compound.

Given that the unknown gas is composed of 60.0% carbon and 40.0% hydrogen, the empirical formula of the gas will be CH2.

The molecular mass of the empirical formula CH2 is 14.02 g/mol. We can calculate the molar mass of the gas using the ideal gas law, PV = nRT:

P is the pressure of the gas (130 kPa), V is the volume of the gas (3.50 L), n is the number of moles of the gas, R is the gas constant (0.08206 L kPa/mol K), and T is the temperature of the gas (25.00°C + 273.15 = 298.15 K).

Solving for n, we get n = PV/RT = (130 kPa)(3.50 L) / (0.08206 L kPa/mol K)(298.15 K) = 1.75 mol.

The molecular mass of the gas is 5.00 g / 1.75 mol = 2.86 g/mol.

As the molecular formula of the gas is a multiple of its empirical formula, the smallest multiple of CH2 with a molecular mass of 2.86 g/mol is C2H4.

Therefore, the molecular formula of the unknown gas is C2H4.