A hydrocarbon gas contains 92.26% carbon and

7.74% hydrogen, by mass. At one atmosphere
pressure and 25°C, 4.20 L of the gas has a mass of
4.47 g. What is the molecular formula for the
compound?

Take a 100 g sample to give you

92.26 g C
7.74 g H.
Convert to moles. moles = grams/molar mass
Look at the moles and find the ratio of the elements to each other with the smallest number being 1.00. The easy way to do that is to divide the smaller number by itself and follow by dividing the other number by the same small number. Round to whole numbers. That will give you the empirical formula.
To find the molar mass, use PV = nRT and solve for n. Then n = grams/molar mass and solve for molar mass.
To find the molecular formula, that is
(mass empirical formula)*x = molar mass
Solve for x and it it as (empirical formula)x.
Post your work if you get stuck.

To find the molecular formula for the compound, we need to determine the empirical formula first. The empirical formula represents the simplest whole number ratio of the atoms present in a compound.

First, we need to convert the mass percentages into moles. To do this, we assume a 100g sample of the compound:

- Carbon: 92.26% of 100g = 92.26g
- Hydrogen: 7.74% of 100g = 7.74g

Next, we need to convert moles of each element to moles of atoms:

- Moles of carbon (C): 92.26g / molar mass of carbon (12.01g/mol) = 7.68 mol
- Moles of hydrogen (H): 7.74g / molar mass of hydrogen (1.01g/mol) = 7.66 mol

Now, we divide the number of moles of each element by the smallest number of moles to get the simplest whole number ratio:

- C: 7.68 mol / 7.66 mol ≈ 1
- H: 7.66 mol / 7.66 mol = 1

Based on this calculation, the empirical formula is CH.

Next, we need to determine the molecular formula from the empirical formula. To do this, we need to know the molar mass of the compound. We can find the molar mass from the experimental data provided.

Given:
- Volume (V) = 4.20 L
- Mass (m) = 4.47 g
- Pressure (P) = 1 atm
- Temperature (T) = 25°C = 298 K

Using the ideal gas law (PV = nRT), we can find the number of moles of the compound:

- P = 1 atm
- V = 4.20 L
- n = ?
- R (ideal gas constant) = 0.0821 L·atm/mol·K
- T = 298 K

n = (P * V) / (R * T)
= (1 atm * 4.20 L) / (0.0821 L·atm/mol·K * 298 K)
= 0.1827 mol

The molar mass of the compound can be calculated by dividing the mass of the compound by the number of moles:

Molar mass = mass / number of moles
= 4.47 g / 0.1827 mol
≈ 24.49 g/mol

Now, we compare the molar mass of the empirical formula (12.01 g/mol for carbon and 1.01 g/mol for hydrogen) to the calculated molar mass (24.49 g/mol).

The ratio between the two is approximately 2.04 for carbon and 24.24 for hydrogen. These ratios suggest that the molecular formula is likely C2H24.

Therefore, the molecular formula for the compound is C2H24.