What is the molecular formula for the gas ?

Question

For a certain gas that contains only carbon and hydrogen the mass percentage of hydrogen is known to be 14.37
It is also known that 3.06 g of the gas has a volume of 1.00 L and a pressure of 0.970 atm at 51.4 oC.

just need to know the step by step process on how to get the answer.

Answer 1

1. Modify the ideal gas equation such that molecular mass (MW)and weight of gas appear.
Ideal gas equation: PV = nRT
since n (moles) = weight / MW = g/MW
so, your equation will become PV = gRT/MW
Given your values, you will end up:
MW = gRT/ PV

2. Plug in the values:

MW = 3.06g * 0.08206 L-atm/mol-K * (51.4 + 273 K) / 0.970atm * 1.00L
MW = 83.98 g/mol
- this is the molecular mass of your gas.

3. Determine the molecular formula of the gas.
-since you have 14.37% H, your C is 85.63%
-assume 100g gas so that you'll have 14.37g H and 85.63g C
-get the number of moles:
H: 14.37g / 1g/mol = 14.37 mol H
C: 85.63g / 12g/mol = 7.13 mol C

- get the mole ratio: that is, 1 mol C is to 2 mol H.
- determine your multiplier such that MW result will be approximately 83.98g/mol. In this case, its 6.

So, your molecular formula is C6H12.

To check,

C: 6 * 12g/mol = 72g/mol
H: 12 * 1g/mol = 12g/mol
total: 84g/mol ~ 83.98g/mol

Answer 2

Use the second part to figure the # of grams in a 22.4 L sample by correcting for non-standard P & T. This value will be the Molar weight of the sample and equal to the sum of the # of H atoms and 12*the # of carbon atoms.

GMW = H + 12C

Then use the first part to get another equation:

H/(H+12C) = .1437

Solve these 2 simultaneously for H and C, the # of hydrogen and carbon atoms in each molecule........