Hydrocarbon empirical formula question

[lastlanding]

Homework Statement

Q. A Hydrocarbon (C_nH_m) is burned completely in oxygen to produce a mixture of CO₂ and H₂O. The total pressure of mixture is 1.200 atm and partial pressure of H₂O is 0.686 atm. What is empirical formula of Hydrocarbon

Homework Equations

pV=nRT
p_a/p_total = n_a/n_total

The Attempt at a Solution

The answer is C₃H₈ aka Propane

Im so confused! I don't even know where to start with this!

 

[Delphi51]

Find the partial pressure for the CO2. The partial pressures of the gases are proportional to the number of molecules, so you've immediately got the ratio of the number of H2O molecules to the number of CO2 molecules. This is almost m/n, but note that because of the H2 there are twice as many H's as H2O's, so you've really got the ratio of m/2 to n. It should then be easy to get the ratio m to n. Then you start guessing - if n=1 does m work out to an even number? If not, try n = 2 and so on.

 

[tomcue]

I understand that this question involves the use of the ideal gas law and partial pressures to determine the empirical formula of the hydrocarbon. To start, we can use the ideal gas law equation, pV=nRT, to calculate the number of moles of the total mixture. From the given information, we know that the total pressure is 1.200 atm and the total volume is not specified, so we can assume a convenient value such as 1 L. The temperature and gas constant are also given constants, so we can rearrange the equation to solve for n, the number of moles.

n = (pV)/(RT) = (1.200 atm * 1 L)/(0.08206 L*atm/mol*K * 298 K) = 0.048 mol

Next, we can use the partial pressure equation, pa/ptotal = na/ntotal, to determine the number of moles of H2O in the mixture. We know that the partial pressure of H2O is 0.686 atm, and we can calculate the total number of moles from the previous step.

na = (pa/ptotal) * ntotal = (0.686 atm * 0.048 mol)/(1.200 atm) = 0.0274 mol

Now, we can use the molar ratio between H2O and the hydrocarbon to determine the number of moles of carbon and hydrogen in the hydrocarbon. From the empirical formula, we know that there are 3 carbon atoms and 8 hydrogen atoms in the molecule. Therefore, for every 3 moles of H2O, there must be 1 mole of CnHm.

nC = (1 mol CnHm)/(3 mol H2O) * 0.0274 mol H2O = 0.00913 mol C
nH = (8 mol CnHm)/(3 mol H2O) * 0.0274 mol H2O = 0.0731 mol H

Finally, we can use these values to determine the empirical formula of the hydrocarbon by dividing the moles of each element by the lowest number of moles, which in this case is 0.00913 mol.

C: 0.00913 mol / 0.00913 mol = 1
H: 0.0731 mol / 0