When #"0.1 mols"# of an unknown hydrocarbon #"C"_x"H"_y# was combusted, it produced #"0.3 mols"# of #"CO"_2# and #"0.4 mols"# of #"H"_2"O"#. What is the molecular formula of this hydrocarbon?

1 Answer

Answer:

#"C"_3"H"_8#

Explanation:

The trick here is to recognize the fact that you're dealing with a hydrocarbon, which means that it will only contain carbon and hydrogen.

Now, the complete combustion of a hydrocarbon produces carbon dioxide, #"CO"_2#, and water, #"H"_2"O"#.

In your case, you know that when #0.1# moles of this hydrocarbon underwent combustion, the reaction produced #0.3# moles of carbon dioxide and #0.4# moles of water.

Now, another important thing to realize here is that all of the carbon that was initially a part of the hydrocarbon is now a part of the carbon dioxide, and all of the hydrogen that was a part of the hydrocarbon is now a part of the water.

Since one mole of carbon dioxide contains #1# mole of carbon, and one mole of water contains #2# moles of hydrogen, it follows that the hydrocarbon contained

#0.3color(red)(cancel(color(black)("moles CO"_2))) * "1 mole C"/(1color(red)(cancel(color(black)("mole CO"_2)))) = "0.3 moles C"#

and

#0.4color(red)(cancel(color(black)("moles H"_2"O"))) * "2 moles H"/(1color(red)(cancel(color(black)("mole H"_2"O")))) = "0.8 moles H"#

Now, let's say that your hydrocarbon has a molecular formula #"C"_x"H"_y#. You know that one mole of this hydrocarbon would produce

  • #xcolor(white)(a)"moles of C"#
  • #ycolor(white)(a)"moles of H"#

If this is the case, you can say that #0.1# moles of this hydrocarbon will produce

#(0.1 xx x)color(white)(a)"moles of C"#
#(0.1 xx y)color(white)(a)"moles of H"#

But you already know how many moles of carbon and hydrogen were produced by the reaction, so you can say that

#0.1 xx x = 0.3 implies x = 0.3/0.1 = 3#

and

#0.1 xx y = 0.8 implies y = 0.8/0.1 = 8#

Therefore, the molecular formula of the hydrocarbon is

#color(green)("C"_3"H"_8) -># propane

http://www.turbosquid.com/3d-models/propane-molecule-structure-3d-max/445795