Question

What volume of oxygen gas is needed to react completely with 0.677 L of carbon monoxide gas (CO) to form gaseous carbon dioxide?
Assume all volume measurements are made
at the same temperature and pressure.

Thanks in advance for all help!!

Answer 1

2CO + O2 ==> 2CO2

When all gases and at the same T and P, one may use a shortcut in which volumes may be used as if they were mols.
0.677 L CO + (2 mols O2/1 mol CO) = L O2 gas needed.

Answer 2

Is there anyway you could explain further?

Answer 3

Well, it's a regular stoichiometry problem if you work it the long way. I can do that and you can see how the two fit together. The problem says all gases at the same conditions but they don't say what those conditions are so I'll just assume everything is at STP which means gases at STP occupy 22.4 L/mol. We could choose any number we wish because the number cancels in the end.

mols CO = 0.677 L x (1 mol/22.4L) = 0.0302.
Now use the coefficients in the balanced equation to convert mols CO to mols O2. That's 0.0302 mols CO x (1 mol O2/2 mols CO) = 0.0302 x 1/2 = 0.0151 mols O2 needed to completely burn the CO.
Now convert mols O2 to L.
0.0151 mols O2 x (22.4 L/mol) = 0.338 L.

Back to the shortcut way. You see I converted to mols by dividing by 22.4 in the first step and converted back to L by multiplying by 22.4 L in the last step. So the shortcut method just doesn't divide by 22.4 first because we know it will cancel in the last step anyway. So the shortcut way we simply convert L CO to L O2 by using the coefficients in the balanced equation.

By the way, we can convert any mol quantity in an equation to any other mol quantity in the same equation by using the coefficients in the balanced equation.
0.677 L CO x (1 mol O2/2 mols CO) = 0.677 x 1/2 = 0.338 L.

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Answer 4

Thank you DrBob222 for your help I get it now!