How many grams of oxygen are required to convert 11.2 L of CO into CO2? Assume STP.

Question

Reaction: 2 CO + O2 --> 2 CO2

Answer 1

First, this question relies on you knowing that the volume of 1 mole of an ideal gas at STP is 22.4 L. You'll then convert 11.2 L of CO to moles by dividing (11.2 L) / (22.4 L /mol) to arrive at 0.5 mol CO.

Now, the ratio of CO to O2 in the reaction is 2:1, so you divide 0.5 mol by 2 to determine that 0.25 mol of O2 are required for the reaction. The molar mass of oxygen is ~16 g/mol. You are working with O2 in this case, so the molar mass will actually be (2 x 16 g/mol), or 32 g/mol.

Finally, you just need to multiply 0.25 mol by 32 g/mol to arrive at your answer: 8 g of oxygen.

Answer 2

Here is the logical answer:

The equation tells us that for every two moles of CO gas, one mole of oxygen gas (O2) reacts with it. We know that from the coefficients of the balanced chemical equation (i.e. the whole numbers in front of the chemical formulas...if no # is there, then it's understood to be "1")

11.2 L of the CO (carbon monoxide) gas is equivalent to 0.5 moles of it at STP. It's a fact that one mole of ANY gas at STP occupies 22.4 L of space, so 11.2 L = 0.5 moles.

Since the equation tells us that there are going to be twice as many moles of CO gas in the reaction as O2 gas, we can assume that 0.25 moles of O2 gas are required in this reaction (or 1/4 of a mole of oxygen gas).

We know from calculating the gram formula mass of O2 that there are almost exactly 32 g of O2 in a mole of O2.

So....0.25 moles of O2 gas would be 1/4 of 32 g of gas, or 8 g of O2. Thus that is your answer!

Here it is set up according to dimensional analysis (actually the easier way to solve these problems once you learn how to do it):

__?___ grams of O2 = (11.2 L of CO/1) x (1 mole of CO/22.4 L of CO) x (1 mole of O2/2 mole of CO) x (32 g of O2/1 mole of O2)

The equal sign is actually a bit deceiving. Its not an actual equivalency, but it helps set up the ratios of solving the problem.

Notice:

---If you multiply all these quantities together, ALL THE UNITS CANCEL (top and bottom) except what you want to end up with, namely grams of O2, which is what you were asked for. Also you wind up with the right answer, 8 grams of O2. (#s on top: 11.2 x 1 x 1 x 32) divided by (#s on bottom: 1 x 22.4 x 2 x 1)

---In the first set of parentheses, you have the GIVEN quantity over 1. The given quantity comes from the information in the problem, thus it can be any number. I like to put it over a unitless "1" just to remind us that it's in the numerator (for purpose of easily cancelling units as we go)

---The subsequent things inside the parentheses are RATIOS and quantities that equivalent to each other, so they cannot be just any number. They come from facts we know (ex: one mole of gas occupies 22.4 L at STP) or from the mole to mole ratios that we get from the balanced chemical equation (ex: 2 moles of CO to every 1 mole of O2). For example, you could use this same procedure to convert inches to miles using equivalencies like 12 in = 1 ft and 5280 ft = 1 mile. The key is just setting up these quantities so that the units you want to get rid of cancel and the units you want to change it to stay in there.

Hope that helps!

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