According to the following reaction, how many moles of oxygen gas are necessary to form 0.293 moles carbon dioxide? benzene (C6H6) (l) + oxygen (g) carbon dioxide (g) + water (g) moles oxygen gas

Answer 1

Hello, Isabella,

We need to balance the equation.

C₆H₆ + O₂ = CO₂ + H₂O (I should add the states, but am lazy and will assume we'll remember them).

This isn't the easiest reaction to balance, but worse are in your future. I always start with the most complex molecule, which benezene narrowly wins in this case. It's not complex, but it does carry a lot of atoms that need homes on the product side. We need whole numbers of molecules, so pencil in a 1 for the C₆H₆. I always use pencil, since balancing often requires we change our first guesses.

1C₆H₆ + O₂ = CO₂ + H₂O

We need to place the 6 carbon and oxygen atoms on the product side. That means we need 6 CO₂ and 3 H₂O molecules.

1C₆H₆ + O₂ = 6CO₂ + 3H₂O

The carbons and hydrogens are balanced, so tackle oxygen next. We have already assigned coefficients for the products based only on the benzene, so add up those oxygens. We get 12 from the carbon dioxide and, uh oh, 3 from the water molecules. I say uh oh, because I know from experience that if there are an odd number of oxygen atoms in the products of a combustion, that there will be a problem: oxygen comes only in pairs, O₂. Sure enough, to get 15 oxygen atoms, we need 7 1/2 oxygen molecules. We can't have half of a molecule. But the solution is easy: Pencil in 7.5 for O₂ and hope no one sees you.

1C₆H₆ + 7.5O₂ = 6CO₂ + 3H₂O

Now be glad you used pencil. Hurry, and simply double every coefficient:

2C₆H₆ + 13O₂ = 12CO₂ + 6H₂O

Yes, that is a perfectly legitimate approach. Do whatever you want initially, and then if things are off by 1/2 or 1/3 a molecule, find a factor that will bring all coefficients to whole numbers and multiply by that number. Check to see they are in their lowest common denominator. If not, divide by that value.

We want 0.293 moles of carbon dioxide gas. Hardly worth the effort, I'm thinking. The question is how many moles of O₂ do we need? The balanced equation says that we'll get 12 moles of CO₂ for every 15 moles of O₂. Again, all this trouble to make carbon dioxide from fresh oxygen and a little carcinogen?

Using the molar ratio of (15 moles CO₂/12 moles O₂), we can find the moles O₂ required:

[(15 moles O₂)/(12 moles CO₂)]*(0.293 moles CO₂) = 0.367 moles O₂

I hope this is clear, and a little entertaining,

Bob

{I forgot to add the states in the final balanced equation. (g, l, etc.) ((_{Actually, I'm still lazy}))}