Question

How do you balance `C_2H_5OH(l) + O_2(g) -> CO_2(g) + H_2O(g)` and determine the mass of `CO_2` produced from the combustion of 100.0 g ethanol?

Answer 1

`C_2H_5OH +2O_2 -> 2CO_2 + 3H_2O`

mass of `CO_2` = 191 g

Explanation:

Part 1: Balancing equation:

`C_2H_5OH + O_2 -> CO_2 + H_2O`

We'll do that by counting the number of atoms on the left and right hand side of the equation and get them to be the same.

L-- Atom--R
2 -- C -- 1
6 -- H -- 2
3 -- O -- 3

Looks like C and H are not balanced. Since there are 2 C on the left and only 1 C on the right, we'll add 2 in front of `CO_2` on the right.

`C_2H_5OH + O_2 ->color(red) 2CO_2 + H_2O`

Updating the atom counts on the right:
L-- Atom--R
2 -- C -- `color(red)cancel(1)2`
6 -- H -- 2
3 -- O -- `color(red)cancel(3)5`

Now that C is balanced, we'll move on to H. There are 6 H on the left and only 2 H on the right, we'll add 3 in front of `H_2O` on the right.

`C_2H_5OH + O_2 -> 2CO_2 + color(red)3H_2O`

Updating the atom counts on the right:
L-- Atom--R
2 -- C -- `cancel(1)2`
6 -- H -- `color(red)cancel(2)6`
3 -- O -- `cancel(3)5`

All that's left now is to balance O. We have 3 O on the left and 5 O on the right. If we add a 2 in front of `O_2` on the left, we'll balance O:

`C_2H_5OH + color(red)2O_2 -> 2CO_2 + 3H_2O`

Updating the atom counts on the right:
L-- Atom--R
2 -- C -- `cancel(1)2`
6 -- H -- `cancel(2)6`
`5color(red)cancel(3)`-- O -- `cancel(3)5`

Part 2: Find mass `CO_2` from mass ethanol, `C_2H_5OH`

The plan is to perform the following 3 steps calculations starting from `"mass " C_2H_5OH` to `"mass "CO_2`

`"mass " C_2H_5OH ->" moles " C_2H_5OH -> " moles " CO_2 -> "mass "CO_2`

• Converting mole to mole will require the stoichiometric coefficient (numbers in front of balanced equation).
• Converting from mass to mole of the same substance will require its molar mass.

In that case, we'll need to find the molar mass of

• `C_2H_5OH=2(12)+5(1)+16+1= 46 g/"mol"`

• `CO_2=12+2(16)= 44 g/"mol"`

Calculations can be set up this way. Notice how the units cancel each other out leaving `"g "CO_2`:
`"mass of "CO_2=100" g " C_2H_5OH` `*(1" mol "C_2H_5OH)/(46" g " C_2H_5OH)` `*(2" mol "CO_2)/(1" mol "C_2H_5OH)*(44" g "CO_2)/(1" mol "CO_2)=191" g " CO_2`