How many moles of CH3OH are needed to produce 3 moles of CO2?

We have 1 atom of C on both sides of the equation. If we consider the atoms of H we will see that on the left we have 4 atoms of H and on the right we have 2 atoms of H. We can change the coefficient for H₂O and write a 2 in front of it.

__ CH₃OH + __ O₂ ----> __ CO₂ + 2 H₂O

Finally we have to balance the atoms of O. We have 4 on the right side of the equation and 3 on the left. To balance them we will have to change the coefficient for O₂ and write 3/2 there.

__ CH₃OH + 3/2 O₂ ----> __ CO₂ + 2 H₂O

Coefficients can't be fractions. To convert 3/2 to an entire number we can multiply all the coefficients by 2. The balanced equation is:

2 CH₃OH + 3 O₂ ----> 2 CO₂ + 4 H₂O

If we take a look at the coefficients we will see that 2 moles of CH₃OH will react with 3 moles of O₂ to give 2 moles of CO₂ and 4 moles of H₂O. So to produce 2 moles of CO₂ we need 2 moles of CH₃OH. So the molar ratio between them is 2:2. We can use that ratio to find the answer to our problem.

2 moles of CH₃OH : 2 moles of CO₂

moles of CH₃OH = 3 moles of CO₂ * 2 moles of CH₃OH/(2 moles of CO₂)

moles of CH₃OH = 3 moles

Answer: 3 moles of CH₃OH are needed to produce 3 moles of carbon dioxide.