Question

Shown below is the overall reaction occuring in the direct methanol fuel cell (DMFC).
CH3OH(aq) + O2(g) → CO2(g) + H2O(l) (not balanced!)
Balance the reaction using the half-reaction method. It may be useful to work out the oxidation states of the reactants and products.
First, show the balanced (half-)reaction that occurs at the anode.
Next, show the balanced (half-)reaction that occurs at the cathode.
Now, show the overall, balanced reaction.

Answer 1

The given unbalanced reaction is

CH₃OH_(aq) + O_2(g) CO_2(g) + H₂O_(l)

Now writing half reactions

Oxidation : CH₃OH   CO₂  

Reduction : O₂    H₂O

Now balancing all atoms except hydrogen and oxygen

So

Oxidation : CH₃OH    CO₂  

Reduction : O₂    H₂O

Now balance the oxygen atom

Oxidation : CH₃OH + H₂O   CO₂  

Reduction : O₂   2H₂O

Now balance the hydrogen atom

Oxidation : CH₃OH + H₂O   CO₂ + 6H⁺

Reduction : O₂ + 4H⁺ 2H₂O

Now balance the charge

Oxidation : CH₃OH + H₂O   CO₂ + 6H⁺ + 6e

Reduction : O₂ + 4H⁺ + 4e 2H₂O

Now making electron gain equivalent to electron lossed

Oxidation : 2CH₃OH + 2H₂O 2CO₂ + 12H⁺ + 12e

Reduction : 3O₂ + 12H⁺ + 12e 6H₂O

Now adding both half reactions , we get

2CH₃OH + 2H₂O +3O₂ + 12H⁺ + 12e 2CO₂ + 12H⁺ + 12e +  6H₂O

So the balanced reaction is

2CH₃OH + 3O₂   2CO₂ + 4H₂O