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I can't seem to figure out this redox reaction.

$$ \ce{CH3COO- + CO2 -> CH3CH2COO-} $$

Is the charge on the carbon in the $\ce{CO2}$ supposed to match the charge on the carbon in the $\ce{CH3COO-}$? I am supposed to build a half reaction using $\ce{H2O}$ and $\ce{H+}$ as needed, but I can't seem to figure out how many electrons are actually transferred. What are the charges on the carbon?

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It helps to use "fully compressed" formulae so you can easily count atoms and figure out how to balance carbons, oxygens, hydrogens, and charges. That is, instead of

  • $\ce{CH3COO- +CO2 -> CH3CH2COO-}$

write it this way:

  • $\ce{C2H3O2- +CO2 -> C3H5O2-}$

Then it's easy to see that this is not a balanced equation. Carbon atoms are the same on each side, but not oxygen or hydrogen atoms. You need two more $\ce{O}$ atoms on the products side. Those have to come from water since that is the only oxygen-containing species you are allowed to use.

  • $\ce{C2H3O2- +CO2 -> C3H5O2- + 2H2O}$

Now oxygen is balanced, but hydrogen is still imbalanced. That can be rectified by adding $\ce{H+}$ into the equation as appropriate.

  • $\ce{C2H3O2- +CO2 +6H+ -> C3H5O2- + 2H2O}$

Now only charge is imbalanced, which can be fixed by adding electrons to complete the balanced half-reaction:

  • $\ce{C2H3O2- +CO2 +6H+ +6e- -> C3H5O2- + 2H2O}$
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