Homework Problem 14.1

[Angela 1K]

The equation that we're supposed to balance is H⁺(aq) + Cr₂O₇^2-(aq) + C₂H₅OH(aq) --> Cr³⁺(aq) + C₂H₄O(aq) + H₂O(l)

According to the solution manual, the balanced oxidation half-reaction should be
C₂H₅OH(aq) --> C₂H₄O(aq) + 2e^- + 2H⁺(aq)

I'm having difficulty figuring out why there's 2 electrons added to the right-hand side when the change in oxidation states of the carbon is only -1 (from -2 to -1). From my understanding, there'd only need be 1 electron.

If someone could please explain, that'd be appreciated! Thanks

[Hannah Chew 2A]

There's 2 carbons that undergo a change in oxidation state, so you need 2 e-. I prefer to look at it as a balance of charge. You need the 2 H+ ions on the right side to balance the hydrogens, and since the left hand side is neutral and right hand side is +2, you need to add 2e- to the right hand side to bring the net charge back to 0.

[Tim Nguyen 2J]

The two H atoms add a net +2 charge to the product side, so you need to add two e- to balance that out.