In this example, it says balance the following redox reaction if it is found to be in a basic solution. All right, so again, many of the steps that we're going to see we've already employed when dealing with acidic solutions. If you haven't watched those videos, I highly recommend you go and take a look at them again. So for step one, we're going to break the full redox reaction into two half reactions. We do this by focusing on the elements that are not oxygen or hydrogen. So here we have manganese with manganese, nitrogen with nitrogen. So our two half reactions would be
MnO
4
-
→
Mn
2
+
N
2
H
4
→
N
3
Now let's look at the other steps. Step 2 for each half reaction balance elements that are not oxygen or hydrogen. So here we have one manganese, 1 manganese. They're balanced and fine. We have two nitrogens 1 nitrogen, so throw a 2 here. For each half reaction, balance the number of oxygens by adding water. So come back up here. We have 4 oxygens here, but none on the product side. So we have to put 4 waters, then we have what 2 * 3? That's six oxygens here as products. So I have to put 6 waters here.
Next, for Step 4, balance. For each half reaction, you're going to balance the number of hydrogens by adding H+. So if we come back up here we have 4 * 2 which is 8 hydrogens. So I have to put 8H+ here. Now both sides have 8 hydrogens. Then we have 6 * 2 which is 12 + 4 which is 16. I need to add 16 H+ ions here. Now both sides have 16 hydrogens. Then we go to step five. We balance the overall charge by adding electron well, the overall charge by adding electrons to the more positively charged side of each half reaction.
So how do we do that? Well, here we're going to say we have -1 and then we have 8 * + 1. So that's plus eight, which means the overall charge on this side is +7. For the product side, we have two manganese ions. So overall chart here is +2. Because water is neutral, it has no charge, so this side has a charge overall of +7. This side here has an overall charge of +2. I have to add enough electrons to the plus seven side so that it is also +2. So how many electrons do I need to add? To go from +7 to +2, you would need to add five electrons.
Let's go to the other side. Both N2H4 and H2O are neutral. They have no charges that we can see. So the overall charge here is 0. Then we have 2 * -1 which is -2, 16 * + 1 is plus 16, so this is plus 14. So we have plus fourteen overall here. Now we have to add enough electrons to the plus fourteen side so it has the same overall charge as a side width 0. So how many electrons do I need to add to go from plus 14 to 0? We have to add 14 electrons. So here now the number of electrons defer, so then you multiply to get the lowest common multiple between them.
O here we'd say that the lowest common multiple that they have between them is 70. So how do we get that? Well, we're going to say I'd have to multiply this here by 14 and multiply this one here by the five. When I do that, I'll get 70 electrons for each half reaction. Now at this point I'm going to bring down everything. Everything is getting multiplied by 14, so 14 MnO4- plus. So we're going to do 8 * 14 here. So when we do 8 * 14 here, that's going to give us a hundred and twelve H+ + 70 electrons. Product side would be 14 Mn2+ + 56 H2O go to the other half reaction everything is getting multiplied by five.
So 5N2H4 plus 30H2O gives me 10 NO3- plus. We're going to have here 80 H+ 70 electrons. Here we're going to combine the half reactions and crossover reaction intermediates. So remember, reaction intermediates are things that look the same except one's a product and one's a reactant. Electrons are always reaction intermediates and they must always completely cancel out. We have all thirty of these H2O's canceling out with 30 from here. That gives us 26 left. All eighty of these H+es cancel out with 80 from here, which leaves us with 32.
Now there's nothing else to cancel out. Nothing else is a reaction. Intermediate Bring down everything. So here bring down all the reactants and you can see the process is pretty long. So 14 Mn2+ + 10 NO3- gives ME 26 H2O. At this point all we've done is balance it if it were in an acidic solution. Now with the basic solution, we do step 7. Balance any remaining H+ by adding an equal amount of OH- to both sides of the equation. When H+ and OH- are on the same side, they combine together to form water. If water is on both sides of the equation, then treat them as reaction intermediates.
All right, so let's see what that means. So we look and see how much H+ we have left. We have 32 left as reactants, so we're going to add 32 OH- to this side, plus 32 OH- to this side. Remember when you have H+ and OH- together, they combine together to give me water. So we're going to have 14 MnO4- + 5 N2H4 + 32 H2O gives me 14 Mn2+ + 10 NO3- + 26 H2O + 32 OH-. Remember we said if water is on both sides, treat them as reaction intermediates. That means that all 26 of these cancel out and we have left here 6. So that means that my balanced equation in basic solution would be this.
OK. And then just bring this 32 OH- closer. So when we do that, this represents my balance equation in basic solution. So again, you can see it's pretty intense with the amount of steps, but as long as you can understand these steps and then use them, you can balance a redox reaction within any basic solution.