Arnav P. answered 04/22/23
Undergraduate Biochemistry Student Specializing in SAT/ACT Prep
When splitting up a redox reaction into two half-reactions, you want to ask yourself "What is being oxidized and what is being reduced?" To answer this, we can look at the oxidation states for each element, and see how they're changing. Let's take the first reaction as an example:
0 +2 -1 +2 -1 0
Mg(s) + CoBr2 --> MgBr2 + Co(s)
As you can see, looking at our oxidation states, Br stayed at -1, Co went from +2 to 0, and Mg went from 0 to +2. Oxidation is an increase in the oxidation state, and reduction is a decrease. So we can say that Co is being reduced and Mg is being oxidized. Now we make up our half reactions. To reduce something, you add electrons, and to oxidize something, you take away electrons. Just add the appropriate amount of electrons to cause the change in oxidation state:
Mg(s) --> Mg(aq) + 2e-
Co(aq) + 2e- --> Co(s)
And these are our 2 half-reactions that make up the overall redox reaction. The Mg reaction is oxidation (you know this because electrons are in the product), and the Co reaction is reduction (electrons are reactants). Try the same process for the second example you gave. You should end up with something like this:
Cu(s) --> Cu(aq) + 2e-
Au(aq) + e- --> Au(s)
(Because the numbers of electrons are different here, you would have to balance the reaction to create a whole overall redox equation, but that's a different topic.)