balance the charge in the two half reactions by multiplying the half reactions by the correct multiplication factors

Balance which equation?

Zn(s) + Fe3+ Zn2+ + Fe(s) (unbalanced)

thats the equation

To balance the charge in two half-reactions, you need to multiply each half-reaction by the appropriate multiplication factors. Here's how you can do it:

Step 1: Write down the two half-reactions you need to balance. For example, let's consider the combustion of hydrogen gas (H2) with oxygen gas (O2) to form water (H2O).

Half-reaction 1: H2 → 2H+ + 2e-
Half-reaction 2: O2 + 4H+ + 4e- → 2H2O

Step 2: Determine the least common multiple (LCM) of the electrons transferred in each half-reaction. In this example, the LCM of 2 and 4 is 4. So, we'll multiply the first half-reaction by 2 and the second half-reaction by 1.

Half-reaction 1 (multiplied by 2): 2H2 → 4H+ + 4e-
Half-reaction 2 (multiplied by 1): O2 + 4H+ + 4e- → 2H2O

Step 3: Check if the charges are now balanced. In this case, the charges are balanced since both sides of each half-reaction have the same total charge.

Step 4: Make sure the number of electrons transferred is the same in both half-reactions. In this example, the number of electrons transferred is the same (4e-).

Step 5: Finally, add the two balanced half-reactions together. Make sure to cancel out any common species on both sides of the equation. In this case, the equation becomes:

2H2 + O2 → 2H2O

By following these steps and multiplying the appropriate half-reactions by the correct multiplication factors, you can balance the charge in the two half-reactions.