Balance the following equations. Show all work.

MnO4- + Zn -> Mn2+ + Zn2+

Here is a site that gives a great deal of information about balancing redox equations.

http://www.chemteam.info/Redox/Redox.html

Hint: Mn changes from an oxidation state of +7 on the left to +2 on the right. Zn changes from zero on the left to +2 on the right.

To balance the given equation MnO4- + Zn -> Mn2+ + Zn2+, we need to make sure that the number of atoms of each element is the same on both sides of the equation.

Let's start by balancing the manganese (Mn) atoms. On the left side, we have 1 Mn atom in MnO4-, and on the right side, we have 1 Mn atom in Mn2+. Since the number of Mn atoms is already balanced, we can move on to the other elements.

Next, let's balance the oxygen (O) atoms. On the left side, we have 4 O atoms in MnO4-, and on the right side, we have 0 O atoms. To balance the oxygens, we need to add 4 O atoms on the right side. We can do this by adding 2 H2O molecules on the right side, as each H2O molecule contains 1 O atom.

The equation now looks like this: MnO4- + Zn -> Mn2+ + Zn2+ + 2 H2O

Now let's balance the hydrogen (H) atoms. On the left side, we have 0 H atoms, and on the right side, we have 4 H atoms in 2 H2O molecules. Since the hydrogen atoms are already balanced, we can move on to the final element.

Finally, let's balance the zinc (Zn) atoms. On the left side, we have 1 Zn atom, and on the right side, we have 1 Zn atom in Zn2+. The zinc atoms are already balanced.

Therefore, the balanced equation is: MnO4- + Zn -> Mn2+ + Zn2+ + 2 H2O

To balance the given equation MnO4- + Zn -> Mn2+ + Zn2+, we need to ensure that there are an equal number of each element on both sides of the equation.

Let's start with the element Zn. There is only one atom of Zn on both sides of the equation, so it is already balanced.

Next, let's balance the element Mn. On the left side, there is one Mn atom present, and on the right side, there is one Mn atom as well. Therefore, Mn is also balanced.

Now, let's balance the oxygen (O) atoms. On the left side, there are 4 oxygen atoms from MnO4-, and on the right side, there are no oxygen atoms. To balance the oxygen atoms, we need to add 4 oxygen atoms to the right side of the equation. We can do this by adding 4 H2O molecules to the right side:

MnO4- + Zn -> Mn2+ + Zn2+ + 4 H2O

Now, let's balance the hydrogen (H) atoms. On the left side, there are no hydrogen atoms, and on the right side, there are 8 hydrogen atoms from the 4 H2O molecules. To balance the hydrogen atoms, we can add 8 H+ ions to the left side of the equation:

MnO4- + Zn + 8 H+ -> Mn2+ + Zn2+ + 4 H2O

Finally, let's balance the charges. On the left side, the total charge is -1 from the MnO4- ion, and on the right side, the total charge is +2 from the Mn2+ and Zn2+ ions. To balance the charges, we can add 3 electrons (e-) to the left side:

MnO4- + Zn + 8 H+ + 3 e- -> Mn2+ + Zn2+ + 4 H2O

Now, the equation is balanced both in terms of atoms and charges.