Since there is no overall charge on the compound the oxidation states must cancel out. Although the oxidation state of hydrides are +1, there are two in the compound that must be accounted for. The same is true for oxygen; although the oxidation number of oxygen is -2, there are four oxygens present accounting for a total of -8. The +2 state contribution from the hydrides and -8 from the oxygens results in a -6 charge. The oxidation state on sulfur must be +6 for the molecule to be neutral.

Since the calcium ion has a charge of +2, the dichromate anion must have a charge of -2. Oxygen always has an oxidation number of -2, so the seven oxygens in the molecule have a total number of -14. That leaves a charge of +12 that the two chromiums must balance out (-2 - (-14) = 12). Each chromium must therefore have an oxidation number of +6.

When applying oxidation numbers there are certain hierarchical rules that must be followed. 

1. The sum of oxidation states of all the elements in a molecule must add up to the overall charge. 

2. Group 1 and Group 2 elements have +1 and +2 oxidation states, respectively.

3. Fluorine has an oxidation state of –1.

4. Hydrogen has an oxidation state of +1 (except in metal hydrides).

5. Oxygen has an oxidation state of –2.

6. Elements of the same group (excluding transition metals) generally have the same oxidation state.

When applying the oxidation state to HNO₃, hydrogen has a +1 oxidation state, and each of the oxygen molecules has a –2 oxidation state. Since there is only one hydrogen molecule and three oxygen molecules, the oxidation state of nitrogen must balance out the charge of the hydrogen molecule and oxygen molecules combined.

Nitrogen must have a +5 oxidation state.

When applying oxidation numbers there are certain hierarchical rules that must be followed. 

1. The sum of oxidation states of all the elements in a molecule must add up to the overall charge. 

2. Group 1 and Group 2 elements have +1 and +2 oxidation states, respectively.

3. Fluorine has an oxidation state of –1.

4. Hydrogen has an oxidation state of +1 (except in metal hydrides).

5. Oxygen has an oxidation state of –2.

6. Elements of the same group (excluding transition metals) generally have the same oxidation state.

Following the oxidation rules, group 1 elements must have an oxidation number of +1.

To balance out the overall charge of zero, the hydrogen in this compound must have an oxidation state of –1. Note that NaH is a metal hydride; therefore, the oxidation state of hydrogen is not necessarily +1.

The sum of oxidation numbers of each element in this compound must add to the total charge of -2. Hydrogen always has an oxidation number of +1, and oxygen always has an oxidation number of -2. 

So, in total for oxygen we have (4) * (-2) = -8, and for hydrogen we have (4) * (+1) = +4.

Combining the oxygen and hydrogen, (+4) + (-8) = -4, so we need an additional +2 to achieve the total charge of -2. Zn must provide this balancing charge, and have an oxidation number of +2.

Oxidation number is a concept that you will also encounter in electrochemistry lectures. It is used to track electrons in an oxidation-reduction reaction. Overall, the sum of the oxidation states of all of the atoms in the molecule must equal the overall charge on the molecule. It is important to remember some of the commonly accepted oxidation states for atoms, so that you can predict the oxidation numbers on other atoms. Here are some key oxidation numbers useful to know for the MCAT:

1. Atoms in elemental form have an oxidation state of 0.

2. Halogens are commonly given an oxidation state of –1.

3. Hydrogen and alkali metals are commonly given an oxidation state of +1.

4. Oxygen is commonly given an oxidation number of –2. 

Keeping these rules in mind, we can assume that the hydrogens and oxygens in the two compounds maintain the same oxidation state. Chlorine, however, is attached to one less oxygen in HClO₃. As a result, the oxidation state of Cl has decreased from +7 to +5, when comparing HClO₄ to HClO₃.

We can calculate the oxidation number in each answer to find the greatest value.

In , oxygen will have a value of and the molecule is neutral. Sulfur must have an oxidation number of to balance the three oxygens.

In , oxygen will have a value of and the molecule is neutral. Carbon must have an oxidation number of  to balance the two oxygens.

In , chlorine will have a value of  and the molecule is neutral. Aluminum must have an oxidation number of  to balance the three chlorines.

In , calcium will have a value of  and the molecule is neutral. Sulfur must have an oxidation number of  to balance the calcium.

is a molecule comprised of a single element; each atom will have an oxidation number of .

To find the oxidation number, first remember that the total charge must be preserved. The total charge of the perchlorate ion is .

Each oxygen will have an oxidation number of . The oxidation of chlorine must be used to balance this negative charge.

The rules for oxidation state note that certain atoms will have constant oxidation values, while others are more likely to vary. Oxygen, for example, will always have an oxidation state of , alkali metals will always have an oxidation state of , and hydrogen will (almost) always have an oxidation state of .

All of the given compounds are neutral, meaning that their oxidation numbers must sum up to zero. Using our listed rules to look at these molecules, we can try to find any missing values.

Chromium in potassium dichromate is the only atom in this set to have an oxidation state of .

The sum of the oxidation numbers of each atom in a molecule must equal the net charge of the molecule.

Oxygen will always have an oxidation number of . In we can find the oxidation number of manganese with the following equation:

Solving this out, we can see that the charge on manganese must be .

In the manganese ions, there is only one atom and the net charge is . The oxidation of this manganese atom must be to balance the ionic charge.

The difference between these oxidation numbers is: