Question

The sum of all the oxidation states of all the atoms in \(\mathrm{H}_{3} \mathrm{PO}_{4}\) is ______

Short answer

The sum of all the oxidation states of all the atoms in H₃PO₄ is \(0\).

Step-by-step solution

Assign oxidation states

We have the compound H₃PO₄, and we need to find the oxidation state of each atom. We can use the following rules to assign oxidation states: 1. The oxidation state of a free element (an atom that is not in a compound) is zero. 2. The oxidation state of a monatomic ion is equal to its charge. 3. Hydrogen has an oxidation state of +1 in most of its compounds. 4. Oxygen has an oxidation state of -2 in most of its compounds. Applying these rules, we can assign the oxidation states: - Hydrogen (H), has an oxidation state of +1 - Phosphorus (P), we will determine later - Oxygen (O), has oxidation state -2

Use the oxidation state sum rule

The sum of the oxidation states of all atoms in a neutral compound is zero. Therefore, we can set up the following equation to find the oxidation state of phosphorus (P): 3(+1) + x + 4(-2) = 0 Where x is the oxidation state of phosphorus. Now let's solve for x.

Solve for the oxidation state of phosphorus

Now we will solve the equation for x: 3(+1) + x + 4(-2) = 0 3 - 8 + x = 0 x = 5 So the oxidation state of phosphorus (P) is +5.

Calculate the sum of oxidation states

Finally, we can now calculate the sum of all the oxidation states of all the atoms in H₃PO₄: sum = 3(+1) + (+5) + 4(-2) sum = 3 + 5 - 8 sum = 0 The sum of all the oxidation states of all the atoms in H₃PO₄ is 0.

Key concepts

Assigning Oxidation States

Understanding the oxidation states of different atoms in a compound is fundamental in chemistry, especially when dealing with redox reactions. To assign oxidation states, chemists follow a hierarchy of rules designed to reflect the electron distribution in various bonding scenarios.

Oxidation states are a theoretical concept where electrons in chemical bonds are assigned to the more electronegative element. The rules for assigning oxidation states include:

• Free elements have an oxidation state of 0.
• For monatomic ions, the oxidation state is the same as its charge.
• Hydrogen usually has an oxidation state of +1.
• Oxygen usually has an oxidation state of -2, except in peroxides or with fluorine.

By using these rules, we can systematically determine the oxidation state of each atom in a compound, which is a crucial first step in understanding the compound's chemical behavior.

Oxidation State Sum Rule

The oxidation state sum rule is simple yet powerful: for a neutral compound, the sum of the oxidation states of all the atoms must equal zero. This is critical when working with compounds where the oxidation states of atoms are not immediately obvious.

To apply this rule, you start by assigning known oxidation states based on the rules mentioned earlier and then solve for the unknown oxidation states to ensure they sum up to zero. In ionic compounds, the sum of oxidation states equals the net charge of the compound. Remember that polyatomic ions will also have a net oxidation state equal to their charge. Hence, the sum rule helps you balance the electron 'accounting' within a molecule or ion, laying the groundwork for further chemical analysis or reaction balance.

Solving for Oxidation State

Once you've assigned the known oxidation states and applied the sum rule, solving for the unknown oxidation state becomes an exercise in algebra. Suppose you've assigned oxidation states to some atoms in a compound, and only one atom's oxidation state remains unknown. You can set up an equation where the sum of all oxidation states equals zero (for neutral compounds) or the compound's charge (for ions).

For example, in the compound H₃PO₄, you would first assign +1 to hydrogen based on rule 3 and -2 to oxygen based on rule 4. You would then introduce a variable for the unknown oxidation state of phosphorus. By solving the ensuing equation, you can find the oxidation state of phosphorus, which, when combined with the known values, will satisfy the sum rule and allow you to fully understand the electron distribution in the compound.