2.1.1 Oxidation Number

In the previous section, we learned that redox reactions involve the transfer of electrons. However, in many reactions, particularly those involving covalent compounds, electrons are not completely transferred but are shared. To keep track of electrons in such cases, chemists use a concept called the oxidation number. It is a powerful bookkeeping tool that allows us to identify which elements are oxidized and which are reduced in any reaction.

Definition

The oxidation number (also known as the oxidation state) is defined as the apparent charge, positive or negative, which an element would have in a compound if the compound were purely ionic.

Simple Explanation: It is a hypothetical charge that an atom would have if all its bonds to atoms of different elements were 100% ionic. It helps us count how many electrons an atom has "lost" or "gained" compared to its neutral state.

Core Concept

The core concept is that oxidation numbers are a formalism used to track electrons. In a purely ionic compound like NaCl, the oxidation number of Na is +1 and Cl is -1, corresponding to the actual ions. In a covalent compound like CO_2, the bonds are polar, and the electrons are shared unequally. The oxidation number tells us the apparent charge carbon and oxygen would have if those shared electrons were completely transferred to the more electronegative atom.

An increase in oxidation number corresponds to oxidation (loss of electrons). A decrease in oxidation number corresponds to reduction (gain of electrons).

Rules for Assigning Oxidation Numbers

To use oxidation numbers correctly, you must follow a set of established rules. These rules are applied in order to determine the oxidation state of an element in a compound or ion.

1. Rule 1: Elements in their free (elemental) state have an oxidation number of zero. - Example: The oxidation number of each atom in O_2, H_2, Cl_2, Fe, and S_8 is 0.

2. Rule 2: The oxidation number of a monatomic ion is equal to its charge. - Example: The oxidation number of Na^+ is +1, Ca^{2+} is +2, Cl^- is -1, and O^{2-} is -2.

3. Rule 3: The oxidation number of fluorine is always -1 in all its compounds. - Example: In HF, NaF, and SF_6, the oxidation number of fluorine is -1.

• Exceptions:
• In peroxides (like H_2O_2 and Na_2O_2), oxygen has an oxidation number of -1.
• In superoxides (like KO_2), oxygen has an oxidation number of -12.
• In compounds with fluorine (like OF_2), oxygen has a positive oxidation number (+2).

5. Rule 5: The oxidation number of hydrogen is usually +1 when bonded to nonmetals and -1 when bonded to metals. - Examples: In H_2O and HCl, hydrogen is +1. In NaH and CaH_2, hydrogen is -1.

6. Rule 6: The oxidation number of Group 1 metals (Li, Na, K, etc.) is always +1. The oxidation number of Group 2 metals (Be, Mg, Ca, etc.) is always +2. - Examples: In NaCl, Na is +1. In MgO, Mg is +2.

7. Rule 7: The sum of the oxidation numbers of all atoms in a neutral compound is zero. - Example: In H_2O, (2 × +1) + (-2) = 0.

8. Rule 8: The sum of the oxidation numbers of all atoms in a polyatomic ion is equal to the charge on the ion. - Example: In the sulphate ion (SO_4^{2-}), the sum of the oxidation numbers of S and four O atoms must equal -2.

Intermediate Level

• We know H is +1 and O is -2.
• The sum must be zero: 2(H) + (S) + 4(O) = 0
• 2(+1) + S + 4(-2) = 0
• 2 + S - 8 = 0
• S = +6

Important Points

• - Oxidation Number (Oxidation State): The apparent charge an atom would have if all bonds were ionic.
• - Oxidation: An increase in oxidation number (loss of electrons).
• - Reduction: A decrease in oxidation number (gain of electrons).
• - Rule 1: Free elements have an oxidation number of 0.
• - Rule 4: Oxygen is usually -2 (exceptions: peroxides, superoxides, fluorides).
• - Rule 5: Hydrogen is usually +1 with nonmetals and -1 with metals.
• - Rule 7: The sum of oxidation numbers in a neutral compound is 0.
• - Rule 8: The sum of oxidation numbers in a polyatomic ion equals the ion's charge.

Remember

• - **Free elements = 0.**
• - **Group 1 = +1, Group 2 = +2.**
• - **Fluorine = -1 always.**
• - **Oxygen = -2 usually.**
• - Hydrogen = +1 with nonmetals, -1 with metals.
• - **Sum in a neutral compound = 0.**
• - **Sum in a polyatomic ion = its charge.**
• - Increase in oxidation number = oxidation.
• - Decrease in oxidation number = reduction.

Common Mistakes

• - Assuming oxygen is always -2. Forgetting the exceptions (like in peroxides, H_2O_2, where oxygen is -1) is a common error.
• - Assuming hydrogen is always +1. In metal hydrides like NaH, hydrogen is -1.
• - Forgetting the charge on a polyatomic ion. When finding the oxidation number of an element in a polyatomic ion like SO_4^{2-}, students often set the sum to zero instead of -2.
• - Incorrectly applying the rules. The rules must be applied in a logical order, starting with the most reliable ones (like Group 1 = +1) and working towards the unknown element.
• - Confusing oxidation number with the actual charge on a covalent atom. In a covalent molecule, the atoms do not have a real charge, but an apparent charge.

Quick Revision

The oxidation number is a fictitious charge assigned to an atom in a compound to keep track of electrons. It is based on the assumption that all bonds are purely ionic. There are specific rules for assigning these numbers: elements in their free state have an oxidation number of 0, the sum of oxidation numbers in a neutral compound is 0, and in a polyatomic ion, it equals the charge of the ion. Fluorine is always -1, oxygen is usually -2, and hydrogen is usually +1 (except in hydrides). By calculating the oxidation numbers of atoms in a reaction, you can determine which elements are oxidized (increase in oxidation number) and which are reduced (decrease).

60-Second Revision

Oxidation number is the hypothetical charge on an atom in a compound. Key rules: free elements are 0, Group 1 is +1, Group 2 is +2, O is usually -2, H is usually +1, F is always -1. The sum of oxidation numbers is 0 for a neutral compound and equals the charge for an ion. An increase in oxidation number is oxidation, and a decrease is reduction. Watch out for exceptions like peroxides where O is -1.

Frequently Asked Questions (FAQs)

Q1. What is the oxidation number of an element in its free state? Answer: The oxidation number of an element in its free (elemental) state is always zero. For example, the oxidation number of each oxygen atom in O_2 is 0, and the oxidation number of an iron atom in Fe metal is 0.

Q2. What is the oxidation number of oxygen in H_2O_2? Answer: The oxidation number of oxygen in hydrogen peroxide (H_2O_2) is -1. This is an exception to the general rule that oxygen is -2. Let's verify: Let the oxidation number of O be x. The oxidation number of H is +1. The sum must be zero: 2(+1) + 2(x) = 0 ⇒ 2 + 2x = 0 ⇒ 2x = -2 ⇒ x = -1.

Q3. How do you calculate the oxidation number of an element in a polyatomic ion? Answer: The sum of the oxidation numbers of all atoms in a polyatomic ion is equal to the charge on the ion. For example, in the permanganate ion (MnO_4^-), let the oxidation number of Mn be x and the oxidation number of O be -2. The sum must be -1: x + 4(-2) = -1 ⇒ x - 8 = -1 ⇒ x = +7.

Q4. What is the oxidation number of hydrogen in sodium hydride (NaH)? Answer: The oxidation number of hydrogen in sodium hydride is -1. This is because hydrogen is bonded to a metal (sodium), and it is an exception to the rule that hydrogen is always +1. Sodium is a Group 1 metal, so its oxidation number is +1. Since NaH is a neutral compound, the sum must be zero: (+1) + (x) = 0 ⇒ x = -1.

Q5. How can you determine if an element is oxidized or reduced? Answer: You determine if an element is oxidized or reduced by comparing its oxidation number before and after the reaction. If its oxidation number increases, the element has been oxidized. If its oxidation number decreases, the element has been reduced.

Q6. What is the difference between an element's actual charge and its oxidation number? Answer: An element's actual charge is the real electrical charge it carries as an ion (e.g., Na^+ has a charge of +1). Its oxidation number is a formal, hypothetical charge assigned by assuming all bonds are purely ionic. For example, in a covalent molecule like CO_2, the atoms do not have a real charge, but the oxidation number of carbon is +4 and that of oxygen is -2.

Q7. What is the oxidation number of chlorine in Cl_2? Answer: The oxidation number of chlorine in Cl_2 is 0, because it is in its elemental form. Rule 1 states that elements in their free state have an oxidation number of zero.

Q8. How do you find the oxidation number of an element in a compound with multiple unknown elements? Answer: This is not possible unless there are enough independent equations. Usually, you will have to use the known rules to assign oxidation numbers to all but one element. The remaining one is then calculated by applying the rule that the sum of the oxidation numbers is either zero (for a neutral compound) or equal to the charge (for a polyatomic ion). If there are two unknown elements, you would need additional information to solve for both.

Multiple Choice Questions (MCQs)

• Q1. What is the oxidation number of sulfur in H_2SO_4?
• A. -2
• B. 0
• C. +2
• D. +6
• Correct Answer: D
• Explanation: The sum of oxidation numbers is zero: 2(+1) + x + 4(-2) = 0 ⇒ x = +6.

• Q2. What is the oxidation number of oxygen in H_2O_2?
• A. -2
• B. -1
• C. 0
• D. +1
• Correct Answer: B
• Explanation: In peroxides, oxygen has an oxidation number of -1. 2(+1) + 2(x) = 0 ⇒ x = -1.

• Q3. What is the oxidation number of hydrogen in NaH?
• A. +1
• B. -1
• C. 0
• D. +2
• Correct Answer: B
• Explanation: Hydrogen bonded to a metal has an oxidation number of -1. Na is +1, so H must be -1 to make the sum zero.

• Q4. What is the oxidation number of manganese in KMnO_4?
• A. +2
• B. +4
• C. +6
• D. +7
• Correct Answer: D
• Explanation: 1(+1) + x + 4(-2) = 0 ⇒ 1 + x - 8 = 0 ⇒ x = +7.

• Q5. What is the oxidation number of chromium in K_2Cr_2O_7?
• A. +3
• B. +4
• C. +6
• D. +7
• Correct Answer: C
• Explanation: 2(+1) + 2(x) + 7(-2) = 0 ⇒ 2 + 2x - 14 = 0 ⇒ 2x = 12 ⇒ x = +6.

• Q6. What is the oxidation number of an element in its free state?
• A. +1
• B. -1
• C. 0
• D. +2
• Correct Answer: C
• Explanation: By definition, elements in their elemental form have an oxidation number of zero.

• Q7. In the reaction Fe → Fe^{3+} + 3e^-, what is the change in oxidation number?
• A. Decrease by 3
• B. Increase by 3
• C. No change
• D. Decrease by 2
• Correct Answer: B
• Explanation: The oxidation number of Fe goes from 0 to +3, which is an increase of 3.

• Q8. Which of the following is the correct oxidation number for oxygen in most compounds?
• A. -1
• B. -2
• C. 0
• D. +2
• Correct Answer: B
• Explanation: The general rule is that oxygen has an oxidation number of -2 in most compounds, with exceptions like peroxides and compounds with fluorine.

• Q9. What is the oxidation number of nitrogen in NO_3^-?
• A. +3
• B. +4
• C. +5
• D. +6
• Correct Answer: C
• Explanation: For the polyatomic ion NO_3^-, the sum must be -1: x + 3(-2) = -1 ⇒ x - 6 = -1 ⇒ x = +5.

• Q10. What is the oxidation number of hydrogen in CH_4?
• A. -1
• B. 0
• C. +1
• D. +4
• Correct Answer: C
• Explanation: Hydrogen bonded to a nonmetal (carbon) has an oxidation number of +1. To check: C is -4 and H is +1. (-4) + 4(+1) = 0.