Unit 4: Stoichiometry of Chemical Reactions

Introduction to Redox Reactions

Earth's atmosphere contains approximately 20% molecular oxygen ($\text{O}<em>2$), which is a chemically reactive gas essential for the metabolism of aerobic organisms and in numerous environmental processes that shape the world. The term "oxidation" originally referred specifically to chemical reactions involving molecular oxygen ($\text{O}</em>2$), but it has since evolved to encompass a broader category known as oxidation-reduction (redox) reactions. A redox reaction is defined as any reaction in which there is a transfer of electrons between chemical species.

Examples of Redox Reactions

A crucial example of a redox reaction involves the transfer of electrons leading to the formation of ionic products, such as the reaction between sodium and chlorine, yielding sodium chloride:

$2\text{Na}(s) + \text{Cl}_2(g) \rightarrow 2\text{NaCl}(s)$

This reaction can be analyzed through half-reactions:

1. Sodium half-reaction:

   $2\text{Na}(s) \rightarrow 2\text{Na}^+(s) + 2e^-$

2. Chlorine half-reaction:

   $\text{Cl}_2(g) + 2e^- \rightarrow 2\text{Cl}^-(s)$

In this context, sodium loses electrons (oxidation), while chlorine gains electrons (reduction). Therefore, sodium can be described as a reducing agent (reductant) and chlorine as an oxidizing agent (oxidant).

Definitions:

• Oxidation: Loss of electrons.

• Reduction: Gain of electrons.

• Reducing agent: Species that is oxidized.

• Oxidizing agent: Species that is reduced.

Non-Electron Transfer Redox Reactions

Not all redox processes involve direct electron transfer. For instance, the reaction:

$\text{H}<em>2(g) + \text{Cl}</em>2(g) \rightarrow 2\text{HCl}(g)$

produces a covalent compound without explicit electron transfer. This demonstrates the need for a more generalized concept: the oxidation number (or oxidation state).

Oxidation Numbers

The oxidation number of an element in a compound indicates the charge its atoms would have if the compound were ionic. Guidelines to assign oxidation numbers are as follows:

1. Oxidation number in elemental substances is zero.

2. Oxidation number of a monatomic ion equals the ion's charge.

3. Common oxidation states:

   • Hydrogen: +1 when with nonmetals; -1 when with metals.

   • Oxygen: -2 in most compounds; -1 in peroxides ($\text{O}_2^{2-}$); +1 when bonded to fluorine.

   • Halogens: -1 for fluorine always; -1 for other halogens unless bonded to oxygen or other halogens (which may have positive oxidation states).

4. The sum of the oxidation numbers for atoms in a molecule or polyatomic ion equals the overall charge.

Notation Convention

• Charge: written as number followed by sign (e.g., 2+).

• Oxidation Number: written as sign followed by number (e.g., +2).

Example: Assigning Oxidation Numbers

1. H₂S:

   • Hydrogen oxidation state: +1.

   • Sulfur's oxidation state:

     $0 = (2 \times (+1)) + (1 \times x) \rightarrow x = 0 - 2 = -2$

   • Thus, oxidation states: H: +1, S: -2.

2. SO₃²⁻:

   • Oxygen oxidation state: -2.

   • Sulfur oxidation state:

     $-2 = (3 \times (-2)) + (1 \times x) \rightarrow x = +4$

3. Na₂SO₄:

   • Sodium: +1, Oxygen: -2.

   • Sulfur oxidation state:

     $(2 \times (+1)) + x + (4 \times (-2)) = 0 \rightarrow 2 + x - 8 = 0 \rightarrow x = +6$

Half-Reaction Method for Balancing Redox Reactions

The half-reaction method proves beneficial when balancing redox reactions in aqueous media, particularly with water, hydronium, and hydroxide ions. Key steps include:

1. Write the two half-reactions for the redox process.

2. Balance all elements except oxygen and hydrogen.

3. Balance oxygen by adding water ($\text{H}_2\text{O}$) molecules.

4. Balance hydrogen by adding conventionally $\text{H}^+$ ions.

5. Balance the charge by adding electrons.

6. Equalize electron transfer by adjusting coefficients accordingly.

7. Combine and simplify half-reactions while canceling identical species on both sides.

8. For basic media, further adjustments with $\text{OH}^-$ may be necessary.

9. Confirm that all atoms and charges are balanced.

Example: Balancing Redox Reactions in Acidic Solution

• Write half-reactions for the reduction of dichromate ($\text{Cr}<em>2\text{O}</em>7^{2-}$) by iron(II) ($\text{Fe}^{2+}$):

• Balanced equations:

1. For iron:

   $\text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^-$

2. For dichromate:

   $\text{Cr}<em>2\text{O}</em>7^{2-} + 14\text{H}^+ + 6e^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}$

Combining Half-Reactions:

After manipulating coefficients, the complete balanced equation combines into:

$6\text{Fe}^{2+} + \text{Cr}<em>2\text{O}</em>7^{2-} + 14\text{H}^+ \rightarrow 6\text{Fe}^{3+} + 2\text{Cr}^{3+} + 7\text{H}_2\text{O}$

Summary of Oxidation-Reduction Reactions

Redox reactions are essential in various chemical processes, defined by their electron transfer characteristics, oxidation numbers, and half-reaction methods. Understanding these principles enables clearer insights into the behavior of reactants and products in chemical reactions, ultimately creating pathways to theoretical applications in chemistry and beyond.