Problem 16 - Chemistry Principles and Practice

Question

Assign the oxidation numbers of all atoms in the following species. (a) \(\mathrm{KMnO}_{4}\) (b) \(\mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{Cl}_{2}\)

Step-by-Step Solution

Answer

In KMnO4, K = +1, Mn = +7, O = -2. In H2O, H = +1, O = -2. In Cl2, Cl = 0.

Step 1: Assign known oxidation numbers

First, identify oxidation numbers that are typically fixed based on the atom's usual charge. Potassium (K) typically has an oxidation number of +1, oxygen (O) has an oxidation number of -2, and hydrogen (H) typically has an oxidation number of +1.

Step 2: Assign oxidation numbers in KMnO4

For \( \mathrm{KMnO}_{4} \), potassium (K) is +1 and oxygen (O) is -2. Let the oxidation number of manganese (Mn) be \( x \). From the formula, \( \mathrm{x + 1 + 4(-2) = 0} \). Solve for \( x \):\[x + 1 - 8 = 0\]\[x = 7\]So, Mn has an oxidation number of +7.

Step 3: Assign oxidation numbers in H2O

In \( \mathrm{H}_{2} \mathrm{O} \), each hydrogen (H) is +1, let oxygen (O) be \( x \). The equation is:\[2(+1) + x = 0\]Solving gives:\[2 + x = 0\]\[x = -2\]Thus, O has an oxidation number of -2, and each H is +1.

Step 4: Assign oxidation numbers in Cl2

In \( \mathrm{Cl}_{2} \), each chlorine (Cl) atom is in its elemental form, so each Cl atom has an oxidation number of 0.

Key Concepts

Chemical Species

Chemical species refer to the broad varieties of atoms, molecules, ions, or any other chemical unit that occurs in a chemical process. They are the basic entities that participate in chemical reactions and determine the reaction's course.

In essence, a chemical species is any chemical substance or ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on a defined timescale.

• An atom, such as oxygen in its elemental form, is a distinct chemical species.
• A molecule like \( \mathrm{H}_2 \) or \(\mathrm{Cl}_2\) is a specific type of chemical species.
• Ions, such as the potassium ion in \(\mathrm{KMnO}_4\), are charged entities also considered chemical species.

Understanding chemical species is crucial because it helps us determine the properties and reactions of chemicals, including their oxidation numbers. Correctly assigning oxidation numbers to atoms within a chemical species is vital for identifying reaction mechanisms, especially in redox reactions.

Oxidation States

Oxidation states, also known as oxidation numbers, are a value assigned to an element in a compound reflecting its degree of oxidation, which relates to the number of electrons it gains or loses. These are essential for determining how electrons are distributed in a chemical reaction.

Here are some facts about oxidation states:

• Elements in their pure form have an oxidation state of zero. For example, in \(\mathrm{Cl}_2\), each chlorine atom has an oxidation state of 0.
• Oxidation states help assess the electron transfer between elements in compounds, exemplified by manganese in \(\mathrm{KMnO}_{4}\), where Mn has an oxidation state of +7.
• Each chemical element's reference state usually has a consistent oxidation state, such as +1 for hydrogen in most compounds and -2 for oxygen.

Assigning the correct oxidation state is critical for understanding chemical reaction pathways, especially in redox chemistry, as it highlights the movement of electrons.

Redox Reactions

Redox reactions are chemical reactions involving the transfer of electrons between two species. The word 'redox' is a combination of reduction and oxidation, both of which occur simultaneously during these reactions.

Understanding redox reactions involves knowing:

• Oxidation refers to the loss of electrons by a molecule, atom, or ion. For example, in \(\mathrm{KMnO}_{4}\), manganese undergoes oxidation, attaining a +7 oxidation state.
• Reduction is the gain of electrons by a molecule, atom, or ion. Consider water, \(\mathrm{H}_2\mathrm{O}\); oxygen often undergoes reduction to its typical -2 state when forming compounds.
• Redox reactions are crucial for various real-world processes like cellular respiration, combustion, and even corrosion.

These reactions rely heavily on the balancing of oxidation numbers, ensuring that the total increase in oxidation numbers in one part of the reaction equals the total decrease in another, maintaining electron conservation.