Question

In each of the following reactions, identify which element is oxidized and which is reduced by assigning oxidation numbers. a. \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{C}(s) \rightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}(g)\) b. \(\mathrm{Mg}(s)+2 \mathrm{HBr}(a q) \rightarrow \mathrm{MgBr}_{2}(a q)+\mathrm{H}_{2}(g)\) c. \(2 \cos (s)+S(s) \rightarrow C o_{2} S_{3}(s)\) d. \(2 \mathrm{Ag}(s)+2 \mathrm{HNO}_{3}(a q) \rightarrow 2 \mathrm{AgNO}_{3}(a q)+\mathrm{H}_{2}(g)\)

Short answer

In the given reactions: a. Iron (Fe) is reduced from +3 to 0, and carbon (C) is oxidized from 0 to +2. b. Magnesium (Mg) is oxidized from 0 to +2, and hydrogen (H) is reduced from +1 to 0. c. Carbon (C) is oxidized from +2 to +4, and sulfur (S) is reduced from 0 to -2. d. Silver (Ag) is oxidized from 0 to +1, and hydrogen (H) is reduced from +1 to 0.

Step-by-step solution

Assign oxidation numbers

: In \(Fe_{2}O_{3}\), oxygen has an oxidation number of -2, so iron has an oxidation number of +3. In \(C(s)\), the oxidation number of carbon is 0. In \(Fe(s)\), the oxidation number of iron is 0. In \(CO(g)\), the oxidation number of carbon is +2 and oxygen is -2.

Determine changed oxidation numbers

: Iron changed from +3 to 0, and carbon changed from 0 to +2.

Identify oxidized and reduced elements

: Iron is reduced (gained electrons) from +3 to 0, and carbon is oxidized (lost electrons) from 0 to +2. b. \(Mg(s)+2 HBr(aq) \rightarrow MgBr_{2}(aq)+H_{2}(g)\)

Assign oxidation numbers

: In \(Mg(s)\), the oxidation number of magnesium is 0. In \(HBr(aq)\), the oxidation number of hydrogen is +1 and bromine is -1. In \(MgBr_{2}(aq)\), the oxidation number of magnesium is +2 and bromine is -1. In \(H_{2}(g)\), the oxidation number of hydrogen is 0.

Determine changed oxidation numbers

: Magnesium changed from 0 to +2, and hydrogen changed from +1 to 0.

Identify oxidized and reduced elements

: Magnesium is oxidized (lost electrons) from 0 to +2, and hydrogen is reduced (gained electrons) from +1 to 0. c. \(2 CO(s)+S(s) \rightarrow Co_{2}S_{3}(s)\)

Assign oxidation numbers

: In \(CO(s)\), the oxidation number of carbon is +2 and oxygen is -2. In \(S(s)\), the oxidation number of sulfur is 0. In \(Co_{2}S_{3}(s)\), the oxidation number of carbon is +4 and sulfur is -2.

Determine changed oxidation numbers

: Carbon changed from +2 to +4, and sulfur changed from 0 to -2.

Identify oxidized and reduced elements

: Carbon is oxidized (lost electrons) from +2 to +4, and sulfur is reduced (gained electrons) from 0 to -2. d. \(2 Ag(s)+2 HNO_{3}(aq) \rightarrow 2 AgNO_{3}(aq)+H_{2}(g)\)

Assign oxidation numbers

: In \(Ag(s)\), the oxidation number of silver is 0. In \(HNO_{3}(aq)\), the oxidation number of hydrogen is +1, nitrogen is +5, and oxygen is -2. In \(AgNO_{3}(aq)\), the oxidation number of silver is +1, nitrogen is +5, and oxygen is -2. In \(H_{2}(g)\), the oxidation number of hydrogen is 0.

Determine changed oxidation numbers

: Silver changed from 0 to +1, and hydrogen changed from +1 to 0.

Identify oxidized and reduced elements

: Silver is oxidized (lost electrons) from 0 to +1, and hydrogen is reduced (gained electrons) from +1 to 0.

Key concepts

Oxidation Numbers

Oxidation numbers, also known as oxidation states, signify the charge of an atom if it were completely ionic. They help us track how electrons are transferred between atoms in chemical reactions.
In simple terms, oxidation numbers allow us to determine which atoms gain or lose electrons during the reaction. For instance, consider the compound \(Fe_{2}O_{3}\). Oxygen typically has an oxidation number of \(-2\), and since there are three oxygen atoms, the total for oxygen is \(-6\).
To balance this, iron must have a total oxidation number of \(+6\), distributed as \(+3\) per iron atom. Similarly, in reactions such as \(Mg + 2HBr \rightarrow MgBr_2 + H_2\), magnesium starts with 0 and ends at \(+2\), indicating it lost electrons. By figuring out these oxidation numbers, you can easily see which substances are oxidized or reduced in a chemical reaction.

Electron Transfer

Electron transfer is the key action in oxidation-reduction reactions, also known simply as redox reactions. In these reactions, electrons move between reactants, which alters their oxidation states.
An element that loses electrons is said to be oxidized, whereas one that gains electrons is reduced. Let's illustrate this with the equation \(Mg + 2HBr \rightarrow MgBr_2 + H_2\). Here, magnesium gives up electrons, going from an oxidation state of 0 to \(+2\), while hydrogen gains electrons, reducing from \(+1\) to 0.

• Oxidation: Loss of electrons is often accompanied by an increase in oxidation number.
• Reduction: Gain of electrons typically results in a decrease in oxidation number.

By understanding who is losing and gaining electrons, you can identify which substances are behaving as reducing or oxidizing agents in the equation.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through the formation and breaking of bonds. Redox reactions are a specific type of chemical reaction characterized by the transfer of electrons.
Consider the reaction \(Fe_{2}O_{3} + 3C \rightarrow 2Fe + 3CO\), where iron and carbon undergo changes. Here, iron is reduced due to the gain of electrons, while carbon is oxidized as it loses electrons. This electron transfer is essential to drive the reaction to completion.

• Reactants: Initial compounds or elements before the reaction takes place.
• Products: New substances formed as a result of the reaction.

In chemical reactions like these, tracking electron transfer through oxidation numbers is crucial. This allows chemistry students to understand how atoms interact and change during the process, which is the foundation of studying chemistry.