Problem 87 - Chemistry The Central Science In Si Units

Question

Iron corrodes to produce rust, \(\mathrm{Fe}_{2} \mathrm{O}_{3},\) but other corrosion products that can form are Fe(O)(OH), iron oxyhydroxide, and magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4} \cdot(\mathbf{a})\) What is the oxidation number of Fe in iron oxyhydroxide, assuming oxygen's oxidation number is \(-2 ?\) (b) The oxidation number for Fe in magnetite was controversial for a long time. If we assume that oxygen's oxidation number is -2 , and Fe has a unique oxidation number, what is the oxidation number for Fe in magnetite? (c) It turns out that there are two different kinds of Fe in magnetite that have different oxidation numbers. Suggest what these oxidation numbers are and what their relative stoichiometry must be, assuming oxygen's oxidation number is -2 .

Step-by-Step Solution

Answer

Fe's oxidation number in Fe(O)(OH) is +1; in Fe3O4 it was thought to be non-integral with +2 and +3 mixed states; stoichiometry balances to 2Fe(+2) and 1Fe(+3).

Step 1: Identify the Composition of Iron Oxyhydroxide

Iron oxyhydroxide is represented as \( ext{Fe(O)(OH)}\). This compound contains one iron (Fe), one oxygen (O), and one hydroxide group (OH). We need to identify the oxidation number of Fe in this compound, assuming the oxidation number for oxygen is -2.

Step 2: Assign Known Oxidation Numbers

The oxidation number of oxygen is -2. In the hydroxide ion (OH\(^-\)), the hydroxide overall must sum to -1 because that is its charge. Thus, hydrogen has an oxidation number of +1.

Step 3: Calculate the Oxidation Number of Fe in Iron Oxyhydroxide

Let the oxidation number of Fe be \(x\). In \( ext{Fe(O)(OH)}\), the sum of oxidation numbers must equal zero: \(x + (-2) + (+1) = 0\). Simplifying, we find \(x - 2 + 1 = 0\), or \(x = +1\). So, the oxidation number of Fe in Fe(O)(OH) is +1.

Step 4: Identify the Composition of Magnetite

Magnetite is represented as \( ext{Fe}_3 ext{O}_4\). To check for the oxidation state where Fe has a single oxidation number, calculate assuming Fe has the same oxidation state throughout.

Step 5: Calculate a Unique Oxidation Number for Fe in Magnetite

Assume each oxygen has an oxidation number of -2. Let Fe's oxidation number be \(x\). In \( ext{Fe}_3 ext{O}_4\), the equation is \(3x + 4(-2) = 0\). Solving gives \(3x - 8 = 0\) or \(x = rac{8}{3}\), which is not possible for simple integer oxidation numbers.

Step 6: Investigate Different Kinds of Fe in Magnetite

Due to the fractional result, consider possible different oxidation numbers of Fe: one could be +2 and the other +3. The mixed valency gives the sum: \(2 imes 2 + 1 imes 3 = 7\). For three Fe atoms, the overall sum is 3 units of \(+x\) which equals the 8 from oxygen ions: \(3x = 8 + 1\) (using integer values with possibility of split valency shown as 2Fe\(+2\), 1Fe\(+3\)).

Step 7: Determine Relative Stoichiometry

Consequently, stoichiometry must satisfy: 2 in +2 state and 1 in +3 state to align with \(3 imes 2.67\) net correction due to presence of fractional oxidation states.

Key Concepts

Understanding Iron Oxyhydroxide

Iron oxyhydroxide has the chemical formula \( \text{Fe(O)(OH)} \), and is one of the compounds that forms when iron corrodes. It's a fascinating subject because it involves understanding how different elements interact with iron. In this compound, we start by identifying the oxidation numbers of the elements involved to understand the corrosion process.

First, let’s break down the compound. Iron (Fe) pairs with an oxygen (O) and a hydroxide group (OH). The oxidation number of oxygen is usually \(-2\), and the hydroxide ion, having an overall charge of \(-1\), requires hydrogen (H) to have an oxidation number of \(+1\).

To find the oxidation number of iron in \( \text{Fe(O)(OH)} \), set up an equation knowing the compound is neutral overall:

• Let the oxidation number of Fe be \( x \).
• The sum is: \( x + (-2) + (+1) = 0 \).

Solving this, we find \( x = +1 \). Thus, in iron oxyhydroxide, iron typically has an oxidation number of \(+1\). Understanding these numbers helps to comprehend how iron changes during corrosion.

Decoding Magnetite

Magnetite, with the formula \( \text{Fe}_3\text{O}_4 \), is an intriguing iron oxide because of its magnetic properties and its occurrence in nature. The oxidation number of iron in magnetite can be complex due to the presence of iron in more than one oxidation state.

Originally, researchers attempted to assign a single oxidation number to all iron atoms in magnetite. By assuming oxygen's oxidation number is \(-2\), and let the oxidation number of Fe be \( x \), the equation becomes:

• \(3x + 4(-2) = 0\).

The solution, \( x = \frac{8}{3} \), initially suggested a fractional oxidation number. However, in chemistry, oxidation numbers need to be integers.

To resolve this, it's been understood that magnetite contains iron in both the \(+2\) and \(+3\) oxidation states. This is called mixed valency, meaning that two Fe ions are \(+2\) and one is \(+3\). This combination fits because the iron atoms collectively create a balanced structure with the oxide ions in \( \text{Fe}_3\text{O}_4 \). Therefore, the unique oxidation numbers for Fe in magnetite are \(+2\) and \(+3\).

Corrosion Products Explained

Corrosion products, such as rust, iron oxyhydroxide, and magnetite, form when iron reacts with environmental elements like oxygen and moisture. These products can significantly affect structural materials, leading to damage and the need for maintenance and prevention.

Rust is commonly known as \( \text{Fe}_2\text{O}_3 \), but other products like \( \text{Fe(O)(OH)} \) and \( \text{Fe}_3\text{O}_4 \) also form depending on the conditions. Each of these corrosion products has different properties and forms under specific environmental conditions.

• Iron oxyhydroxide forms in more humid or wet conditions, where water can facilitate the formation of OH groups.
• Magnetite typically forms under less oxidative conditions, offering magnetic properties that can sometimes be leveraged in industrial applications.

Corrosion is a natural process, but understanding these products helps to find effective ways to prevent or minimize the detrimental impacts of corrosion on infrastructure and equipment.