Question

Iron corrodes to produce rust, \(\mathrm{Fe}_{2} \mathrm{O}_{3},\) but other corrosion products that can form are \(\mathrm{Fe}(\mathrm{O})(\mathrm{OH}),\) iron oxyhydroxide, and magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) . (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 .

Short answer

The oxidation number of Fe in iron oxyhydroxide is +3. If Fe had a unique oxidation number in magnetite, it would be +8/3, which is not a whole number, so there are two different oxidation numbers of Fe in magnetite. These oxidation numbers are Fe(+2) and Fe(+3) with either a 1:2 or 2:1 stoichiometric ratio, assuming oxygen's oxidation number is -2.

Step-by-step solution

Determine the formula of iron oxyhydroxide

The formula for iron oxyhydroxide is given as Fe(O)(OH).

Assign oxidation numbers

Let the oxidation number of Fe be x. According to the problem statement, the oxidation number of O is -2. Since OH has a -1 charge, the oxidation number of hydrogen in OH is +1.

Write the equation using the sum of oxidation numbers

The sum of oxidation numbers of all elements in the compound must be equal to zero. This gives us the equation: x + (-2) + (-1) = 0

Solve for x

Solving the equation for x, we get: x = 2 + 1 = 3. Therefore, the oxidation number of Fe in iron oxyhydroxide is +3. #b) Oxidation number of Fe in magnetite assuming a unique oxidation number for Fe#

Determine the formula of magnetite

The formula for magnetite is given as Fe3O4.

Assign oxidation numbers

Let the oxidation number of Fe be x. According to the problem statement, the oxidation number of O is -2.

Write the equation using the sum of oxidation numbers

The sum of oxidation numbers of all elements in the compound must be equal to zero. This gives us the equation: 3x + 4(-2) = 0

Solve for x

Solving the equation for x, we get: 3x = 8, x = 8/3. Therefore, if Fe has a unique oxidation number in magnetite, the oxidation number of Fe would be +8/3, which is not a whole number. #c) Relative stoichiometry of the two different oxidation numbers of Fe in magnetite#

Assign oxidation numbers

Let the oxidation numbers of the two different kinds of Fe in magnetite be x and y. According to the problem statement, the oxidation number of O is -2.

Write the equation using the sum of oxidation numbers

The sum of oxidation numbers of all elements in the compound must be equal to zero. This gives us the equation: x + 2y + 4(-2) = 0

Suggest possible oxidation numbers and stoichiometry

Since x and y must be whole numbers and have a sum that equals 8, the possible values of x and y are: - x = +2 and y = +3. In this case, the Fe(+2) and Fe(+3) ions are in a 1:2 ratio. - x = +3 and y = +2. In this case, the Fe(+3) and Fe(+2) ions are in a 2:1 ratio. Considering the 1:2 and 2:1 stoichiometric ratios, we can suggest that the oxidation numbers and relative stoichiometry of the two different kinds of Fe in magnetite are Fe(+2) and Fe(+3) with a 1:2 or 2:1 ratio, assuming oxygen's oxidation number is -2.

Key concepts

Oxidation States

When we talk about the oxidation state (also referred to as oxidation number) in chemistry, we describe the degree of oxidation of an atom within a compound. The oxidation state is an indicator of the hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic. One fundamental rule is that the sum of the oxidation states for all atoms in a molecule or polyatomic ion equals the charge on the molecule or ion.

Oxidation states are often represented by integers, which can be positive, negative, or zero. In determining the oxidation state of an atom, there are several guidelines: The oxidation state of pure elements is always zero; for a simple monoatomic ion, it is equal to the ion's charge; oxygen typically has an oxidation state of -2 (except in peroxides or when bonded to fluorine); and hydrogen generally has a +1 oxidation state (except when bonded to metals in hydrides).

In our exercise, determining the oxidation state of iron in compounds like iron oxyhydroxide and magnetite is critical for understanding their chemical behavior. For example, iron's oxidation state in Fe(O)(OH) is calculated by adding the known oxidation states of oxygen and hydrogen and setting the total equal to zero due to the compound being neutral. This allows us to infer iron's oxidation state as +3.

Chemical Stoichiometry

Moving on from individual atoms to whole reactions, chemical stoichiometry is the math behind the science of chemistry. It involves the quantitative relationship between reactants and products in a chemical reaction. Stoichiometry allows chemists to predict how much product will form from a certain amount of reactants and vice versa. This principle is based on the conservation of mass where the total mass of the reactants equals the total mass of the products.

The stoichiometry of a reaction is often described by a balanced chemical equation that equates the number of moles of reactants to the number of moles of products. In our exercise on magnetite, we need to consider that it contains two types of iron ions, and the stoichiometry of these ions is crucial to understanding the compound's formation and properties.

To determine the possible stoichiometry of the two different kinds of iron in magnetite (Fe_{3}O_4), we leverage the conservation of mass and charge balance to deduce that one type of iron must be Fe(II) and the other Fe(III), with their amounts following a 1:2 or 2:1 ratio to maintain charge neutrality in the compound. The stoichiometric coefficients reflect the relative amounts of each type of iron ion, ensuring that the compound as a whole is balanced both in terms of mass and charge.

Redox Chemistry

The term 'redox' is a portmanteau for reduction-oxidation reaction, which is a type of chemical reaction that involves a transfer of electrons between two species. It's the heart of many processes such as combustion, corrosion, photosynthesis, and even metabolism in living organisms. Understanding redox chemistry is critical for deciphering the behavior of elements during chemical reactions.

In a redox reaction, one species will lose electrons (oxidation) and another will gain electrons (reduction). This shift in electron density is what alters the oxidation states of the atoms involved. The substance that gains electrons is called the oxidizing agent because it causes the other substance to be oxidized; conversely, the substance that loses electrons is the reducing agent because it causes the other substance to be reduced.

In relation to our magnetite problem, the iron in different oxidation states implies that redox reactions occurred to produce the distinct Fe(II) and Fe(III) ions present in the compound. Such redox processes are fundamental in forming the diverse iron oxide compounds, including the rusting of iron to form iron oxyhydroxide, magnetite, and other corrosion products. By comprehending redox chemistry, students can better appreciate the intricacies of chemical reactions and the transformations of elements under various conditions.