7.3.4. Limitations of Concept of Oxidation Number

Sometimes, we come across with certain compounds in which the oxidation number of a particular element in the compound is in fraction. Examples are: C₃O₂ [where oxidation number of carbon is (4/3)], Br₃O₈ [where oxidation number of bromine is (16/3)] and Na₂S₄O₆ (where oxidation number of sulphur is 2.5).

In some chemical compounds, the oxidation states of elements do not result in whole numbers but fractions. For example, in C₃O₂, carbon has an average oxidation state of 4/3, indicating that not all carbon atoms are in the same oxidation state. Similarly, in Br₃O₈, bromine has an average of 16/3, and in Na₂S₄O₆, sulfur has an average oxidation number of 2.5. These fractions indicate that within the compounds, the element exhibits multiple oxidation states.

Think of a classroom where two students are always at the top of their class, while one student usually struggles with grades. If we calculated the average test score for the three, it wouldn’t exactly reflect the individual performance, but rather, it combines their scores into a broader view. Similarly, fractional oxidation numbers provide an average which can help to understand the behavior of elements in compounds better.

We know that the idea of fractional oxidation number is unconvincing to us, because electrons are never shared/transferred in fraction. Actually this fractional oxidation state is the average oxidation state of the element under examination and the structural parameters reveal that the element for whom fractional oxidation state is realised is present in different oxidation states.

The concept of fractional oxidation states might seem confusing as it implies that electrons are shared or transferred in parts, which is not the case in reality. Instead, the fractional oxidation numbers indicate that an element is present in multiple oxidation states in a compound. For example, the structure of C₃O₂ shows that out of three carbon atoms, two have a +2 oxidation state and one has a 0 state, resulting in an average of +4/3. The actual states of the atoms reveal the complexity behind the fractional number.

Imagine a basketball team where some players score high points in certain games, while others have lower scores. If we average their scores, one player may have a score of 30 points in one game and 10 in another, resulting in an average of 20. However, this average does not reflect their individual game performances accurately. Similarly, fractional oxidation numbers give an average rather than a complete picture of electron states.

Structure of the species C₃O₂, Br₃O₈ and S₄O₆²⁻ reveal the following bonding situations:

          +2    0    +2

O = C = C* = C = O Structure of C₃O₂ (carbon suboxide) Structure of Br₃O₈ (tribromooctaoxide) Structure of S₄O₆²⁻ (tetrathionate ion)

The structures of these compounds provide insight into how different oxidation states exist within a single species. In C₃O₂, two carbon atoms are bonded in a +2 oxidation state, while the central carbon exists in a 0 state. Similarly, in Br₃O₈, terminal bromines hold a +6 state, while the middle bromine has a +4 oxidation state. For the tetrathionate ion S₄O₆²⁻, external sulfur atoms show a +5 state while internal ones are at 0. This variability highlights that while the average may suggest a fraction, actual bonding reveals whole numbers.

Consider a fruit salad with various fruits mixed together. While the salad overall represents a mix of flavors, each fruit maintains its unique taste. The average flavor profile of the salad may be appealing, but it’s the distinct flavors of each fruit that truly create the dish. Similarly, the complex structures of compounds containing fractional oxidation numbers reveal their distinct oxidation states, clarifying the overall 'flavor' of the compound's oxidation state.

We may thus, in general, conclude that the idea of fractional oxidation state should be taken with care and the reality is revealed by the structures only. Further, whenever we come across with fractional oxidation state of any particular element in any species, we must understand that this is the average oxidation number only. In reality (revealed by structures only), the element in that particular species is present in more than one whole number oxidation states.

In conclusion, the fractional oxidation numbers are useful for providing an average but should be interpreted carefully. The true oxidation states can only be understood through the structural representations, which reveal that the elements often exist in multiple oxidation states within a compound. Recognizing this helps us effectively grasp the chemistry behind various compounds and their properties.

Think of a company's employees sharing average salaries. The average might be useful, yet it doesn't reflect the individual salaries of high earners and low earners in the team. Just as understanding these individual salaries gives clearer insight into company dynamics, examining oxidation states through structure offers a truer picture of the element's behavior in compounds.

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