Use oxidation numbers to show that the fermentation of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) to carbon dioxide and ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) is a redox reaction.

Understanding oxidation numbers is crucial for identifying redox reactions. An oxidation number is a figure assigned to an element in a chemical species that represents the number of electrons lost or shared as compared to its elemental state. In simple terms, it's like a bookkeeping system to track electrons during a chemical reaction.

For example, in a molecule of glucose, \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \), the oxidation number for each carbon atom is 0, because this is the standard for elements in their basic, uncombined form. When analyzing the products of glucose fermentation, such as ethanol, \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) and carbon dioxide (CO2), different oxidation numbers are necessary. In ethanol, the carbon atoms have differing oxidation states because of the distinct nature of their bonds. In carbon dioxide, each carbon atom is assigned an oxidation number of +4 due to the nature of its double bonds with oxygen.

Recognizing these changes in oxidation numbers helps indicate what is losing electrons (oxidation) and what is gaining electrons (reduction) during the reaction.

A redox reaction is characterized by the transfer of electrons between chemical species, resulting in changes in their oxidation states. This transfer leads to one species being oxidized (losing electrons) and another being reduced (gaining electrons). Understanding a redox reaction is essential for delving into the chemistry behind processes like the fermentation of glucose.

Fermentation is an anaerobic process, meaning it occurs without oxygen. During the conversion of glucose into ethanol and carbon dioxide, electrons are redistributed among the carbon atoms, changing their oxidation numbers. The shift in electrons confirms that a redox reaction is taking place, with certain carbon atoms being oxidized, while others are reduced.

The process of chemical equation balancing involves ensuring that the number of atoms for each element, and the total charge, are the same on both the reactant and product sides. This law of conservation of mass is paramount because, in a chemical reaction, matter is neither created nor destroyed.

For example, in the fermentation of glucose, the balanced chemical equation is \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} + 2 \mathrm{CO}_{2} \). This balance reflects that there are six carbon atoms, twelve hydrogen atoms, and six oxygen atoms on both sides of the equation, demonstrating that mass is conserved through the reaction.

Oxidation and reduction are two halves of a redox reaction. Often remembered by the mnemonic 'OIL RIG'—which stands for 'Oxidation Is Loss, Reduction Is Gain'—these processes refer to the loss and gain of electrons, respectively.

In the context of glucose fermentation, oxidation involves glucose's carbon atoms increasing their oxidation number, as seen by the carbon going from 0 in glucose to +4 in carbon dioxide. This increase indicates a loss of electrons. Conversely, reduction involves the decrease in the oxidation number—like the carbon atoms in glucose that end up in ethanol, moving from 0 to -1. This is a clear sign of a gain of electrons. The simultaneous occurrence of these two processes is what makes a reaction redox.