Question

The "Chemistry in Focus" segment Yellow Jeans? discusses the oxidation- reduction reaction required to turn the dye used in denim jeans from yellow to blue. The reaction is from leucoindigo to indigo. The reaction can be expressed as \(\mathrm{Na}_{2} \mathrm{C}_{16} \mathrm{~N}_{2} \mathrm{H}_{10} \mathrm{O}_{2} \rightarrow \mathrm{C}_{16} \mathrm{~N}_{2} \mathrm{H}_{10} \mathrm{O}_{2} .\) Explain how from this reaction you know that the leucindigo is oxidized to form indigo.

Short answer

In the given reaction, \(\mathrm{Na_{2} C_{16} N_{2} H_{10} O_{2} \rightarrow C_{16} N_{2} H_{10} O_{2}}\), leucoindigo is oxidized to form indigo. The carbon atoms in the leucoindigo molecule have an average oxidation state of -1/4, while the carbon atoms in the indigo molecule have an average oxidation state of 0. Since there is an increase in the oxidation state of the carbon atoms, it indicates that leucoindigo is oxidized to form indigo during the reaction.

Step-by-step solution

Determine the Oxidation States of Leucoindigo

To determine whether leucoindigo is oxidized, we need to find the oxidation states of the carbon atoms in leucoindigo, which has the molecular formula: \(\mathrm{Na_{2}C_{16}N_{2}H_{10}O_{2}}\). Its structure consists of an indigo molecule with two additional sodium ions and two hydrogen atoms that are bonded to two oxygen atoms. Let's assign oxidation numbers to the atoms in the leucoindigo molecule (ignoring the sodium ions): - Hydrogen: +1 (as H is bonded to O) - Oxygen: -2 (O is bonded to C) - Nitrogen: -3 (N is bonded to C but we can ignore it as it is not changing during the reaction) We can now use this information to find the oxidation state of the carbon atoms in the leucoindigo molecule as follows: \[(+1) \cdot 10 + (-2) \cdot 2 + (-3) \cdot 2 + x \cdot 16 = 0\] \[x \cdot 16 = -4\] \[x = -\dfrac{1}{4}\] Thus, the carbon atoms in the leucoindigo molecule have an average oxidation state of -1/4.

Determine the Oxidation States of Indigo

Now that we have determined the oxidation states of the atoms in leucoindigo, we can do the same for indigo, which has the molecular formula: \(\mathrm{C_{16}N_{2}H_{10}O_{2}}\). Indigo is formed by removing the two sodium ions and hydrogen atoms from leucoindigo. The oxidation states of the atoms in the indigo molecule are as follows: - Hydrogen: +1 (as H is bonded to C) - Oxygen: -2 (O is bonded to C) - Nitrogen: -3 (N is bonded to C but we can ignore it as it is not changing during the reaction and N doesn't lose or gain electrons) Using this information, we can find the average oxidation state of the carbon atoms in the indigo molecule: \[(+1) \cdot 10 + (-2) \cdot 2 + (-3) \cdot 2 + x \cdot 16 = 0\] \[x \cdot 16 = 0\] \[x = 0\] Thus, the carbon atoms in the indigo molecule have an average oxidation state of 0.

Compare the Oxidation States to Determine if Leucoindigo is Oxidized

Comparing the average oxidation states of the carbon atoms in both leucoindigo (-1/4) and indigo (0) molecules, we can see that there is an increase in the oxidation state of the carbon atoms in the reaction. An increase in oxidation state represents oxidation. Therefore, the leucoindigo molecule is oxidized to form the indigo molecule during the reaction.

Key concepts

Redox Chemistry Education

Redox chemistry, short for reduction-oxidation chemistry, is a fundamental concept in chemistry that deals with the transfer of electrons between substances. It plays a crucial role in a variety of chemical reactions including combustion, corrosion, and biological processes. Understanding the principles of redox chemistry enables students to explain how certain chemical changes occur.

For instance, when learning about redox reactions, one should become comfortable with the terms 'oxidation' and 'reduction'. Oxidation refers to the loss of electrons, often associated with an increase in the oxidation state, while reduction is the gain of electrons, typically marked by a decrease in the oxidation state. It is helpful to remember this with the mnemonic 'OIL RIG' - Oxidation Is Loss, Reduction Is Gain.

In an oxidation-reduction (redox) reaction, there is a transfer of electrons from the reducing agent (the substance being oxidized) to the oxidizing agent (the substance being reduced). The significance of teaching redox chemistry lies in its ubiquitous presence in chemical reactions, making it essential knowledge for anyone delving into the science of materials, energy, and living systems.

Oxidation States Determination

In redox chemistry, determining oxidation states is imperative for identifying what is being oxidized and what is reduced in a reaction. Oxidation states (also known as oxidation numbers) offer insight into the electronic structure of a compound and the potential changes it can undergo during a reaction.

To determine an oxidation state, we assign numbers to each atom based on certain rules. These include assigning an oxidation state of 0 to a pure element, +1 to hydrogen when bonded with non-metals, -2 to oxygen in most cases, and using known oxidation states of ions in compounds. The sum of oxidation states in a neutral molecule must equal zero, while in an ion, it must equal the ion's charge.

Once the oxidation states are determined for each element in a reactant and product, changes in these states indicate which atoms are oxidized and which are reduced. For example, in the given exercise, we observed that the carbon atoms in leucoindigo had an average oxidation state of -1/4, which changed to 0 in indigo, demonstrating the oxidation of leucoindigo.

Chemical Reactions in Dye Processing

Chemical reactions play an integral role in dye processing, often involving complex redox reactions that give fabrics their vibrant colors. For industrial applications like dyeing denim jeans, the synthesis and application of the dye involve carefully controlled chemical processes. Understanding redox reactions is particularly valuable in this context as it relates to the changing oxidation states and, consequently, the color of the dye.

For instance, as explained in the textbook exercise, indigo dyeing involves an oxidation-reduction reaction where the initially colorless leucoindigo is turned into the blue indigo we know. This is achieved by oxidizing leucoindigo. Dye manufacturers exploit redox chemistry to create pigments that are colorfast and resistant to fading. In the jeans-making process, this knowledge allows for the precise application of dyes, ensuring the iconic blue color is consistent and long-lasting.

The application of redox principles in dye chemistry is a perfect example of the interplay between chemical knowledge and practical applications, highlighting how critical an understanding of oxidation states is in real-world processes.