Question

In the superconducting ceramic \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\), what is the average oxidation state of copper, assuming that \(Y\) and Ba are in their expected oxidation states? Yttrium can be replaced with a rare-earth element such as La, and Ba can be replaced with other similar elements without fundamentally changing the superconducting properties of the material. However, general replacement of copper by any other element leads to a loss of superconductivity.In what respects is the electron configuration of copper different from that of the other two metallic elements in this compound?

Short answer

The average oxidation state of copper in the superconducting ceramic \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\) is -7/3. The electron configurations of Cu, Y, and Ba are [Ar] 4s¹ 3d¹⁰, [Kr] 5s² 4d¹, and [Xe] 6s², respectively. Copper has a partially filled d-orbital, while yttrium and barium have filled s-orbitals, which is the difference responsible for copper's unique contribution to the superconducting properties of the material.

Step-by-step solution

Determine the oxidation states of Yttrium (Y) and Barium (Ba)

Yttrium (Y) is a transition metal and has an oxidation state of +3. Barium (Ba) is an alkaline earth metal and has an oxidation state of +2.

Calculate the total positive charge

Now we need to calculate the total positive charge in the compound. In the given compound, \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\), we have one Y atom, two Ba atoms, and three Cu atoms. Total positive charge = (1 x +3) + (2 x +2) + (3 x oxidation state of Cu)

Calculate the total negative charge

Oxygen (O) has an oxidation state of -2 in compounds. In the given compound, there are 7 oxygen atoms. Total negative charge = 7 x (-2)

Balance the overall charge

To find the oxidation state of Cu (in the compound), equate the total positive charge with the total negative charge: (1 x +3) + (2 x +2) + (3 x oxidation state of Cu) = 7 x (-2)

Solve for the oxidation state of copper

Now, we will solve the equation to find the average oxidation state of copper in the compound. +3 + 4 + 3(oxidation state of Cu) = -14 3(oxidation state of Cu) = -14 - 4 - 3 3(oxidation state of Cu) = -21 Oxidation state of Cu = -7/3 Thus, the average oxidation state of copper in the compound \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\) is -7/3.

Comparing electron configurations of Cu, Y, and Ba

To find the differences in electron configurations between copper and the other two metallic elements (yttrium and barium), let’s determine their electron configurations: Yttrium (Y): [Kr] 5s² 4d¹ Barium (Ba): [Xe] 6s² Copper (Cu): [Ar] 4s¹ 3d¹⁰ Comparing these electron configurations, we observe that copper (Cu) has a partially filled d-orbital, while yttrium (Y) and barium (Ba) have filled s-orbitals. This suggests that the superconductivity of the ceramic material is highly dependent on the unique electron configuration of copper. If copper is replaced by any other element, the material loses its superconducting properties.

Key concepts

Oxidation State Calculation

Understanding how to calculate the oxidation states of elements within a compound is a foundational concept in chemistry. Oxidation states, also known as oxidation numbers, provide insight into the electron distribution among the atoms in a compound and can predict how atoms will react. They are often used in redox reactions, coordination chemistry, and understanding the behavior of metals in different compounds.

In general, the oxidation state is the charge that an atom would have if the compound was composed of ions. To determine the average oxidation state of an element in a compound, steps are involved which include knowing the common oxidation states of other elements, summing the total charges, and ensuring that the overall charge of the compound is balanced. For example, in the compound \(\mathrm{YBa}_{2} \mathrm{Cu}_{3}\mathrm{O}_{7}\), the known oxidation states are +3 for Yttrium (Y), +2 for Barium (Ba), and -2 for Oxygen (O).

Oxidation state calculation involves setting up an equation based on the principle that the sum of the oxidation states in a neutral compound is zero. By combining the known oxidation states and solving the resulting equation, one can determine the unknown oxidation state, such as the average oxidation state of copper (Cu) in the ceramic compound which turns out to be -7/3.

Electron Configuration

The electron configuration of an atom describes the distribution of electrons in its atomic orbitals. Understanding the electron configuration is vital as it determines the chemical and physical properties of the element, including its reactivity and the types of bonds it can form. In general, elements follow the Aufbau principle, which states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels.

For instance, yttrium (Y) has the electron configuration [Kr] 5s² 4d¹, exhibiting a filled s-orbital and one electron in a d-orbital. Barium (Ba) follows with [Xe] 6s², showing again a completely filled s-orbital. In contrast, copper (Cu) has a more complex configuration: [Ar] 4s¹ 3d¹⁰. Copper has a unique case where it has a partially filled s-orbital and a completely filled d-orbital, highlighting its ability to lose electrons easily from the s-orbital and lend its d-electrons for bonding.

Distinguishing Electron Configurations

This difference in electron configuration is significant, particularly for copper's role in superconductivity. In superconducting materials, the electron structure highly influences their ability to conduct electricity with zero resistance. Copper's unique configuration is crucial for maintaining superconductivity in \(\mathrm{YBa}_{2} \mathrm{Cu}_{3}\mathrm{O}_{7}\). If copper were replaced, the superconductivity would be lost, underlining the importance of the electron configuration in understanding and designing functional materials.

Superconducting Ceramics

Superconducting ceramics are materials that exhibit zero electrical resistance and the expulsion of magnetic fields when cooled below a certain critical temperature. These fascinating materials have become the subject of intensive research due to their promising applications in magnetic levitation, energy-efficient power transmission, and advanced computing systems.

Superconducting ceramics like \(\mathrm{YBa}_{2} \mathrm{Cu}_{3}\mathrm{O}_{7}\), often referred to as 'high-temperature' superconductors, revolutionized the field since they superconduct at temperatures higher than conventional metallic superconductors. This is significant because it reduces the cooling requirements, making them more practical for real-world applications.

Role of Copper in Superconductivity

The critical role played by copper in \(\mathrm{YBa}_{2} \mathrm{Cu}_{3}\mathrm{O}_{7}\) relates to its electron configuration and the underlying quantum mechanical attributes. Copper's unique electron structure facilitates the formation of Cooper pairs—tightly bound electron pairs that move without resistance through the crystal lattice. Replacement of copper with any other element disrupts this delicate pairing mechanism, leading to a loss in superconducting properties. Understanding the oxidation states and electron configurations of the constituent elements of superconducting ceramics is crucial in designing and synthesizing new materials with improved superconducting temperatures and characteristics.