/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 86 In the superconducting ceramic \... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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

Expert verified
The average oxidation state of copper in \(\mathrm{YBa}_{2}\mathrm{Cu}_{3}\mathrm{O}_{7}\) is \(8/3\). The uniqueness of copper's electron configuration, with a filled 3d subshell (3d10) and one electron in the 4s subshell (4s1), provides stability and superconducting properties to the compound that cannot be replicated by replacing it with any other element. In contrast, the other two metallic elements in the compound, yttrium (Y) and barium (Ba), have either a partially filled or empty d subshell.

Step by step solution

01

Determine the oxidation states of Y and Ba

First, we need to find the oxidation states of Y and Ba in the compound. Yttrium (Y) is part of the group 3 elements and has a common oxidation state of +3. Barium (Ba) is part of the group 2 elements and has a common oxidation state of +2.
02

Calculate the total oxidation state of the compound

The formula for this superconducting ceramic is \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\). So, we have the following oxidation states for each element in the compound: - Yttrium (Y): +3 - Barium (Ba): +2 (since we have 2 Ba atoms, we multiply the oxidation state by 2) - Copper (Cu): unknown (let's represent it as x, as we have 3 Cu atoms) - Oxygen (O): -2 (since we have 7 O atoms, we multiply the oxidation state by 7) Now, we can calculate the total oxidation state of the compound by adding the oxidation states of each element: Total Oxidation State = +3 + (2 * +2) + (3 * x) + (7 * -2)
03

Solve for the average oxidation state of copper (Cu)

Since this is a neutral compound, the total oxidation state of the compound must be equal to zero. We can use this information to solve for x (average oxidation state of copper): +3 + (2 * +2) + (3 * x) + (7 * -2) = 0 Solving this equation for x, we get: 3x = 8 x = 8/3 So, the average oxidation state of copper in the compound is 8/3.
04

Compare the electron configuration of copper with Y and Ba

We will now compare the electron configuration of copper (Cu) with yttrium (Y) and barium (Ba). The electron configurations for these elements are: - Copper (Cu): [Ar] 3d10 4s1 - Yttrium (Y): [Kr] 4d1 5s2 - Barium (Ba): [Xe] 6s2 Copper's electron configuration is unique because it has a filled 3d subshell (3d10) and one electron in the 4s subshell (4s1). This filled d orbital provides stability to the compound and is likely responsible for its superconducting properties. On the other hand, both Yttrium (Y) and Barium (Ba) have either a partially filled or empty d subshell, and as a result, the properties provided by copper's electron configuration cannot be replicated by replacing it with any other element. This is why the replacement of copper leads to a loss of superconductivity in this compound.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Superconducting Materials
Superconducting materials are unique substances that, when cooled below a certain temperature known as the critical temperature, conduct electricity without resistance. This leads to the possibility of creating highly efficient energy systems and has applications in medical imaging, transportation, and more. One of the fascinating aspects of superconductors is the perfect diamagnetism they exhibit, which means they can repel magnetic fields completely.
These materials can dramatically change their electrical properties based on temperature and composition. The ceramic compound YBa₂Cu₃O₇ is one such superconducting material. Its properties are largely due to the specific arrangement of its elements, especially copper, which plays a critical role. The distinctive electron configuration and oxidation states of copper uplift its superconducting qualities.
  • Critical Temperature: The temperature below which a material becomes superconducting.
  • Applications: Especially useful in MRI machines, maglev trains, and advanced research fields.
Explaining Electron Configuration
The electron configuration of an element describes the distribution of electrons in its atomic orbitals. It is a key factor that influences the chemical properties and reactivity of an element. In the context of transition metals, the electron configuration can vary notably as these elements have partially filled d orbitals.
Copper (Cu) features an unusual electron configuration, [Ar] 3d extsuperscript{10} 4s extsuperscript{1}. Unlike many other metals, copper has a completely filled d-orbital and a single electron in the s-orbital. This makes copper stable and allows it’s d-electrons to participate actively in bonding. The unique electron configuration is believed to contribute significantly to copper's ability to maintain superconducting properties.
  • Significance: The filled d orbital in copper stabilizes the atomic structure.
  • Role in Bonding: Allows d-electrons to engage effectively in chemical interactions.

Yttrium (Y) and Barium (Ba), in contrast, have their outer orbitals in a different configuration, specifically [Kr] 4d extsuperscript{1} 5s extsuperscript{2} for Yttrium and [Xe] 6s extsuperscript{2} for Barium. Their d-orbitals are either empty or partially filled, resulting in distinct chemical behaviors compared to copper.
Characteristics of Transition Metals
Transition metals, found in the middle section of the periodic table, are known for their ability to form colorful compounds, conduct electricity and heat, and display various oxidation states. These unique features arise from their electronic structure, particularly the involvement of d orbitals. Copper, Yttrium, and Barium in the superconducting compound YBa₂Cu₃O₇, although they all are metals, belong to different positions in the periodic table. Copper, being a transition metal, has d-orbitals that are completely filled, which is unusual and gives it special properties, including its role in superconductivity. This ability to have multiple oxidation states makes copper versatile in chemical reactions.
  • Varied Oxidation States: Ability to lose different numbers of electrons leading to multiple stable states.
  • Electronic Structure: Involvement of d-orbitals allows for unique chemical bonding.
The comparison of these metals within the compound clarifies why copper cannot be easily replaced without losing the superconducting properties, as its d-orbital plays a pivotal role that yttrium or barium's orbitals cannot replicate. This highlights the importance of transition metals in advanced materials science.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An ester is a compound formed by a condensation reaction between a carboxylic acid and an alcohol. Use the index to find the discussion of esters in Chapter 25, and give an example of a reaction forming an ester. How might this kind of reaction be extended to form a polymer (a polyester)?

Skin cells from the body do not differentiate when they are simply placed in a tissue culture medium; that is, they do not organize into the structure of skin, with different layers and different cell types. What is needed to cause such differentiation to occur? Indicate the most important requirements on any material used.

Consider para-azoxyanisole, which is a nematic liquid crystal in the temperature range of \(21{ }^{\circ} \mathrm{C}\) to \(47^{\circ} \mathrm{C}\) : (a) Write out the Lewis structure for this molecule, showing all lone-pair electrons as well as bonds. (b) Describe the hybrid orbitals employed by each of the two nitrogens. What bond angles do you anticipate about the nitrogen atom that is bonded to oxygen? (c) Replacing one of the \(-\mathrm{OCH}_{3}\) groups in para-azoxyanisole by \(\mathrm{a}\) \(-\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) group causes the melting point of the substance to drop; the liquid crystal range changes to \(19{ }^{\circ} \mathrm{C}\) to \(76^{\circ} \mathrm{C}\). Explain why this substitution produces the observed changes in properties. (d) How would you expect the density of para-azoxyanisole to change upon melting at \(117^{\circ} \mathrm{C}\) ? Upon passing from the nematic to the isotropic liquid state at \(137{ }^{\circ} \mathrm{C}\) ? Explain.

What properties of the typical nematic liquid crystalline molecule are likely to cause it to reorient when it is placed in an electrical field that is perpendicular to the direction of orientation of the molecules?

State whether each statement is true or false, and why. (a) A typical band gap energy for an insulator is \(400 \mathrm{~kJ} / \mathrm{mol}\) (b) The conduction band is higher in energy than the valence band. (c) Electrons can conduct well if they are in a filled valence band. (d) Holes refer to empty atomic sites in a solid crystal.

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.