Problem 24 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The compound \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\), which shows super-conductivity, has copper in oxidation state \(\ldots \ldots \ldots \ldots \ldots \ldots\), assume that the rare earth element yttrium is in its usual \(+3\) oxidation state.

Step-by-Step Solution

Answer

The average oxidation state of copper is approximately +2.33.

Step 1: Determine Oxidation States for Known Elements

Identify the oxidation states of yttrium (Y), barium (Ba), and oxygen (O) within the compound. Yttrium is given in its +3 state and barium, being an alkaline earth metal, is typically in the +2 state. Oxygen, a non-metal, usually has an oxidation state of -2.

Step 2: Write the Chemical Formula with Oxidation States

The chemical formula is \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\). Assign the oxidation states for each known element: \(\mathrm{Y}^{+3}\), \(\mathrm{Ba}^{+2}\), and \(\mathrm{O}^{-2}\). This results in the formula: \(\mathrm{Y}^{+3}(\mathrm{Ba}^{+2})_{2}(\mathrm{Cu}^{x})_{3}(\mathrm{O}^{-2})_{7}\).

Step 3: Apply the Charge Balance Rule

The sum of all oxidation states in the compound must equal zero, because the compound is neutral. Set up the balance equation: \(+3 + 2(2) + 3x + 7(-2) = 0\).

Step 4: Solve the Balance Equation

Plug the known values into the equation and solve for \(x\):\[3 + 4 + 3x - 14 = 0 \3x - 7 = 0 \3x = 7 \x = \frac{7}{3} \approx +2.33\]

Step 5: Interpret the Oxidation State of Copper

The oxidation state of copper in this compound is approximately +2.33. This indicates that the copper atoms have a mixed oxidation state, alternating between +2 and +3, to maintain the overall neutrality of the compound.

Key Concepts

Superconductivity

Superconductivity is a phenomenon where a material can conduct electricity without any resistance when cooled below a certain temperature. This means that there is no energy loss in the form of heat, making superconductors highly efficient.
Some materials known for superconductivity include certain metal alloys and ceramic compounds. In particular, the compound \( \mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7} \), often referred to as YBCO, is famous for exhibiting superconductivity at relatively higher temperatures compared to other superconductors.

• Why is this important? Superconductors can have profound applications such as in MRI machines, maglev trains, and powerful electromagnets for particle accelerators because they allow for large currents with no energy loss.
• Temperature dependency: The superconductivity happens at a "critical temperature" below which the resistance drops to zero.

This unique property does not occur in all materials and is heavily dependent on the structure and composition of the compound.

Chemical formula

A chemical formula represents the elements within a compound and the proportion of each participating atom. The compound \( \mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7} \) is a copper-oxide superconductor, which consists of Yttrium (Y), Barium (Ba), Copper (Cu), and Oxygen (O).
The subscripts in the chemical formula indicate the number of each type of atom in one formula unit of the compound.

• Yttrium (Y): 1 atom per formula unit.
• Barium (Ba): 2 atoms per formula unit.
• Copper (Cu): 3 atoms per formula unit.
• Oxygen (O): 7 atoms per formula unit.

The correct interpretation of a chemical formula is crucial in determining the properties and behavior of the compound, especially in calculations involving the oxidation states of the elements.

Charge balance

Charge balance is an important concept in chemistry that ensures that a compound is electrically neutral. This means that the total charge contributed by the positively charged cations must balance the total charge from the negatively charged anions.
For the compound \( \mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7} \), we must assign oxidation states to each element to find the neutral charge scenario.

• Yttrium (Y): commonly +3
• Barium (Ba): typically +2
• Oxygen (O): usually -2

To determine the oxidation state of copper (Cu), we set up the equation, accounting for the known oxidation states: \[+3 + 2(2) + 3x + 7(-2) = 0\] Here, \(x\) represents the oxidation state of copper.
Solving the equation determined \(x\) to be approximately +2.33, indicating that copper has a mixed oxidation state in this compound, contributing to the charge balance.