Thermal decomposition of $AgNO _3$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is _____
Correct Answer: 6
Solution and Explanation
To solve this problem, we need to analyze the thermal decomposition of silver nitrate (\( \text{AgNO}_3 \)) and determine the number of electrons in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons.
1. Analyzing the Decomposition Reaction:
The thermal decomposition of silver nitrate (\( \text{AgNO}_3 \)) produces two gases: silver (Ag) and nitrogen dioxide (\( \text{NO}_2 \)). The decomposition reaction can be written as:
\[ \text{2AgNO}_3 \xrightarrow{\Delta} 2\text{Ag} + 2\text{NO}_2 + \text{O}_2 \]
2. Identifying the Paramagnetic Gases:
The gases produced in the reaction are silver vapor (\( \text{Ag} \)) and nitrogen dioxide (\( \text{NO}_2 \)). Both are paramagnetic due to the presence of unpaired electrons. However, \( \text{NO}_2 \) has more unpaired electrons compared to silver, making it the gas with the higher number of unpaired electrons.
3. Determining the Number of Electrons in the Antibonding Molecular Orbitals:
In \( \text{NO}_2 \), the nitrogen dioxide molecule has an odd number of electrons in its molecular orbitals. The molecular orbital theory tells us that the electrons in antibonding orbitals are those that occupy the higher energy levels and correspond to the unpaired electrons. The number of unpaired electrons in \( \text{NO}_2 \) is 3, and the total number of electrons present in the antibonding molecular orbitals is 6 (2 electrons per antibonding orbital). Therefore, the total number of electrons in the antibonding molecular orbitals is 6.
Final Answer:
The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is 6.
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Concepts Used:
Molecular Orbital Theory
The Molecular Orbital Theory is a more sophisticated model of chemical bonding where new molecular orbitals are generated using a mathematical process called Linear Combination of Atomic Orbitals (LCAO).
Molecular Orbital theory is a chemical bonding theory that states that individual atoms combine together to form molecular orbitals. Due to this arrangement in MOT Theory, electrons associated with different nuclei can be found in different atomic orbitals. In molecular orbital theory, the electrons present in a molecule are not assigned to individual chemical bonds between the atoms. Rather, they are treated as moving under the influence of the atomic nuclei in the entire molecule.
