Molecular Orbital Theory

To solve this problem, we need to analyze the thermal decomposition of silver nitrate ( ) 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 ( ) produces two gases: silver (Ag) and nitrogen dioxide ( ). The decomposition reaction can be written as:

2. Identifying the Paramagnetic Gases:
The gases produced in the reaction are silver vapor ( ) and nitrogen dioxide ( ). Both are paramagnetic due to the presence of unpaired electrons. However, 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 , 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 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.