JEE Advanced 2022 Paper 2 · Q05 · Molecular Orbital Theory
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 _____.
Reveal answer + step-by-step solution
Correct answer:6
Solution
Step 1 — the decomposition. 2 AgNO$_3$ $\xrightarrow{\Delta}$ 2 Ag + 2 NO$_2$ + O$_2$. The two paramagnetic gases are NO$_2$ (1 unpaired electron, odd-electron molecule) and O$_2$ (2 unpaired electrons, triplet ground state).
Step 2 — pick the gas with more unpaired electrons: O$_2$ (2 unpaired e$^-$).
Step 3 — count antibonding electrons in O$_2$ (16 e$^-$ total). MO configuration: $(\sigma 1s)^2 (\sigma^*1s)^2 (\sigma 2s)^2 (\sigma^*2s)^2 (\sigma 2p_z)^2 (\pi 2p_x)^2 (\pi 2p_y)^2 (\pi^*2p_x)^1 (\pi^*2p_y)^1$.
Antibonding electrons: $\sigma^*1s$ (2) + $\sigma^*2s$ (2) + $\pi^*2p_x$ (1) + $\pi^*2p_y$ (1) = 6.
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