Animated Solution for Chemistry - Coordination Compounds: In an experiment, $m$ grams of a compound $\text{X}$ (gas/liquid/solid) taken in a container is loaded in a balance as shown in figure I below. In the presence of a magnetic field, the pan with $\text{X}$ is either deflected upwards (figure II), or deflected downwards (figure III), depending on the compound $\text{X}$. Identify the correct statement(s)

Imagine you are standing in a laboratory, looking at a highly sensitive balance. On one side of this balance rests a small sample of a chemical compound, suspended perfectly between the poles of a powerful electromagnet. This setup is a classic representation of a Gouy balance, an ingenious device designed to measure the magnetic susceptibility of materials.

When the electromagnet is turned off, the balance is perfectly level. But the moment you flip the switch and the magnetic field surges through the sample, something magical happens. The pan either dips downwards, seemingly pulled by an invisible hand, or it rises upwards, as if repelled by the very space it occupies. This macroscopic movement is a direct consequence of the microscopic, quantum mechanical properties of the electrons within the sample.

Diamagnetism

To understand this phenomenon, we must dive into the electronic structure of the compounds. Electrons possess a property called 'spin', which makes them act like tiny bar magnets.

If a substance contains unpaired electrons, these tiny magnets align themselves with the external magnetic field. This alignment creates a net force of attraction, pulling the sample deeper into the magnetic field. We call these substances paramagnetic, and on our balance, they will cause a downward deflection.

Conversely, if all the electrons in a substance are perfectly paired, their individual magnetic moments cancel each other out. However, the external magnetic field still interacts with their orbital motion, inducing a tiny opposing magnetic field according to Lenz's Law. This results in a weak repulsion. We call these substances diamagnetic, and they will cause an upward deflection on the balance.

Let's put our four chemical suspects on the balance and predict their behavior based on their electronic configurations.

Suspect A: Water ($H_{2}O$) In a water molecule, oxygen shares its electrons with two hydrogen atoms to form covalent bonds, and it holds onto two lone pairs. Every single electron is happily paired up. With zero unpaired electrons, water is strictly diamagnetic. Therefore, it will be repelled by the magnetic field, causing an upward deflection. Statement (A) is absolutely correct.

Suspect B: Potassium Ferrocyanide ($K_4[Fe(CN{)}_6]$) This is a classic coordination complex. The central iron ion is in a $+2$ oxidation state, giving it a $3d^6$ electron configuration. The crucial detail here is the cyanide ($C{N}^{-}$) ligand. Cyanide is a strong field ligand, meaning it creates a large crystal field splitting energy (${\Delta }_o$). Because this splitting is so large, it is energetically favorable for all six $d$-electrons to pair up in the lower-energy $t_{2g}$ orbitals, leaving the $e_g$ orbitals empty ($t_{2g}^6{e}_g^0$). Since all electrons are paired, the complex is diamagnetic and will deflect upwards. Statement (B) is correct.

Suspect C: Oxygen Gas ($O_2$) If you draw a simple Lewis structure for oxygen, you might mistakenly think all its electrons are paired in a double bond. However, nature is more complex! According to Molecular Orbital (MO) Theory, the two highest-energy electrons in an $O_2$ molecule occupy degenerate ${\pi }^{\ast }$ antibonding orbitals. Following Hund's Rule, they remain unpaired with parallel spins. These two unpaired electrons make oxygen gas strongly paramagnetic. It will be attracted by the magnetic field, causing a downward deflection. Statement (C) is correct.

Suspect D: Benzene ($C_6{H}_6$) Benzene is a highly stable aromatic ring. All of its carbon and hydrogen atoms are bonded through a network of $\sigma$ bonds, and its remaining electrons form a delocalized, perfectly paired $\pi$ electron cloud. With no unpaired electrons, benzene is diamagnetic and should deflect upwards. Since statement (D) claims it deflects downwards, it is incorrect.

By bridging the gap between quantum electron configurations and observable physical forces, we can confidently conclude that statements (A), (B), and (C) accurately describe the behavior of these compounds in a magnetic field. It is a beautiful reminder that the rules governing the smallest particles dictate the behavior of the world we can see and touch.