Determining whether the C2+ ion is paramagnetic or diamagnetic requires understanding how electrons are arranged in molecular orbitals. The magnetic properties of molecules are governed by the specific distribution of their electrons in space. Determining this magnetic behavior requires a detailed understanding of how atomic orbitals combine to form molecular orbitals. The outcome hinges entirely on whether the ion possesses any unpaired electrons.
Understanding Molecular Magnetism
Magnetic behavior is categorized into two states: diamagnetism and paramagnetism, based entirely on the presence or absence of unpaired electrons.
A diamagnetic substance contains only paired electrons, meaning every electron occupies an orbital with an electron of opposite spin. When placed in an external magnetic field, diamagnetic materials are weakly repelled.
In contrast, a paramagnetic substance is characterized by having at least one unpaired electron. This lone electron acts as a tiny magnet, resulting in a weak attraction to an external magnetic field. Determining the magnetic state of C2+ requires uncovering its precise electron configuration.
The Necessity of Molecular Orbital Theory
Traditional models of chemical bonding, such as Lewis structures or Valence Bond Theory, are insufficient for accurately predicting the magnetic properties of diatomic molecules. These models often treat electron pairs as localized between two atoms, failing to account for the full interaction of all electrons. For C2+, these simple approaches would lead to an incorrect prediction of its magnetic state.
The correct framework is Molecular Orbital Theory (MOT), which treats electrons as occupying orbitals delocalized across the entire molecule. MOT describes how atomic orbitals combine to form an equal number of new molecular orbitals (MOs). These MOs are categorized as lower-energy bonding orbitals (\(\sigma\) and \(\pi\)) that stabilize the molecule, and higher-energy antibonding orbitals (\(\sigma^\) and \(\pi^\)) that destabilize it.
Types of Molecular Orbitals
The \(\sigma\) (sigma) orbitals are formed by the head-on overlap of atomic orbitals, concentrating electron density along the internuclear axis. The \(\pi\) (pi) orbitals are formed by the side-by-side overlap, concentrating electron density above and below the internuclear axis. Systematically filling these molecular orbitals according to quantum mechanical rules provides the accurate electron distribution needed to determine unpaired electrons.
Applying Molecular Orbital Theory to C2+
To determine the electron configuration of C2+, we first calculate the total number of valence electrons. A neutral carbon atom has four valence electrons. The neutral C2 molecule has eight valence electrons (four from each atom). Since C2+ is a cation with a \(+1\) charge, it has lost one electron, resulting in a total of seven valence electrons.
These seven electrons are placed into the molecular orbitals following the Aufbau principle, Hund’s rule, and the Pauli exclusion principle. For carbon, \(s\)–\(p\) mixing occurs, which places the \(\pi_{2p}\) orbitals lower in energy than the \(\sigma_{2p}\) orbital. Therefore, the \(\pi_{2p}\) orbitals are filled first.
The filling sequence for the seven valence electrons is \(\sigma_{2s}^2\) and \(\sigma_{2s}^{2}\). The remaining three electrons are placed into the degenerate \(\pi_{2p}\) set (consisting of \(\pi_{2p_x}\) and \(\pi_{2p_y}\)). Following Hund’s rule, the first two electrons fill the \(\pi_{2p}\) set singly. The final, seventh valence electron must then pair up in one of these \(\pi_{2p}\) orbitals. This results in one orbital having two paired electrons and the other having a single, unpaired electron. The resulting valence configuration is \(\sigma_{2s}^2 \sigma_{2s}^{2} \pi_{2p}^3\).
The Magnetic State of C2+
The application of Molecular Orbital Theory reveals the presence of an unpaired electron in the C2+ ion. The seven valence electrons fill the molecular orbitals, resulting in the configuration \(\sigma_{2s}^2 \sigma_{2s}^{2} \pi_{2p_x}^2 \pi_{2p_y}^1\) (or vice-versa).
Because C2+ possesses a single unpaired electron, it is classified as paramagnetic. This means the C2+ ion will be weakly attracted to an externally applied magnetic field.