Metal carbonyls having formula \(M(\mathrm{CO})_{x}\), where \(x\) is the number of carbonyl units co-ordinated to metal \(M\) are formed by Fe, \(\mathrm{Cr}\) and Ni. If effective atomic number of each metal is 36, what are the formula of metal carbonyls?

Effective atomic number (EAN) is a key concept in coordination chemistry, especially for metal carbonyls. It equates to the total number of protons that an atom's nucleus would have if the metal's electron cloud were to mimic the nearest noble gas configuration. In other words, it's the sum of the atom's actual protons plus the number of electrons donated by attached ligands like carbonyl (CO) groups.

When ligands bind to a metal, they can donate electron pairs, increasing the metal's total electron count. Researchers have observed that stable configurations often occur when metals in complexes have an EAN equivalent to the next noble gas. For example, iron (Fe), which has an atomic number of 26, often forms stable complexes when its EAN is 36, identical to the noble gas krypton. In the case of the metal carbonyls, each CO group contributes two electrons, which aids in achieving the desired EAN.

Coordination chemistry involves the study of compounds in which a central metal atom or ion is surrounded by non-metal ions or molecules, known as ligands. Metal carbonyls fall under this category, with carbon monoxide acting as a ligand. These compounds are characterized by the nature of the bond between the metal and the carbonyl group, where the metal atom provides vacant orbitals for bonding and the ligands offer electron pairs.

Coordination chemistry is not just about the formation of complexes, but also about understanding the properties and reactivities of these compounds. The structure, bond angles, and overall geometry around the central metal will affect the physical and chemical behavior of the complex. Transition metals are especially prolific in forming such complexes due to their d orbitals, which can accept electron pairs from ligands like CO, NH₃, or H₂O.

The periodic table is a chemist's roadmap, organizing chemical elements by their atomic numbers, electron configurations, and recurring properties. To solve problems involving metal carbonyls, one must be adept at reading and extracting information from the periodic table, such as atomic numbers and group configurations.

A clear grasp of the periodic table allows students to understand that the transition metals like Fe, Cr, and Ni – which frequently form metal carbonyls – reside in the d-block of the table. This central location is key, as these elements have unfilled d orbitals that are instrumental in forming complexes with ligands. Furthermore, knowing the atomic numbers and positions of elements on the periodic table helps in predicting and explaining trends in their chemical behavior.

Electron counting is a fundamental technique in coordination chemistry that involves tallying electrons to predict stability and reactivity in metal complexes. It can be split into two approaches: the neutral method and the oxidation state method. The neutral method treats all species as neutral, while the oxidation state method takes into consideration the charges.

For metal carbonyls, electron counting helps in determining the number of ligands that can attach to the metal center to satisfy its EAN. In studying the complexes mentioned in the exercise, we use electron counting to ensure that the metal achieves an electronic configuration resembling that of a noble gas. Given the rule that each CO ligand donates two electrons, this method simplifies calculating the number of CO ligands needed to achieve a certain EAN.