Question

Which of the following is a decreasing order of oxidation states of the central atoms? (a) \(\mathrm{PCl}_{5}, \mathrm{HIO}_{4}, \mathrm{Cl}_{2} \mathrm{O}_{7}^{2-}, \mathrm{Cl}_{2} \mathrm{O}\) (b) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}, \mathrm{Cl}_{2} \mathrm{O}, \mathrm{HIO}_{4}, \mathrm{PCl}_{5}\) (c) \(\mathrm{HIO}_{4}, \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}, \mathrm{PCl}_{5}, \mathrm{Cl}_{2} \mathrm{O}\) (d) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}, \mathrm{HIO}_{4}, \mathrm{Cl}_{2} \mathrm{O}, \mathrm{PCl}_{5}\)

Short answer

The correct decreasing order of oxidation states of the central atoms is (c) HIO4, Cr2O72-, PCl5, Cl2O.

Step-by-step solution

Determine the Oxidation State of P in PCl5

For PCl5, each Cl atom has an oxidation state of -1. Since there are 5 Cl atoms, the total oxidation state contributed by chlorine is -5. Phosphorus (P) must balance this out so that the compound has a neutral charge. Therefore, the oxidation state of P is +5.

Determine the Oxidation State of I in HIO4

In HIO4, the oxidation state of H is +1 and oxygen is always -2 except in peroxides. There are 4 O atoms giving -8. To find the oxidation state of I, we add up the charges and set it equal to 0 because the compound is neutral: 1 + x + (-8) = 0. Solving for x gives I an oxidation state of +7.

Determine the Oxidation State of Cl in Cl2O7 2-

In Cl2O7 2-, oxygen has an oxidation state of -2. With 7 O atoms, the total is -14. The compound has a -2 charge, so the sum of all oxidation states is -2. For two Cl atoms, we write: 2x + (-14) = -2. Solving for x gives each Cl an oxidation state of +6.

Determine the Oxidation State of Cl in Cl2O

For Cl2O, oxygen is -2. With 1 O atom, this is -2. Cl2 must balance it out to make the compound neutral. We write: 2x + (-2) = 0. Solving for x gives each Cl an oxidation state of +1.

Determine the Oxidation State of Cr in Cr2O7 2-

For Cr2O7 2-, oxygen has an oxidation state of -2. With 7 O atoms, the total is -14. The compound has a -2 charge, so the sum of all oxidation states is -2. For two Cr atoms, we write: 2x + (-14) = -2. Solving for x gives each Cr an oxidation state of +6.

Arrange the Central Atoms in Decreasing Order of Their Oxidation States

From the above calculations, P in PCl5 is +5, I in HIO4 is +7, Cl in Cl2O7 2- is +6, Cl in Cl2O is +1, and Cr in Cr2O7 2- is +6. The decreasing order is: I is +7, Cr and Cl in Cl2O7 2- are +6, P in PCl5 is +5, and Cl in Cl2O is +1.

Match the Order to the Given Choices

The correct choice that represents the central atoms in decreasing order of their oxidation states is the one that shows I first, followed by Cr and Cl in Cl2O7 2- (as they are the same), then P and finally Cl in Cl2O. The correct option is (c) HIO4, Cr2O72-, PCl5, Cl2O.

Key concepts

Chemical Bonding

Chemical bonding is the fundamental concept in chemistry that explains how atoms combine to form compounds. Atoms can achieve a more stable electronic configuration by either sharing electrons (covalent bonding), transferring electrons (ionic bonding), or through weak intermolecular forces. For instance, in the compound PCl₅, phosphorus and chlorine atoms form covalent bonds by sharing electrons. On the other hand, in the ions like Cl₂O₇^2-, aside from covalent bonding within the molecule, there is an ionic character due to the overall charge.

To understand the properties and reactivity of a compound, one must evaluate not just the types of bonds but also the oxidation states of the atoms involved. In our example of PCl₅, while the bonds formed between phosphorus and chlorine are covalent, the number of shared electrons also leads to the concept of oxidation state or number, which is crucial in predicting the behavior of the element in reactions.

Oxidation Number Calculation

Calculating oxidation numbers is vital for understanding the electron transfer in chemical reactions. The oxidation number is a theoretical charge on an atom if the compound was composed entirely of ions. By using certain rules - such as hydrogen usually having an oxidation state of +1 and oxygen having an oxidation state of -2 - the oxidation states of unknown atoms in compounds can be deduced. For example, the oxidation state of phosphorus in PCl₅ can be calculated knowing that chlorine typically has an oxidation state of -1.

Oxidation number calculation is not just arithmetic but a way to understand the electron distribution in compounds. This understanding is necessary for predicting the outcome of chemical reactions, such as redox reactions wherein the transfer of electrons changes the oxidation states of the reactants. When students learn to calculate oxidation states correctly, they unlock insights into a wide variety of chemical processes.

Inorganic Chemistry

Inorganic chemistry is the branch of chemistry that studies the behavior and synthesis of inorganic compounds, which are compounds without carbon-hydrogen bonds. This includes a vast range of substances, from salts to metals and minerals. The oxidation states of the elements play an essential role in this field, as they can determine the color, magnetic properties, and reactivity of compounds. For instance, transition metals can have multiple oxidation states, leading to varied colored compounds and catalytic activities.

Understanding the concepts of inorganic chemistry helps students to reason why certain compounds are more reactive or why certain reactions occur in the first place. By analyzing the oxidation states in compounds such as HIO₄, Cr₂O₇^2-, and Cl₂O, students can predict potential products of a chemical reaction and the conditions under which a reaction might proceed. The reasoning behind the ordering of central atoms according to their oxidation states, as in the textbook exercise, is a quintessential skill in inorganic chemistry.