Question

Give the oxidation numbers for the underlined atoms in the following molecules and ions: (a) \(\underline{\mathrm{Cs}}_{2} \mathrm{O}\) (b) \(\mathrm{Ca} \underline{\mathrm{I}}_{2}\) (c) \(\mathrm{Al}_{2} \mathrm{O}_{3}\) (d) \(\mathrm{H}_{3} \mathrm{~A}_{\mathrm{s} \mathrm{O}_{3}}\) (e) \(\mathrm{TiO}_{2}\) (f) \(\mathrm{MoO}_{4}^{2-},(\mathrm{g}) \mathrm{PtCl}_{4}^{2-}\) (h) \(\underline{\mathrm{Pt}} \mathrm{Cl}_{6}^{2-}\) (i) \(\underline{\mathrm{Sn}} \mathrm{F}_{2},(\mathrm{j}) \underline{\mathrm{ClF}}_{3},(\mathrm{k}) \underline{\mathrm{Sb} \mathrm{F}_{6}^{-}}\)

Short answer

(a) +1, (b) -1, (c) +3, (d) +3, (e) +4, (f) +6, (g) +4, (h) +4, (i) +2, (j) +3, (k) +5.

Step-by-step solution

Cs in Cs2O

In the compound \(\mathrm{Cs}_2\mathrm{O}\), cesium (Cs) is an alkali metal, which typically has an oxidation number of \(+1\). Oxygen generally has an oxidation number of \(-2\). Since there are two cesium atoms each with \(+1\), the total positive charge is \(+2\). This balances the \(-2\) from the single oxygen atom. Therefore, the oxidation number of the underlined \(\mathrm{Cs}\) is \(+1\).

I in CaI2

In \(\mathrm{Ca}\underline{\mathrm{I}}_2\), iodine (I) typically has an oxidation number of \(-1\). Calcium, an alkaline earth metal, has an oxidation number of \(+2\). Since there are two iodine atoms, each must balance half of the +2 charge from calcium, resulting in an oxidation number of \(-1\) for each iodine. Thus, the oxidation number for the underlined \(\mathrm{I}\) in \(\mathrm{Ca}\underline{\mathrm{I}}_2\) is \(-1\).

Al in Al2O3

In \(\mathrm{Al}_2\mathrm{O}_3\), aluminum (Al) generally has an oxidation number of \(+3\). Oxygen, as established before, generally has an oxidation number of \(-2\). With three oxygen atoms, the total negative charge is \(-6\). Each aluminum atom must have a \(+3\) oxidation state to balance the \(-6\) total, so the oxidation number for Al in \(\mathrm{Al}_2\mathrm{O}_3\) is \(+3\).

As in H3AsO3

In \(\mathrm{H}_3\mathrm{AsO}_3\), hydrogen has an oxidation number of \(+1\) and oxygen has \(-2\). With three hydrogens, this is \(+3\), and with three oxygens, it is \(-6\). For the compound to be neutral, arsenic (As) must have an oxidation state that brings the total back to zero. Solving for As's oxidation state: \(3(-2) + 3(+1) + \text{As number} = 0\), leading to \(+3\). Thus, the oxidation number of As in \(\mathrm{H}_3\mathrm{AsO}_3\) is \(+3\).

Sn in SnF2

In \(\underline{\mathrm{Sn}}\mathrm{F}_2\), fluorine typically has an oxidation number of \(-1\). Since there are two fluorine atoms, this makes the total negative charge \(-2\). To balance this in a neutral compound, tin (Sn) must have an oxidation number of \(+2\). Therefore, the oxidation number of \(\mathrm{Sn}\) in \(\underline{\mathrm{Sn}}\mathrm{F}_2\) is \(+2\).

Cl in ClF3

In \(\underline{\mathrm{ClF}}_3\), fluorine has an oxidation state of \(-1\). With three fluorines, the total is \(-3\). Chlorine must offset this charge to maintain a neutral compound. Thus, the oxidation state of chlorine is \(+3\). Hence, the oxidation number of \(\mathrm{Cl}\) in \(\underline{\mathrm{ClF}}_3\) is \(+3\).

Sb in SbF6−

For \(\underline{\mathrm{Sb}}\mathrm{F}_6^-\), each fluorine has \(-1\), totaling \(-6\) from the six fluorines. The entire ion has a charge of \(-1\), so \(\text{Sb} + (-6) = -1\). Solving for \(\text{Sb}\), its oxidation state is \(+5\). Therefore, the oxidation number of \(\mathrm{Sb}\) in \(\underline{\mathrm{Sb}}\mathrm{F}_6^-\) is \(+5\).

Key concepts

Oxidation State

The oxidation state, also known as the oxidation number, is a concept used to track how many electrons are lost or gained by an atom in a chemical reaction. It's a simple way to keep track of electron transfer during redox reactions. Typically, the oxidation state is represented by integers, which can be positive, negative, or zero. For example, in water ( H_2O ), oxygen has an oxidation state of -2 , while hydrogen is +1 . This method plays an essential role in identifying the changes in electrons during chemical reactions and ensures charge balancing within a compound. When considering an oxidation state, remember:

• Pure elements have an oxidation state of 0.
• Fluorine in compounds is always -1 .
• Alkali metals (e.g., Li, Na, K ) always have a +1 oxidation state.
• Alkaline earth metals (e.g., Mg, Ca ) have a +2 oxidation state.
• Hydrogen is usually +1 , except in metal hydrides where it's -1 .

Using these guidelines, you can assign oxidation numbers to many chemical compounds.

Chemical Compounds

Chemical compounds are formed when two or more different types of atoms bond together. They can be composed of molecules or ions, depending on the nature of the atoms involved and how they bond. Understanding the structure of chemical compounds is key to predicting their chemical behavior, such as reactivity, and also determining oxidation states.
Within a compound, the atoms are held together by chemical bonds, which can be ionic or covalent:

• Ionic bonds form when electrons are transferred from one atom to another, leading to the formation of charged ions. A typical example is sodium chloride (NaCl), where sodium (Na) loses an electron to become Na^+ , and chlorine (Cl) gains that electron to become Cl^- .
• Covalent bonds occur when atoms share electrons, such as in water ( H_2O ), where oxygen shares electrons with hydrogen atoms.

The awareness of how these bonds work aids in determining the oxidation states of the atoms in a compound.

Redox Reactions

Redox reactions, or reduction-oxidation reactions, are processes where the transfer of electrons takes place between atoms. They are remarkable for simultaneously involving both reduction (gain of electrons) and oxidation (loss of electrons). Understanding redox reactions is crucial for many fields, including chemistry, biology, and even environmental science. Redox reactions are responsible for processes such as cellular respiration and photosynthesis.
In a redox reaction, two main agents come into play:

• The oxidizing agent , which gains electrons and is reduced during the reaction.
• The reducing agent , which loses electrons and is oxidized in the process.

To determine what's happening in a redox reaction, look at the changes in oxidation states of the participating atoms. When an atom's oxidation state increases, it's undergoing oxidation. Conversely, if an atom's oxidation state decreases, it's being reduced. Through this, you can identify which compounds act as oxidizing and reducing agents in the reaction.

Charge Balancing

Charge balancing is an essential principle that mandates the total charge within a compound must equal the combined oxidation states of all atoms involved. This concept ensures that compounds are electrically neutral or reflect the specific charge on ions.
When applying charge balancing:

• Consider the total positive and negative charges. For example, in MgCl_2 , magnesium ( Mg ) has a +2 oxidation state and each chlorine ( Cl ) ion has a -1 state. The charges balance as the positive +2 of magnesium is equal to the combined -2 from two Cl^- ions.
• In complex ions, such as sulfate ( SO_4^{2-} ), ensure each atom's oxidation state contributes to the ion's total charge. Here, sulfur's oxidation state aligns such that the sum of oxidation numbers is -2 , mirroring the ion's overall negative charge.

Proper charge balancing helps in verifying that you’ve assigned the correct oxidation states and can further ensure the valid interpretation of chemical formulas and reactions.