Question

Based on knowledge of the electronic configuration of titanium, state which of the following compounds of titanium is unlikely to exist: \(\mathrm{K}_{3} \mathrm{TiF}_{6}, \mathrm{~K}_{2} \mathrm{Ti}_{2} \mathrm{O}_{5}, \mathrm{TiCl}_{3},\) \(\mathrm{K}_{2} \mathrm{TiO}_{4}, \mathrm{~K}_{2} \mathrm{TiF}_{6}\)

Short answer

\(\mathrm{K}_{2} \mathrm{TiO}_{4}\) is unlikely to exist because it requires titanium in an uncommon +6 oxidation state.

Step-by-step solution

Determine the Electronic Configuration of Titanium

The atomic number of titanium is 22. This means its electronic configuration is \([\mathrm{Ar}]\ 3d^2 4s^2\). Titanium can exhibit different oxidation states, commonly +2, +3, and +4 due to its ability to lose electrons from the 3d and 4s orbitals.

Assess Titanium Oxidation States in Each Compound

Calculate the expected oxidation state of titanium in each compound by examining the charges of the other elements present:- In \(\mathrm{K}_{3}\mathrm{TiF}_{6}\), potassium (K) has an oxidation state of +1 and fluorine (F) has -1, resulting in titanium having +3 oxidation state.- In \(\mathrm{K}_{2} \mathrm{Ti}_{2} \mathrm{O}_{5}\), potassium is +1 and oxygen is -2, titanium needs to balance this charge with a +5 oxidation state.- In \(\mathrm{TiCl}_{3}\), chlorine (Cl) is -1, resulting in titanium having +3 oxidation state.- In \(\mathrm{K}_{2} \mathrm{TiO}_{4}\), potassium is +1 and oxygen is -2, titanium needs an oxidation state of +6 to balance it.- In \(\mathrm{K}_{2} \mathrm{TiF}_{6}\), titanium has a +4 oxidation state because each fluorine contributes a -1 charge.

Identify the Unlikely Oxidation State for Titanium

Titanium commonly exhibits oxidation states of +2, +3, and +4. While oxidation states +5 and +6 are theoretically possible, they are quite rare and unstable due to electron configuration reasons. Therefore, a compound with titanium in either +5 or +6 oxidation state is unlikely to exist or be stable.

Determine the Unlikely Compound

Based on the expected oxidation states:- \(\mathrm{K}_{2} \mathrm{Ti}_{2} \mathrm{O}_{5}\) requires titanium in a +5 oxidation state.- \(\mathrm{K}_{2} \mathrm{TiO}_{4}\) requires titanium in a +6 oxidation state.Both of these are non-common and unstable for titanium, but \(\textbf{+6 is especially uncommon}\). Thus, \(\mathrm{K}_{2} \mathrm{TiO}_{4}\) is the least likely compound to exist.

Key concepts

Oxidation States

Oxidation states, or oxidation numbers, indicate the degree of oxidation or reduction of an element within a compound. These numbers indicate how many electrons an atom gains, loses, or appears to use in a chemical bond. Usually, they are assigned based on a set of rules:

• Pure elements always have an oxidation state of zero.
• In simple ionic compounds, the oxidation state of an element equals the charge on the ion.
• For compounds, the sum of oxidation states equals the overall charge of the compound.

For titanium, a transition metal, reaching oxidation states like +2, +3, and +4 is more common due to its electronic configuration \(\text{[Ar]}\ 3d^2 4s^2\). This configuration allows it to lose electrons easily. However, oxidation states of +5 and +6, which would require the removal of more electrons, are not typical. Thus, compounds with titanium in unusually high oxidation states tend to be unstable.

Titanium Compounds

Titanium compounds are essential in many industrial applications due to their desirable properties such as resistance to corrosion and lightweight nature. Common titanium compounds include:

• TiCl₃: Used in chemical synthesis and as catalysts.
• K₃TiF₆: Serves as a source for creating titanium metal.
• K₂TiF₆: Also used in producing titanium metal and alloys.

These compounds usually involve titanium in +3 or +4 oxidation states, as they are more stable and synthetically accessible. Titanium's propensity to form compounds in these states is linked to its ability to share or lose a select number of electrons, stabilizing the resulting compound. Rarely, titanium can be forced into higher oxidation states, but these tend to be less stable and are not often found in practical applications.

Unstable Oxidation States

Unstable oxidation states are those that are not energetically favorable for a given element, making the compounds containing them more likely to decompose or react further to reach a more stable state. For titanium, while +2, +3, and +4 are stable, the higher oxidation states like +5 and +6 are unstable. They require significant energy input to form and are not typically stable without specific conditions. This is because

• Titanium's higher oxidation states require a removal of more electrons than usual, disrupting the stable electron configuration.
• Such states do not readily form bonds that result in lower energy, making them less stable in typical environments.

Hence, compounds predicting a +5 or +6 oxidation state in titanium may not exist naturally or require unusual conditions to produce and maintain.

Chemical Bonding

Chemical bonding is the force that holds atoms together in a compound. It largely determines the properties of the compound formed. Titanium, like many transition metals, can form:

• Covalent bonds, where it shares electrons, often observed in lower oxidation states.
• Ionic bonds, especially when in compounds with non-metals, typical in its higher oxidation states.
• Metallic bonds, though more rare and usually seen in pure metal forms or alloys.

The nature of the bond affects a compound's stability and properties. For example, in the presence of highly electronegative elements like fluorine or oxygen, titanium may form ionic bonds, such as in K₂TiF₆. These bonds result in higher melting points and robust structural integrity. For compounds predicting higher oxidization states, such as K₂TiO₄, the bonding cannot compensate for the instability caused by an uncommon oxidation number, making them less likely to sustain practical conditions.