Question

(a) What are the conjugate bases of the acids HF, \(\left[\mathrm{HSO}_{4}\right]^{-},\left[\mathrm{Fe}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}\) and \(\left[\mathrm{NH}_{4}\right]^{+} ?\) (b) What are the conjugate acids of the bases \(\left[\mathrm{HSO}_{4}\right]^{-}\) \(\mathrm{PH}_{3},\left[\mathrm{NH}_{2}\right]^{-}\) and \([\mathrm{OBr}]^{-} ?\) (c) What is the conjugate acid of \([\mathrm{VO}(\mathrm{OH})]^{+} ?\) (d) \(\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}\) has a \(\mathrm{p} K_{\mathrm{a}}\) value of \(2.5 .\) Comment on the fact that when \(\mathrm{TiCl}_{3}\) dissolves in dilute hydrochloric acid, the main solution species is \(\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}\)

Short answer

(a) F⁻, SO₄²⁻, Fe(OH)₂₆²⁺, NH₃. (b) H₂SO₄, PH₄⁺, NH₃, HOBr. (c) VOH(OH)²⁺. (d) Ti(OH)₂₆³⁺ is stable in acidic solution due to its pKₐ value of 2.5.

Step-by-step solution

Identifying Conjugate Bases

The conjugate base is formed by removing a proton (H⁺) from the acid. For each given acid, remove an H⁺ to determine the conjugate base.1. **HF**: Removing a proton gives \[F^-.\]2. **\([\mathrm{HSO}_{4}]^{-}\)**: Removing a proton gives \[[\mathrm{SO}_{4}]^{2-}.\]3. **\([\mathrm{Fe(OH)}_{2}]_{6}^{3+}\)**: Removing a proton gives \[[\mathrm{Fe(OH)}_{2}]_{6}^{2+}.\]4. **\([\mathrm{NH}_{4}]^{+}\)**: Removing a proton gives \[[\mathrm{NH}_{3}].\]

Identifying Conjugate Acids

The conjugate acid is formed by adding a proton (H⁺) to the base. For each given base, add an H⁺ to determine the conjugate acid.1. **\([\mathrm{HSO}_{4}]^{-}\)**: Adding a proton gives \[[\mathrm{H_{2}SO}_{4}].\]2. **PH₃**: Adding a proton gives \[[\mathrm{PH}_{4}]^{+}.\]3. **\([\mathrm{NH}_{2}]^{-}\)**: Adding a proton gives \[[\mathrm{NH}_{3}].\]4. **\([\mathrm{OBr}]^{-}\)**: Adding a proton gives \[[\mathrm{HOBr}].\]

Finding the Conjugate Acid of a Complex

For the complex ion \([\mathrm{VO}( ext{OH})]^+\), add a proton to form its conjugate acid. Adding a proton gives \[[\mathrm{VOH}(\text{OH})]^2+.\]

Understanding the Behavior of \([\mathrm{Ti}\left(\mathrm{OH}_2\right)_6]^{3+} \) in Acidic Solution

\([\mathrm{Ti}\left(\mathrm{OH}_2\right)_6]^{3+}\) has a \( pK_a \) value of 2.5, indicating it is a relatively strong acid. When \(\mathrm{TiCl}_3\) dissolves in dilute hydrochloric acid, the main species in the solution is \([\mathrm{Ti}\left(\mathrm{OH}_2\right)_6]^{3+}\) due to the acidic environment favoring the formation and stability of the hydrated complex rather than its hydrolyzed or deprotonated forms.

Key concepts

Proton Transfer Reactions

Proton transfer reactions are fundamental to understanding acid-base chemistry. They involve the transfer of a hydrogen ion, or proton ( ext{H}^+), between molecules. In these reactions, acids donate protons, and bases accept them. This transfer results in the formation of two new species: the conjugate base of the acid and the conjugate acid of the base.
- For instance, when hydrochloric acid ( ext{HCl}) donates a proton to water, it forms its conjugate base, chloride ion ( ext{Cl}^-), and the conjugate acid of water, the hydronium ion ( ext{H}_3 ext{O}^+).
- Similarly, if ammonia ( ext{NH}_3) accepts a proton, it forms its conjugate acid, ammonium ( ext{NH}_4^+).

Recognizing the conjugate acid-base pairs in a reaction is crucial because it helps predict the direction and products of the reaction. This concept also shows how reversible reactions can occur, emphasizing the dynamic nature of chemical equilibria. Understanding these basics is key to mastering more complex biochemical and industrial processes.

pKa and Acid Strength

The strength of an acid is often measured by its dissociation in water, which is quantified by the acid dissociation constant, known as K_a. A related concept, pKa, is the negative logarithm of K_a: hence, \( \text{pKa} = -\log(\text{K}_a) \). The lower the pKa value, the stronger the acid, as it means the acid dissociates more in solution.
- Strong acids, with low pKa values, such as hydrochloric acid (HCl), completely dissociate in solution.
- Weak acids, like acetic acid, have higher pKa values and do not fully dissociate.

In the problem's context, \( \left[\text{Ti}\left(\text{OH}_2\right)_6\right]^{3+} \) has a pKa of 2.5, marking it as a relatively strong acid. This strong acid behavior influences its predominant presence in solution when \( \text{TiCl}_3 \) is dissolved in an acidic medium.
For practical applications, pKa values guide the prediction of reaction outcomes, especially in buffer solutions and acid-base titrations.

Complex Ions

Complex ions are composed of a central metal atom or ion bonded to surrounding molecules or ions, called ligands. These ligands donate electron pairs to form coordinate covalent bonds. Complex ions can play a significant role in reactions, especially those involving proton transfers or acid-base chemistry.
- The formation of complex ions often involves metal cations interacting with neutral molecules like water or anions.
- For example, \( \left[\text{Fe}\left(\text{OH}_2\right)_{6}\right]^{3+} \) is a complex ion formed by iron surrounded by water molecules acting as ligands.

Complexation can influence the reactivity and solubility of the compounds involved. In the conjugate acid context, when such a complex accepts or donates a proton, its formation or stability might change, which alters its chemical behavior.
Understanding how complex ions work helps in predicting the behavior of transition metal compounds in various environments, including biological systems and industrial processes.