Problem 15 - Chemistry Matter and Change

Question

Write ionization equations and base ionization constant expressions for the following bases. \begin{equation} \begin{array}{ll}{\text { a. hexylamine }\left(\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_{2}\right)} & {\text { c. carbonate ion }\left(\mathrm{CO}_{3}^{2-}\right)} \\ {\text { b. propylamine }\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2}\right)} & {\text { d. hydrogen sulfite ion }\left(\mathrm{HSO}_{3}^{-}\right)}\end{array} \end{equation}

Step-by-Step Solution

Answer

Write ionization equations and expressions for each base as shown. Include equilibrium constants.

Step 1: Ionization equation for hexylamine

Hexylamine is a weak base, and in water it accepts a proton from water to form its conjugate acid and hydroxide ion. The ionization equation for hexylamine is: \[\text{C}_6\text{H}_{13}\text{NH}_2(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{C}_6\text{H}_{13}\text{NH}_3^+(aq) + \text{OH}^-(aq)\]

Step 2: Base ionization constant for hexylamine

The base ionization constant expression represents the equilibrium concentration of products and reactants for the ionization of hexylamine: \[K_b = \frac{[\text{C}_6\text{H}_{13}\text{NH}_3^+][\text{OH}^-]}{[\text{C}_6\text{H}_{13}\text{NH}_2]}\]

Step 3: Ionization equation for propylamine

Propylamine, another weak base, accepts a proton from water. The ionization equation is: \[\text{C}_3\text{H}_7\text{NH}_2(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{C}_3\text{H}_7\text{NH}_3^+(aq) + \text{OH}^-(aq)\]

Step 4: Base ionization constant for propylamine

The equilibrium constant expression for the ionization of propylamine is represented as: \[K_b = \frac{[\text{C}_3\text{H}_7\text{NH}_3^+][\text{OH}^-]}{[\text{C}_3\text{H}_7\text{NH}_2]}\]

Step 5: Ionization equation for carbonate ion

The carbonate ion, as a base, accepts a proton in water to form bicarbonate ion and a hydroxide ion: \[\text{CO}_3^{2-}(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{HCO}_3^-(aq) + \text{OH}^-(aq)\]

Step 6: Base ionization constant for carbonate ion

The base ionization constant expression for the carbonate ion is: \[K_b = \frac{[\text{HCO}_3^-][\text{OH}^-]}{[\text{CO}_3^{2-}]}\]

Step 7: Ionization equation for hydrogen sulfite ion

The hydrogen sulfite ion can act as a base by accepting a proton in water to form sulfurous acid and a hydroxide ion: \[\text{HSO}_3^-(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{SO}_3(aq) + \text{OH}^-(aq)\]

Step 8: Base ionization constant for hydrogen sulfite ion

The equilibrium constant expression for the ionization of hydrogen sulfite ion is: \[K_b = \frac{[\text{H}_2\text{SO}_3][\text{OH}^-]}{[\text{HSO}_3^-]}\]

Key Concepts

Base Ionization Constant

The Base Ionization Constant, often represented as \(K_b\), is a crucial parameter in chemistry. It quantifies the strength of a base in aqueous solution. Bases accept protons from water, resulting in the formation of their conjugate acid and hydroxide ions.
This constant is derived from the equilibrium expression of the ionization reaction:

• When a base is added to water, an equilibrium is established between the base, its conjugate acid, and hydroxide ions.
• The expression for \(K_b\) reflects the concentrations of these species at equilibrium.
• Mathematically, it is represented as: \[K_b = \frac{[\text{conjugate acid}][\text{OH}^-]}{[\text{base}]}\]

High \(K_b\) values indicate a stronger base able to accept protons more readily, whereas low \(K_b\) values suggest a weaker base with less willingness to gain protons.

Weak Bases

Weak bases are substances that only partially ionize in water. This means that in a solution, they do not convert fully into hydroxide ions (\( \text{OH}^- \)) and their conjugate acids.
For example, propylamine (\( \text{C}_3\text{H}_7\text{NH}_2 \)) and hexylamine (\( \text{C}_6\text{H}_{13}\text{NH}_2 \)) are both primary amines acting as weak bases.
When dissolved in water, these weak bases:

• Accept protons from the water forming their conjugate acids \( \text{C}_3\text{H}_7\text{NH}_3^+ \) and \( \text{C}_6\text{H}_{13}\text{NH}_3^+ \), respectively.
• Generate hydroxide ions \( \text{OH}^- \).
• Reach an equilibrium state where the concentrations of reactants and products remain constant.

This incomplete ionization is key to their classification as weak bases, distinguishing them from strong bases, which completely dissociate.

Equilibrium Concentration

In the context of ionization reactions, equilibrium concentration is a key concept. It refers to the concentration of all reactants and products once the reaction has reached equilibrium.
When a weak base is dissolved in water, it establishes an equilibrium state:

• Initially, the base is present in its molecular form. Over time, it slowly ionizes.
• As it accepts protons and forms products, the rate of ionization decreases until it equals the rate of the reverse reaction.
• At this point, concentrations of all species become stable and do not change further.

This state can be described mathematically by the equilibrium constant expression \(K_b\), highlighting the balance between products and reactants. Knowing these equilibrium concentrations is vital for understanding the behavior of the solution and predicting the pH.

Proton Transfer

Proton transfer is a central theme in acid-base chemistry, underpinning how bases and acids interact in solution. In this process, a proton \(( \text{H}^+ )\) is transferred from one molecule to another.
In the case of weak bases:

• They act as proton acceptors, meaning they take \( \text{H}^+ \) ions from water molecules.
• This results in the formation of a conjugate acid and an increase in hydroxide ion concentration \(( \text{OH}^- )\).

Understanding this proton transfer allows us to write balanced ionization equations. For example:

• In propylamine ionization: \[ \text{C}_3\text{H}_7\text{NH}_2(\text{aq}) + \text{H}_2\text{O}(\text{l}) \rightleftharpoons \text{C}_3\text{H}_7\text{NH}_3^+(\text{aq}) + \text{OH}^-(\text{aq}) \]
• Shows how a base removes a proton from water to reach equilibrium.

This interaction is a core principle in determining the basicity of a substance, affecting its behavior and reactions in solution.