Problem 15 - Chemistry Matter and Change

Question

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

Step-by-Step Solution

Answer

a) Ionization equation: \(\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_{2} + \mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_3^{+} + \mathrm{OH}^{-}\); Kb: \(\frac{[\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_3^{+}] [\mathrm{OH}^{-}]}{[\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_{2}]}\) b) Ionization equation: \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2} + \mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_3^{+} + \mathrm{OH}^{-}\); Kb: \(\frac{[\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_3^{+}] [\mathrm{OH}^{-}]}{[\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2}]}\) c) Ionization equation: \(\mathrm{CO}_{3}^{2-} + \mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{HCO}_3^{-} + \mathrm{OH}^{-}\); Kb: \(\frac{[\mathrm{HCO}_3^{-}] [\mathrm{OH}^{-}]}{[\mathrm{CO}_{3}^{2-}]}\) d) Ionization equation: \(\mathrm{HSO}_{3}^{-} + \mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{SO}_{3}^{2-} + \mathrm{OH}^{-}\); Kb: \(\frac{[\mathrm{SO}_{3}^{2-}] [\mathrm{OH}^{-}]}{[\mathrm{HSO}_{3}^{-}]}\)

Step 1: a. Hexylamine

For hexylamine, the ionization equation in water is: \(\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_{2} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_3^{+} (aq) + \mathrm{OH}^{-} (aq)\) Now, we can write the base ionization constant expression, Kb: \[K_b = \frac{[\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_3^{+}] [\mathrm{OH}^{-}]}{[\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{NH}_{2}]}\]

Step 2: b. Propylamine

For propylamine, the ionization equation in water is: \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \rightleftharpoons \mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_3^{+} (aq) + \mathrm{OH}^{-} (aq)\) Now, we can write the base ionization constant expression, Kb: \[K_b = \frac{[\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_3^{+}] [\mathrm{OH}^{-}]}{[\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2}]}\]

Step 3: c. Carbonate ion

For the carbonate ion, the ionization equation in water is: \(\mathrm{CO}_{3}^{2-} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \rightleftharpoons \mathrm{HCO}_3^{-} (aq) + \mathrm{OH}^{-} (aq)\) Now, we can write the base ionization constant expression, Kb: \[K_b = \frac{[\mathrm{HCO}_3^{-}] [\mathrm{OH}^{-}]}{[\mathrm{CO}_{3}^{2-}]}\]

Step 4: d. Hydrogen sulfite ion

For the hydrogen sulfite ion, the ionization equation in water is: \(\mathrm{HSO}_{3}^{-} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \rightleftharpoons \mathrm{SO}_{3}^{2-} (aq) + \mathrm{OH}^{-} (aq)\) Now, we can write the base ionization constant expression, Kb: \[K_b = \frac{[\mathrm{SO}_{3}^{2-}] [\mathrm{OH}^{-}]}{[\mathrm{HSO}_{3}^{-}]}\]

Key Concepts

Ionization Constant

The ionization constant, often denoted as \( K_b \) for bases, is a numerical value that describes the extent to which a base will ionize in water. For acids, the constant is \( K_a \). This constant gives us an idea of the strength of the base or acid. A higher \( K_b \) value means the base more completely ionizes, indicating greater base strength.
A base's ionization can be represented by an equation, showing the base reacting with water to create its corresponding ion and hydroxide ions. Using these chemical equations, we can determine the concentration of ions at equilibrium, and from there, calculate the ionization constant by plugging the equilibrium concentrations into the expression for \( K_b \).
Understanding the \( K_b \) value helps in predicting the behavior of bases in solution, which is crucial for many chemical processes.

Base Ionization

Base ionization refers to the process wherein a base reacts with water, resulting in the formation of its conjugate acid and hydroxide ions. This process is an equilibrium reaction, meaning it can proceed in both directions until a balance is reached.

• The general form of a base ionization equation is: \( ext{Base} + ext{Water} \rightleftharpoons ext{Conjugate Acid} + ext{OH}^- \).

In this reversible reaction, bases like hexylamine, propylamine, carbonate ion, and hydrogen sulfite ion donate an electron pair to hydrogen from water, leading to the release of \( ext{OH}^- \).
Once the equilibrium is achieved, the concentrations of the base, its conjugate acid, and OH ions are fixed. These concentrations allow us to calculate the base ionization constant \( K_b \), providing insights into the base's behavior in aqueous solutions.

Hexylamine

Hexylamine, a type of amine, is a weak base with the molecular formula \( ext{C}_6 ext{H}_{13} ext{NH}_2 \). When it dissolves in water, hexylamine undergoes ionization, a process where it accepts a proton from water, forming its conjugate acid.

• The ionization equation for hexylamine is: \( ext{C}_6 ext{H}_{13} ext{NH}_2(aq) + ext{H}_2 ext{O}(l) \rightleftharpoons ext{C}_6 ext{H}_{13} ext{NH}_3^+(aq) + ext{OH}^-(aq) \).

This equation shows that hexylamine increases the concentration of \( ext{OH}^- \) ions, characteristic behavior of a base.
By using the equilibrium concentrations of the reactants and products depicted in the ionization equation, one can write the base ionization constant expression \( K_b \). For hexylamine, it is calculated as \[ K_b = \frac{[\text{C}_6 \text{H}_{13} \text{NH}_3^+] [\text{OH}^-]}{[\text{C}_6 \text{H}_{13} \text{NH}_2]} \].

Propylamine

Propylamine is another amine, with the chemical formula \( ext{C}_3 ext{H}_7 ext{NH}_2 \). Just like hexylamine, it typically acts as a weak base. In water, propylamine bases undergo base ionization, reacting with water molecules to form ions.

• The ionization equation is: \( ext{C}_3 ext{H}_7 ext{NH}_2(aq) + ext{H}_2 ext{O}(l) \rightleftharpoons ext{C}_3 ext{H}_7 ext{NH}_3^+(aq) + ext{OH}^-(aq) \).

This equation shows that propylamine accepts protons from water, thereby increasing the concentration of hydroxide ions in the solution.
The base ionization constant \( K_b \) is specific for each weak base, including propylamine. It is expressed as: \[ K_b = \frac{[\text{C}_3 \text{H}_7 \text{NH}_3^+] [\text{OH}^-]}{[\text{C}_3 \text{H}_7 \text{NH}_2]} \]. Calculating \( K_b \) helps to assess the base strength of propylamine in comparison with other bases.

Carbonate Ion

The carbonate ion \( ext{CO}_3^{2-} \) is an anion known for its role in buffering systems and water chemistry. It acts as a base when in solution.

• The ionization process is represented by the equation: \( ext{CO}_3^{2-}(aq) + ext{H}_2 ext{O}(l) \rightleftharpoons ext{HCO}_3^-(aq) + ext{OH}^-(aq) \).

In this reaction, the carbonate ion increases the amount of \( ext{OH}^- \) ions, exemplifying typical basic behavior.
The ionization constant \( K_b \) helps quantify the degree of ionization of the carbonate ion in water, as shown in the expression: \[ K_b = \frac{[\text{HCO}_3^-] [\text{OH}^-]}{[\text{CO}_3^{2-}]} \].
This constant plays a significant role in understanding how carbonate ion acts in environments like natural water systems and industrial processes.

Hydrogen Sulfite Ion

Hydrogen sulfite ion, symbolized as \( ext{HSO}_3^- \), is another example of a weak base that can react with water. This reaction is crucial in systems like acid rain chemistry.

• Its ionization equation is: \( ext{HSO}_3^-(aq) + ext{H}_2 ext{O}(l) \rightleftharpoons ext{SO}_3^{2-}(aq) + ext{OH}^-(aq) \).

The equation illustrates the process where hydrogen sulfite ion dissociates to form sulfate ions and \( ext{OH}^- \) ions, thus behaving as a base in aqueous solution.
The corresponding base ionization constant expression is: \[ K_b = \frac{[\text{SO}_3^{2-}] [\text{OH}^-]}{[\text{HSO}_3^-]} \].
This reaction is instrumental in predicting the effects of sulfur compounds in various environments, including natural water bodies and atmospheric phenomena.