Problem 12 - Chemistry Matter and Change

Question

Write ionization equations and acid ionization constant expressions for a. \(\mathrm{HClO}_{2} \quad\) b. HNO_ \(_{2} \quad\) c. HIOeach acid.

Step-by-Step Solution

Answer

Ionization equations: a. \(\mathrm{HClO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{ClO}_{2}^{-}\) b. \(\mathrm{HNO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{NO}_{2}^{-}\) c. \(\mathrm{HIO} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{IO}^{-}\) Acid ionization constant expressions: a. \(K_{\mathrm{a1}} = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{ClO}_{2}^{-}]}{[\mathrm{HClO}_{2}]}\) b. \(K_{\mathrm{a2}} = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{NO}_{2}^{-}]}{[\mathrm{HNO}_{2}]}\) c. \(K_{\mathrm{a3}} = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{IO}^{-}]}{[\mathrm{HIO}]}\)

Step 1: Write the ionization equation

Write the ionization equation for each acid by showing how it reacts with water to form hydronium ions (H3O+) and the corresponding conjugate base: a. \(\mathrm{HClO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{ClO}_{2}^{-}\) b. \(\mathrm{HNO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{NO}_{2}^{-}\) c. \(\mathrm{HIO} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{IO}^{-}\)

Step 2: Write the acid ionization constant expression

Write the K_a expression for each acid by using the ionization equation to form an equilibrium constant expression: For a general ionization equation, \(\mathrm{HA} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{A}^{-}\), we have the Ka expression: \[K_a = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{A}^{-}]}{[\mathrm{HA}]}\] Applying this to our three acids, we get: a. \(K_{\mathrm{a1}} = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{ClO}_{2}^{-}]}{[\mathrm{HClO}_{2}]}\) b. \(K_{\mathrm{a2}} = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{NO}_{2}^{-}]}{[\mathrm{HNO}_{2}]}\) c. \(K_{\mathrm{a3}} = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{IO}^{-}]}{[\mathrm{HIO}]}\)

Key Concepts

Ionization Equations

Ionization equations are mathematical representations that show how an acid reacts with water to form ions. This is a critical step in understanding acid behavior in aqueous solutions.

• In an ionization reaction, the acid (let's use \[\text{HA}\] as a general formula for the acid) donates a proton \(\text{H}^+\) to a water molecule, resulting in the formation of hydronium ions (\(\text{H}_{3}\text{O}^+\)) and a conjugate base (\(\text{A}^-\)).
• For example, consider chlorous acid (\(\text{HClO}_{2}\)) undergoing ionization: \[\text{HClO}_{2} + \text{H}_2\text{O} \rightleftharpoons \text{H}_{3}\text{O}^+ + \text{ClO}_{2}^-\]

The double arrows in the reaction show that the process is reversible and reaches equilibrium. This means that the reaction can proceed in both directions depending on the concentration of the involved ions.

Conjugate Base

When an acid donates a proton, the remaining part of the acid becomes its conjugate base. This is a fundamental concept in acid-base chemistry.

• The conjugate base of an acid is simply the original acid molecule minus one \(\text{H}^+\) ion.
• Referring back to our example of chlorous acid, when \(\text{HClO}_{2}\) loses a \(\text{H}^+\), it forms its conjugate base, \(\text{ClO}_{2}^-\).

The concept is important because it helps us understand the acid's role in equilibrium reactions. In a reversible reaction, the conjugate base can potentially reaccept a proton from water, transforming back into the acid.

• Each acid in its ionization reaction forms a conjugate base:
  • \(\text{HNO}_{2}\) becomes \(\text{NO}_{2}^-\)
  • \(\text{HIO}\) becomes \(\text{IO}^-\)

Acid Ionization Constant

The acid ionization constant, symbolized as \(K_a\), is a measure of the strength of an acid in solution. It reflects how completely an acid ionizes to release protons.

• The higher the \(K_a\) value, the stronger the acid, meaning it ionizes more completely.
• In the ionization of an acid \(\text{HA}\), its \(K_a\) expression is: \[K_a = \frac{[\text{H}_{3}\text{O}^+][\text{A}^-]}{[\text{HA}]}\]

Using this equation, you can calculate the \(K_a\) for our example acids:

• For \(\text{HClO}_{2}\), the acid ionization constant is given by: \[K_{a1} = \frac{[\text{H}_{3}\text{O}^+][\text{ClO}_{2}^-]}{[\text{HClO}_{2}]}\]
• For \(\text{HNO}_{2}\): \[K_{a2} = \frac{[\text{H}_{3}\text{O}^+][\text{NO}_{2}^-]}{[\text{HNO}_{2}]}\]
• And \(\text{HIO}\): \[K_{a3} = \frac{[\text{H}_{3}\text{O}^+][\text{IO}^-]}{[\text{HIO}]}\]

Understanding \(K_a\) helps predict how an acid will behave in different chemical environments, making it a vital tool in both academic and practical chemistry applications.