Problem 105 - Chemistry An Atoms First Approach

Question

Write out the stepwise \(K_{\mathrm{a}}\) reactions for the diprotic acid \(\mathrm{H}_{2} \mathrm{SO}_{3}\).

Step-by-Step Solution

Answer

The stepwise dissociation reactions for the diprotic acid H2SO3 are as follows: 1. First dissociation reaction: \[ \mathrm{H}_{2} \mathrm{SO}_{3} \rightleftharpoons \mathrm{HSO}_{3}^- + \mathrm{H}^{+} \] with Ka1 expression: \[ K_{a1} = \frac{[\mathrm{HSO}_{3}^-][\mathrm{H}^+]}{[\mathrm{H}_{2} \mathrm{SO}_{3}]} \] 2. Second dissociation reaction: \[ \mathrm{HSO}_{3}^- \rightleftharpoons \mathrm{SO}_{3}^{2-} + \mathrm{H}^{+}\] with Ka2 expression: \[ K_{a2} = \frac{[\mathrm{SO}_{3}^{2-}][\mathrm{H}^+]}{[\mathrm{HSO}_{3}^-]} \]

Step 1: Write the first dissociation reaction.

For the first step of dissociation, one proton (H⁺) will be lost from the H2SO3 molecule, forming a bisulfite ion (HSO3−) and releasing a hydrogen ion (H⁺). The equation for this reaction is: \[ \mathrm{H}_{2} \mathrm{SO}_{3} \rightleftharpoons \mathrm{HSO}_{3}^- + \mathrm{H}^{+} \]

Step 2: Write the expression for the first dissociation constant (Ka1).

The dissociation constant (Ka1) for this first reaction represents the degree to which H2SO3 dissociates into HSO3− and H⁺. The Ka1 expression is as follows: \[ K_{a1} = \frac{[\mathrm{HSO}_{3}^-][\mathrm{H}^+]}{[\mathrm{H}_{2} \mathrm{SO}_{3}]} \]

Step 3: Write the second dissociation reaction.

After the first proton has been lost from H2SO3, the bisulfite ion (HSO3−) can lose another proton (H⁺). The equation for this second reaction is: \[ \mathrm{HSO}_{3}^- \rightleftharpoons \mathrm{SO}_{3}^{2-} + \mathrm{H}^{+}\]

Step 4: Write the expression for the second dissociation constant (Ka2).

The second dissociation constant (Ka2) represents the degree to which HSO3− dissociates into SO3²⁻ and H⁺. The Ka2 expression is as follows: \[ K_{a2} = \frac{[\mathrm{SO}_{3}^{2-}][\mathrm{H}^+]}{[\mathrm{HSO}_{3}^-]} \] Now we have the dissociation reactions and the corresponding Ka expressions for the diprotic acid, H2SO3.

Key Concepts

Dissociation Constant

The dissociation constant, often denoted as \( K_a \), is a crucial value in understanding how acids dissociate, or break apart, in water. When an acid dissolves in water, it splits into ions. For each step of this process, there's a specific dissociation constant that provides a measure of the extent of dissociation.
The dissociation constant helps predict how strong or weak an acid is. A larger \( K_a \) value indicates a stronger acid, meaning it dissociates more in water and releases more hydrogen ions \( (H^+) \). Conversely, a smaller \( K_a \) value signals a weaker acid, which does not dissociate as much.
For diprotic acids like \( \mathrm{H}_2\mathrm{SO}_3 \) (sulfurous acid), there are two dissociation constants: \( K_{a1} \) for the first proton release and \( K_{a2} \) for the second proton release. Typically, \( K_{a1} \) is larger than \( K_{a2} \), reflecting that the first proton is generally more easily released than the second.

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the concentrations of reactants and products remain constant over time. This happens because the forward and reverse reactions occur at the same rate. In the context of acid dissociation, equilibrium is reached when the rate of the acid molecules dissociating into ions is equal to the rate at which the ions recombine into acid molecules.
When writing the equilibrium expression for a dissociation reaction, it involves the concentrations of the reactants and products. For example, for the dissociation of \( \mathrm{H}_2\mathrm{SO}_3 \) in its first step, the equilibrium expression is:
\[ K_{a1} = \frac{[\mathrm{HSO}_3^-][\mathrm{H}^+]}{[\mathrm{H}_2 \mathrm{SO}_3]} \]
This equation shows the relationship between the concentration of the dissociated ions and the remaining undissociated acid at equilibrium. It's crucial to understand that at equilibrium, the concentrations are constant, but this doesn't mean the whole system is static. Instead, reactions continue to happen in both directions at the same steady pace.

Acid Dissociation Reaction

Acid dissociation reactions are the chemical processes in which an acid releases hydrogen ions into a solution, usually water. This is indicated by the formula of the acid splitting into different products.
In the case of diprotic acids, they dissociate in a stepwise manner, losing one proton at a time. Let's take \( \mathrm{H}_2\mathrm{SO}_3 \) as an example:

• **First Dissociation:**\( \mathrm{H}_2\mathrm{SO}_3 \rightleftharpoons \mathrm{HSO}_3^- + \mathrm{H}^+ \)
• **Second Dissociation:** \( \mathrm{HSO}_3^- \rightleftharpoons \mathrm{SO}_3^{2-} + \mathrm{H}^+ \)

Each of these reactions has its own distinct equilibrium, and thus, its own dissociation constant (\( K_a1 \) and \( K_a2 \)).
Understanding the dissociation process is vital for predicting how an acid behaves in different environments, which is fundamental in chemical reactions, environmental science, and industrial applications.