Question

Calculate the percent dissociation for a \(0.22-M\) solution of chlorous acid \(\left(\mathrm{HClO}_{2}, K_{\mathrm{a}}=1.2 \times 10^{-2}\right)\)

Short answer

\[x \approx 0.04\text{ M}\] #tag_title# (Step 5: Calculate the percent dissociation)#tag_content# Percent dissociation = \(\frac{[H^+]}{[HA]_{initial}}\) x 100 Percent dissociation ≈ \(\frac{0.04}{0.22}\times 100 \approx 18.18 \%\)

Step-by-step solution

(Step 1: Write the Ka expression for HClO₂)

The dissociation reaction for HClO₂ is given by: HClO₂ ↔ H⁺ + ClO₂⁻ The Ka expression is: Ka = \(\frac{[H^+][ClO_2^-]}{[HClO_2]}\)

(Step 2: Set up the ICE table)

Set up the Initial, Change, and Equilibrium (ICE) table: \(|\quad \quad| [HClO_2] \quad | [H^+] \quad | [ClO_2^-] \quad\) \(---|---|---\) \(Initial| 0.22\ | 0\ \quad \quad | 0\quad \quad \ \) \(---|---|---\) \(Change\ | -x\ \quad\ | +x\ \quad\ | +x\quad \ \) \(---|---|---\) \(Equilibrium | 0.22-x\ | x\ \quad \ | x\quad \ \)

(Step 3: Substitute the equilibrium concentrations into the Ka expression)

Substitute equilibrium concentrations of H⁺, ClO₂⁻, and HClO₂, from the ICE table, into the Ka expression: \(1.2 \times 10^{-2} = \frac{x \cdot x}{0.22 - x}\)

(Step 4: Solve for x - the concentration of H⁺ ions)

In most cases, when the Ka value is very small, x can be considered negligible compared to the initial concentration (0.22 in this case). By making this approximation, we get: \(1.2 \times 10^{-2} \approx \frac{x^2}{0.22}\) Now, solve for x: \[x = \sqrt{0.22\times1.2 \times 10^{-2}}\]

Key concepts

Acid Dissociation

Acid dissociation is a fundamental concept in chemistry. When an acid, such as chlorous acid (HClO₂), is dissolved in water, it dissociates into ions. This means it breaks apart into a hydrogen ion (H⁺) and a conjugate base ion (in this case, ClO₂⁻). Understanding how acids dissociate in solution helps us predict the behavior of acids under different conditions and their strength.
The degree to which an acid dissociates in a solution is an indicator of its strength. Strong acids dissociate completely, while weak acids only partially dissociate. Chlorous acid is a weak acid, which means it doesn't fully dissociate in solution. To describe how much of the acid dissociates, we often calculate the percent dissociation, which shows the extent of ion separation. This is essential for predicting the acid's chemical reactivity and properties.

Equilibrium Constant (Ka)

The equilibrium constant for an acid, denoted as Ka, is crucial for understanding the strength of the acid. Ka reflects the balance between the concentration of dissociated ions and the undissociated acid in a solution. It’s formulated by dividing the product of the concentrations of the products (H⁺ and ClO₂⁻) by the concentration of the reactant (HClO₂). Mathematically, it is expressed as:
\[ Ka = \frac{[H^+][ClO_2^-]}{[HClO_2]} \]
A high Ka value indicates a strong acid because it suggests a greater extent of ionization. In contrast, a low Ka value points to a weaker acid with less ionization. For chlorous acid, the given Ka is 1.2 × 10⁻². This relatively small value implies it's a weak acid. Understanding Ka can help you predict how an acid behaves in various chemical reactions, such as determining the pH of solutions or understanding buffer systems.

Calculation Steps

Solving problems involving acid dissociation begins with writing down the dissociation reaction and Ka expression. For chlorous acid, this reaction is: HClO₂ ↔ H⁺ + ClO₂⁻ Next, setting up an ICE (Initial, Change, Equilibrium) table helps organize the concentrations throughout the dissociation process. Starting concentrations are placed in the table, followed by changes upon dissociation, and finally, the equilibrium concentrations are deduced.
Once the equilibrium concentrations are established, substitute them back into the Ka expression to form an equation, like this: \[ 1.2 imes 10^{-2} = \frac{x^2}{0.22 - x} \] Here, the assumption that x is small allows us to simplify the expression, leading to: \[ x \approx \sqrt{0.22 \times 1.2 \times 10^{-2}} \]
This approximation is often suitable for weak acids with small Ka values, as it makes solving for x easier and provides an estimate of the H⁺ ion concentration needed to calculate percent dissociation.

Chemistry Problem Solving

When tackling chemistry problems like calculating percent dissociation, it's essential to follow systematic steps. Start by identifying the dissociation equation and writing the equilibrium constant expression. Use tools like the ICE table to track changes in concentration. This step-by-step method keeps your work organized and reduces errors.
Don't forget to consider approximations when applicable, especially with weak acids where Ka is small compared to initial concentrations. This simplification often makes solving the problem quicker and more straightforward but check its validity by ensuring it doesn’t result in significant errors. If an approximate solution implies a large percent dissociation (generally over 5%), recalculate without approximations. This is crucial for ensuring the accuracy of concentration measurements and understanding the acid’s behavior in different solution conditions.
By approaching chemistry problems methodically, you'll build confidence in tackling complex calculations and developing a deeper understanding of chemical equilibria and reactions.