Question

Calculate the percent dissociation for a \(0.22-M\) solution of chlorous acid \(\left(\mathrm{HClO}_{2}, K_{\mathrm{a}}=0.012\right)\)

Short answer

The percent dissociation for a 0.22 M solution of chlorous acid (HClO2) is approximately 23.36%.

Step-by-step solution

Write the acid dissociation equation for HClO2

The dissociation of chlorous acid in water can be represented by the following equation: \( HClO_2 \rightleftharpoons H^+ + ClO_2^- \)

Set up the equilibrium expression using the given Ka value

We can write the equilibrium expression for the above reaction as: \( K_a = \frac{[H^+][ClO_2^-]}{[HClO_2]} \) Since Ka is given as 0.012, we can plug it into the equation: \(0.012 = \frac{[H^+][ClO_2^-]}{[HClO_2]} \)

Set up an ICE table and calculate the concentrations at equilibrium

Let x represent the concentration of ions that dissociate from HClO2. ICE table: | | HClO2 | H+ | ClO2- | | --- | --- | --- | --- | | Initial | 0.22 | 0 | 0 | | Change | -x | +x | +x | | Equilibrium | 0.22-x | x | x | Now, we can plug these values into the equilibrium expression: \( 0.012 = \frac{x^2}{0.22-x} \)

Solve the equation for x, the concentration of dissociated ions

Make the assumption that x is much smaller than 0.22, so the equation can be simplified as: \( 0.012 = \frac{x^2}{0.22} \) Solve for x: \( x^2 = 0.012(0.22) \) \( x^2 = 0.00264 \) \( x = 0.0514 \) So, the concentration of the dissociated ions (H+ and ClO2-) is approximately 0.0514 M.

Calculate the percent dissociation

Now, we can calculate the percent dissociation using the following formula: Percent dissociation = \( \frac{[\text{dissociated ions}]}{[\text{initial concentration of HClO}_2]} \) × 100 Percent dissociation = \( \frac{0.0514}{0.22} \times 100 \) Percent dissociation ≈ 23.36% Thus, the percent dissociation for a 0.22 M solution of chlorous acid (HClO2) is approximately 23.36%.

Key concepts

Acid Dissociation

Acid dissociation is the process by which an acid releases a proton (H^+) in solution, forming its conjugate base. In our example of chlorous acid (HClO_2), the dissociation is shown by the equation:
\[ HClO_2 \rightleftharpoons H^+ + ClO_2^- \]
Here, the acid HClO_2 releases a proton, producing H^+ ions and the chlorite ion, ClO_2^-. This is essential for understanding acidity and pH in chemistry. The extent to which the dissociation occurs is defined by the equilibrium between the reactants and products. Not all acids dissociate completely, which is why calculating percent dissociation becomes important.

Equilibrium Expression

The equilibrium expression is a mathematical way to express the balance between reactants and products in a reversible chemical reaction. For the dissociation of chlorous acid:
\[ K_a = \frac{[H^+][ClO_2^-]}{[HClO_2]} \]
Here, K_a is the acid dissociation constant, which provides a measure of the strength of the acid. A large K_a indicates a strong acid that dissociates completely, while a smaller K_a means the acid is weaker and only partially dissociates. By plugging the concentration values into this expression, we can find out how far the dissociation reaction has proceeded.

ICE Table

An ICE table is a tool used in chemistry to calculate the changes and final concentrations of substances in an equilibrium reaction. ICE stands for Initial, Change, and Equilibrium. Let's look at our previous example:

• Initial: Concentrations before the reaction starts are written down. For HClO_2 , it is 0.22 M , while H^+ and ClO_2^- are 0 M.
• Change: Represents the change in concentrations as the reaction proceeds. Since each mole of HClO_2 produces one mole of both H^+ and ClO_2^- , the change for HClO_2 is -x , and for the products, it's +x .
• Equilibrium: Lists the concentrations at equilibrium, (0.22-x) for HClO_2 and (x) for the others.

Using the ICE table helps systematically set up and solve for unknown concentrations at equilibrium.

Ka Value

The K_a value is a crucial concept in acid-base chemistry. It represents the acid dissociation constant and is unique for each acid. In our exercise, the K_a for chlorous acid ( HClO_2 ) is given as 0.012. This number tells us how readily the acid donates a proton to the solution.

A small K_a value, like in this scenario, indicates a weaker acid that doesn't fully dissociate in solution. We use this constant in the equilibrium expression to find the concentration of dissociated and undissociated particles. This helps determine the acid's behavior in various chemical environments. Knowing K_a is crucial for calculating percent dissociation, which reflects how much of the acid is ionized compared to its initial concentration.