91Ó°ÊÓ

The dissociation constant, abbreviated as \( K_a \), is a crucial parameter for understanding the behavior of weak acids in solution. It is a measure of the extent to which an acid can donate protons to the solution. For weak acids, \( K_a \) values are typically small. In our exercise, the weak acid \( HA \) has a dissociation constant of \( 4.9 \times 10^{-8} \). This small \( K_a \) suggests that \( HA \) does not dissociate significantly in water.
This dissociation can be expressed by the equilibrium equation:

• \( HA \rightleftharpoons H^+ + A^- \)

The equilibrium constant expression is given by:

• \( K_a = \frac{[H^+][A^-]}{[HA]} \)

For weak acids, we often assume that the concentration of the undissociated acid \([HA]\) at equilibrium is approximately equal to its initial concentration, simplifying calculations. This is especially valid when \( K_a \) is much smaller than the initial concentration of the acid.

Percentage ionization is the fraction of the original acid that has dissociated in solution, expressed as a percentage. It's an important concept because it quantifies how much of the weak acid is dissociated into ions at a given concentration. For the problem provided, the percentage ionization helps us understand how effective the weak acid is at ionizing under certain conditions.
The formula for percentage ionization is:

• \( \text{Percentage Ionization} = \left(\frac{[H^+]}{[HA]_0}\right) \times 100\% \)

In our example, after solving for \([H^+]\), or \(x\), and finding it to be \(7.0 \times 10^{-5} \text{ M}\), we calculate:

• \( \text{Percentage Ionization} = \left(\frac{7.0 \times 10^{-5}}{0.1}\right) \times 100\% \approx 0.07\% \)

This means only a very small fraction of the acid dissociates, which is consistent with the behavior of weak acids whose \( K_a \) value is small.

Calculating the pH of a solution is a fundamental skill in chemistry, particularly when working with weak acids. The pH is derived from the concentration of hydrogen ions in the solution and is a measure of its acidity or alkalinity. For the hydrogen ion concentration \([H^+]\) obtained as \(7.0 \times 10^{-5}\), the pH is calculated using the formula:

• \( \text{pH} = -\log([H^+]) \)

Thus, for our weak acid solution, the pH is:

• \( \text{pH} = -\log(7.0 \times 10^{-5}) \approx 4.15 \)

This pH value indicates a weakly acidic solution. Understanding the pH helps characterize the solution's properties, such as its corrosiveness and reaction behavior. Additionally, a precise pH calculation requires attention to approximation validity, especially for weak acids where the initial acid concentration does not change much.