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Understanding the pH of a solution is crucial because it indicates how acidic or basic that solution is. The pH is calculated using the formula:
\[ pH = -\log[H^+] \]
In the context of a diprotic acid \( H_{2}A \), determining the pH involves calculating the concentration of hydrogen ions \( [H^+] \) in the solution. From the exercise, we can derive that for a 0.10 M \( H_{2}A \) solution with a pH of 3.30, the concentration of hydrogen ions is \( 5.0 \times 10^{-4} \) M. This is found by taking the inverse log of the pH value:
\[ [H^+] = 10^{-pH} \]
This process is essential for understanding the solution's acidity and is a foundation for analyzing acid dissociation and the related constants.

The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. It expresses the equilibrium between the acid (HA) and its ions (H鈦� and A鈦�). For a diprotic acid like \( H_{2}A \) with two dissociable protons, there are two constants: Ka鈧� and Ka鈧� for the first and second dissociation steps, respectively. The formula to calculate Ka is:
\[ Ka = \frac{[H^+][A^-]}{[HA]} \]
During the first dissociation of a diprotic acid, Ka鈧� can be determined by the concentration of hydrogen ions squared, divided by the initial concentration of the acid minus the ion concentration, as indicated in the exercise solution. These constants help chemists understand how the acid will behave in different environments.

The relationship between Ka and pKa is another fundamental aspect of acid-base chemistry. The pKa value is simply the negative logarithm of the Ka value, which provides a more convenient way to express acid strength. The formula to find pKa is:
\[ pKa = -\log(Ka) \]
As seen in the exercise, once the Ka鈧� value is calculated, the corresponding pKa鈧� can be determined. As the magnitude of Ka decreases, indicating a weaker acid, the pKa value increases. Knowing the pKa helps predict the extent of dissociation of an acid at various pH levels, which is vital for controlling reactions in a laboratory or industrial setting.

The acidity of salt solutions is determined by the nature of the ions in the solution. Salts derived from a weak acid and a strong base, like NaHA, can often form solutions with acidic pH because the conjugate base (A鈦�) from the weak acid has the ability to accept a proton from water and generate additional hydrogen ions. This effect is related to the hydrolysis of the anion.

In the provided problem, we infer that since solutions of NaHA are acidic, Ka鈧� must be significantly smaller than Kw, the ion product constant for water, and the related pKa鈧� must be greater than 7 to result in a pH less than 7. By extension, since pKa鈧� is also fairly small, the acid's second dissociation step must be weaker than the first, as the given pKa鈧� options also imply.