The following observations are made about a diprotic acid \(\mathrm{H}_{2} \mathrm{A} :(\mathrm{i}) \mathrm{A} 0.10 \mathrm{M}\) solution of \(\mathrm{H}_{2} \mathrm{A}\) has \(\mathrm{pH}=3.30 .\) (ii) \(\mathrm{A} 0.10 \mathrm{M}\) solution of the salt NaHA is acidic. Which of the following could be the value of \(\mathrm{p} K_{a 2}\) for \(\mathrm{H}_{2} \mathrm{A} :\) (i) \(3.22,\) (ii) 5.30 , (iii) \(7.47,\) or (iv) 9.82\(?\)

Understanding the calculation of pH is crucial when working with solutions in chemistry, particularly for acidic or basic ones. pH is a scale used to specify the acidity or basicity of an aqueous solution. It is defined as the negative logarithm (base 10) of the concentration of hydronium ions (\text{H}_{3}\text{O}^+)\text{ in moles per liter. The equation used to calculate pH is:}
\[ \text{pH} = -\log([\text{H}_{3}\text{O}^+]) \]
For example, if the concentration of \text{H}_{3}\text{O}^+ in a solution is 5.01 \times 10^{-4} M, the pH is calculated as 3.30. This simple relationship can help us to understand the degree of acidity or basicity in any given solution.

The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for the dissociation reaction of the acid into anions and hydrogen ions in water. The higher the Ka value, the stronger the acid, as it tends to donate protons more completely.
For a generic acid dissociation reaction:\[ \text{HA} \rightleftharpoons \text{A}^- + \text{H}^+ \]
The acid dissociation constant can be calculated as follows:\[ K_a = \frac{[\text{A}^-][\text{H}^+]}{[\text{HA}]} \]
The related term pKa is the negative logarithm of Ka and is used for its simplicity:
\[ \text{pKa} = -\log(K_a) \]
This concept is essential when solving problems related to acid strength and the predictability of their behavior in solution.

Weak acids partially dissociate in solution, establishing an equilibrium between the undissociated acid and the ions produced. The equilibrium concentrations of the products and reactants are governed by the Ka value of the weak acid.
For a diprotic acid (H2A), the first deprotonation can be represented as:\[ \text{H}_2\text{A} \rightleftharpoons \text{H}^+ + \text{HA}^- \]
For the second deprotonation:\[ \text{HA}^- \rightleftharpoons \text{A}^{2-} + \text{H}^+ \]
Each deprotonation step has its Ka value, denoted as Ka1 and Ka2, respectively. The degree to which each step proceeds impacts the pH of the solution and the overall ionic composition. Equilibrium calculations often require assumptions and logical reasoning to simplify the process and yield a solution, a process which can be crucial in solving complex equilibria.

Salt hydrolysis occurs when anion or cation components of a salt react with water, potentially affecting the pH of the solution. For instance, the salt of a weak acid and strong base will typically undergo anion hydrolysis, making the solution basic. Conversely, salts formed from strong acids and weak bases often result in acidic solutions due to cation hydrolysis.
For a generic salt such as NaHA, derived from a weak acid (H2A), the anion (HA-) may react with water:\[ \text{HA}^- + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{A} + \text{OH}^- \]
If the second dissociation constant (pKa2) of the weak acid is high, indicating a very weakly acidic second hydrogen, the amount of OH- produced can increase, creating a more acidic solution. Therefore, an understanding of salt hydrolysis is necessary to predict and control the pH of salt solutions.