What will be the \(\mathrm{pH}\) and \(\% \alpha\) (degree of hydrolysis) respectively for the salt \(\mathrm{BA}\) of \(0.1 \mathrm{M}\) concentration? Given : \(K_{a}\) for \(\mathrm{H} A=10^{-6}\) and \(K_{b}\) for \(B O H=10^{-6}\) (a) \(5,1 \%\) (b) \(7,10 \%\) (c) \(9,0.01 \%\) (d) \(7,0.01 \%\)

Salt hydrolysis is a crucial concept to understand when dealing with the pH of solutions, especially in the context of salts derived from weak acids, weak bases, or both. When a salt dissolves in water, its constituent ions may react with water in a process known as hydrolysis, which influences the pH of the solution.

In the case where a salt, such as BA, comes from the combination of a weak acid (HA) and a weak base (BOH), both the anion (A-) and the cation (B+) have the potential to hydrolyze. If the weak acid and weak base are of equal strength, as indicated by their identical ionization constants in our exercise, the effect of the anions and cations on the pH balances out.

This neutrality is interesting because even though both ions can interact with water, producing OH- (hydroxide ions) from the base component and H+ (hydrogen ions) from the acid component, their equal tendencies to donate or accept a proton result in a pH that is close to 7, which is neutral on the pH scale. The degree of hydrolysis, represented by \(\alpha\), is a measure of the extent to which these ions react with water and it is typically small when the parent acid and base are weak and their ionization constants are low.

Understanding ionization constants, designated as \(K_a\) for acids and \(K_b\) for bases, is fundamental in predicting how acids and bases will behave in a solution. These constants are a measure of the strength of an acid or base—how readily they dissociate into ions in an aqueous solution.

For weak acids or bases, the ionization constants are relatively small, as in the given problem where \(K_a = K_b = 10^{-6}\). A small constant indicates that the substance does not fully ionize in water; only a small fraction of the molecule dissociates to form ions.

Understanding this concept helps one make an educated guess about the pH of the resulting solution when such substances are involved. Since the provided \(K_a\) and \(K_b\) are equal, and because they're both small, it indicates that both the acid HA and the base BOH weakly dissociate in water contributing an equal but limited amount of H+ and OH- to the solution. This balance leads to a neutral solution in the case of our exercise, forecasting a pH near 7.

Calculating the pH of a solution is a common task in chemistry that quantifies the acidity or basicity of that solution. The pH scale ranges from 0 to 14 with 7 being neutral. Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic.

For the given exercise, the pH calculation is particularly straightforward because the salt originates from a weak acid and a weak base with equal ionization constants. This rarity results in a neutral pH, which is 7.

Typically, the pH is calculated by determining the concentration of hydrogen ions [\br(H^+)] in the solution. In neutral, pure water, \[H^+] = 10^{-7}\ M\], which corresponds to a pH of 7. In the exercise, since the salt does not significantly alter this concentration due to equal ionization tendencies of the conjugate acid and base, we maintain a neutral pH. When the degree of hydrolysis \(\alpha\) is sought, it could be computed from the ionization constant and the salt concentration, then expressed as a percentage to represent the extent of the reaction between the ions and water. However, in this neutral case, the percentage of hydrolysis will be exceedingly small, reflecting the limited interaction with the water molecules.