Problem 186 - A Complete Resource Book in Chemistry for JEE Main

Question

Hydrolysis constant \(K_{A}\) and \(K_{B}\) of two salts of weak acids HA and \(\mathrm{HB}\) are \(10^{-8}\) and \(10^{-6}\) respectively. If the dissociation constant of third acid \(\mathrm{HC}\) is \(10^{-2}\). The order of acidic strengths of three acids will be (a) \(\mathrm{HA}>\mathrm{HB}>\mathrm{HC}\) (b) \(\mathrm{HB}>\mathrm{HA}>\mathrm{HC}\) (c) \(\mathrm{HC}>\mathrm{HA}>\mathrm{HB}\) (d) \(\mathrm{HA}=\mathrm{HB}=\mathrm{HC}\)

Step-by-Step Solution

Answer

(c) \(HC>HA>HB\)

Step 1: Understanding Hydrolysis Constant

The hydrolysis constant, \( K_A \) or \( K_B \), of a salt derived from a weak acid or base reflects how easily the acid or base dissociates in solution. A larger value indicates weaker acidic strength because the compound is less likely to donate a proton.

Step 2: Relating Hydrolysis Constant and Acid Strength

For weak acids \( HA \) and \( HB \) with hydrolysis constants \( 10^{-8} \) and \( 10^{-6} \) respectively, we understand that \( HA \) is a stronger acid than \( HB \) since \( 10^{-8} < 10^{-6} \). A smaller hydrolysis constant means less ionization of the salt and thus stronger undissociated acid.

Step 3: Comparing Dissociation Constant

The acid \( HC \) has a dissociation constant \( K \) of \( 10^{-2} \). Since dissociation constants express the strength of acids directly, \( HC \) is stronger than both \( HA \) and \( HB \), given its considerable difference from the hydrolysis constants.

Step 4: Establishing the Order of Acidic Strengths

Comparing all values, \( HC \) has the highest dissociation constant and thus is the strongest acid. Following this, \( HA \) is stronger than \( HB \) as it has the lower hydrolysis constant. Therefore, the order of acidic strengths is \( HC > HA > HB \).

Key Concepts

Hydrolysis Constant

The hydrolysis constant is a measure used to describe the extent to which a salt can dissociate in water. This is especially relevant for salts derived from weak acids or bases. Unlike strong acids or bases, weak ones do not fully ionize in water. When studying hydrolysis, we look at the ionization of the salts formed by these weak acids and bases.
- A **lower** hydrolysis constant indicates a stronger weak acid, because the acid itself remains largely undissociated. - Conversely, higher values imply that the salt ionizes more, revealing a weaker undissociated acid.To illustrate, a hydrolysis constant of \(10^{-8}\) suggests the acid is relatively strong among weak acids, staying largely together rather than dissociating. When you see a value like \(10^{-6}\), it suggests more ionization of the salt, indicating a weaker acid.

Dissociation Constant

The dissociation constant, often represented by \( K_a \), indicates the tendency of an acid to donate protons. It's a direct measure of a weak acid's strength on its own. For weak acids, the dissociation constant determines:- How readily they release hydrogen ions into solution.- A larger \( K_a \) value means a stronger acid since it more readily donates protons.In the context of our problem, \( HC \) has a dissociation constant of \(10^{-2}\). This signals a strong acid compared to typical weak acids, which usually have much smaller \( K_a \) values. Therefore, when comparing to hydrolysis constants of \( HA \) and \( HB \), this dissociation constant clearly ranks \( HC \) as the strongest among them.

Weak Acids

Weak acids are those that do not completely ionize in water. They maintain a balance between their ionized and unionized forms in solution. This trait differentiates them from strong acids, which fully dissociate.Key characteristics of weak acids include:- They establish an equilibrium in solution between protonated and deprotonated forms.- The acidic strength as represented by their \( K_a \) or hydrolysis constants is often small compared to strong acids.In this problem, \( HA \) and \( HB \) are both categorized as weak acids. Their ability to donate protons is determined by analyzing their hydrolysis constants. Between two weak acids, the one with the smaller hydrolysis constant is stronger since the acid itself stays mostly together, resisting ionization.

Chemical Equilibrium

Chemical equilibrium is a state where the rate of the forward reaction equals the rate of the reverse reaction. This balance occurs in all reversible reactions, including the behavior of weak acids and their hydrolysis.With weak acids like \( HA \) and \( HB \), equilibrium is reached with the ions and the undissociated molecules. This equilibrium helps us understand their acidic strength because it indicates how much of the acid remains undissociated versus dissociated:- A weak acid at equilibrium will partially ionize, meaning both the ionized and non-ionized forms co-exist.- In hydrolysis and dissociation, reaching equilibrium is crucial, as it helps to calculate and confirm hydrolysis or dissociation constants.Thus, for weak acids, understanding equilibrium concepts is important to determine their acidity in practical scenarios. This knowledge helps in establishing relative strength through constants obtained at equilibrium.