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

Question

Hydrolysis constant \(\mathrm{K}_{\mathrm{A}}\) and \(\mathrm{K}_{\mathrm{B}}\) 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

The order of acidic strengths is HC > HA > HB.

Step 1: Define hydrolysis constant and its relation to dissociation constant

The hydrolysis constant \( K_h \) is the equilibrium constant for the hydrolysis reaction of a salt. For a salt of a weak acid, the relationship between the hydrolysis constant \( K_h \) and the dissociation constant of the acid \( K_a \) is given by: \( K_w = K_a \times K_h \), where \( K_w \) is the ion product of water, \( 1 \times 10^{-14} \).

Step 2: Calculate dissociation constant for HA

Given \( K_h \) for HA's salt is \( 10^{-8} \), use \( K_w = K_a \times K_h \) to find \( K_a \) for HA: \( 1 \times 10^{-14} = K_a \times 10^{-8} \). Thus, \( K_a = \frac{1 \times 10^{-14}}{10^{-8}} = 10^{-6} \).

Step 3: Calculate dissociation constant for HB

Similarly, given \( K_h \) for HB's salt is \( 10^{-6} \), use \( K_w = K_a \times K_h \) to find \( K_a \) for HB: \( 1 \times 10^{-14} = K_a \times 10^{-6} \). Thus, \( K_a = \frac{1 \times 10^{-14}}{10^{-6}} = 10^{-8} \).

Step 4: Compare dissociation constants

We have \( K_a(\text{HC}) = 10^{-2} \), \( K_a(\text{HA}) = 10^{-6} \), and \( K_a(\text{HB}) = 10^{-8} \). The strength of acidity is directly proportional to the dissociation constant: higher \( K_a \) means stronger acid.

Step 5: Conclude the order of acidity

By comparing \( K_a \) values, we find that \( K_a(\text{HC}) > K_a(\text{HA}) > K_a(\text{HB}) \), leading to the conclusion that \( \text{HC} > \text{HA} > \text{HB} \) in terms of acidic strength.

Key Concepts

Hydrolysis Constant

The hydrolysis constant, denoted as \( K_h \), plays a crucial role in understanding how salts dissociate in a solution. It is essentially the equilibrium constant for the hydrolysis reaction of a salt. This means that it measures the extent to which a salt reacts with water to form an acidic or basic solution. The relationship between the hydrolysis constant and the dissociation constant of the acid (\( K_a \)) is given by the equation:

• \( K_w = K_a \times K_h \)

Here, \( K_w \) is the ion product of water, which has a constant value of \( 1 \times 10^{-14} \) at 25°C. Thus, when you know the hydrolysis constant and this relationship, it's straightforward to determine the dissociation constant, which provides insight into the acidity of the substance.

Dissociation Constant

The dissociation constant, represented by \( K_a \), is a measure of an acid's strength. It quantifies the tendency of an acid to donate its proton to water, forming the hydronium ion \( H_3O^+ \). Higher values of \( K_a \) indicate a stronger acid because it shows a greater tendency to dissociate into its ions.

• The equation for dissociation of an acid \( HA \) is given by: \( HA \rightleftharpoons H^+ + A^- \)
• The dissociation constant \( K_a \) is derived from the concentrations of these species at equilibrium.

Knowing the \( K_a \) values for different acids allows you to compare their strengths directly. In this problem, calculating \( K_a \) for each acid gives us a clear view of which is the strongest and which is the weakest.

Equilibrium Constant

The equilibrium constant is a broad term that encompasses various specific constants, such as the \( K_h \) and \( K_a \). It expresses the ratio of concentrations of products to reactants at equilibrium and is key to predicting the direction a chemical reaction will take.

• For the dissociation of acids, it refers to \( K_a \).
• For hydrolysis reactions of salts, it correlates with \( K_h \).

The principle remains the same: if the equilibrium constant is high, the reaction favors the products, which in the context of acidity, translates to a stronger acid. Conversely, a lower equilibrium constant signifies weaker dissociation, and hence, a weaker acid. These constants are essential in chemical calculations and predictions of reaction behaviors.

Salt Hydrolysis

Salt hydrolysis is a process where a salt reacts with water to produce an acidic or basic solution. This process is essential for understanding how salts can influence the pH of a solution. Salts composed of cations from weak bases or anions from weak acids often undergo hydrolysis.

• The resulting solution's nature (acidic, neutral, or basic) depends on the strengths of the acid and base from which the salt was formed.
• If the anion is the conjugate base of a weak acid, it will tend to accept protons, leading to an alkaline solution.
• If the cation is the conjugate acid of a weak base, it will tend to donate protons, resulting in an acidic solution.

Understanding salt hydrolysis helps in predicting whether a solution will be acidic or basic based on the nature of the salt involved. This knowledge ties back to the hydrolysis constant \( K_h \), indicating the extent of this reaction in water, impacting the overall acidity or basicity of the solution.