Problem 194 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements is/are correct about the ionic product of water ? (a) At \(25^{\circ} \mathrm{C}, \mathrm{K}\) (dissociation constant of water \()>\mathrm{K}_{\mathrm{w}}\) (ionic product of water) (b) \(K_{w}\) of boiling water is greater than \(10^{-14}\). (c) Ionic product of water at \(25^{\circ} \mathrm{C}\) is \(10^{-14}\) (d) \(\mathrm{pH}+\mathrm{pOH}=\mathrm{pK}_{\mathrm{w}^{\circ}}\)

Step-by-Step Solution

Answer

Statements (b), (c), and (d) are correct. Statement (a) is incorrect.

Step 1: Understanding Ionic Product of Water

The ionic product of water, denoted as \( K_w \), is the product of the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in water. At \( 25^{\circ} \text{C} \), \( K_w = 10^{-14} \). The value of \( K_w \) increases with temperature increase.

Step 2: Analyzing Statement (a)

Statement (a) suggests \( K \) (the dissociation constant of water) is greater than \( K_w \). Typically, the dissociation constant and the ionic product are considered equivalent in the context of water at constant temperature. Thus, this statement is not correct.

Step 3: Analyzing Statement (b)

As temperature increases (boiling water is at \(100^{\circ} \text{C}\)), the \( K_w \) value indeed becomes greater than \( 10^{-14} \) because the dissociation of water increases with temperature, leading to more \( H^+ \) and \( OH^- \) ions.

Step 4: Analyzing Statement (c)

This statement asserts that at \( 25^{\circ} \text{C} \), the ionic product \( K_w \) is \( 10^{-14} \). This is a standard textbook fact and hence correct.

Step 5: Analyzing Statement (d)

The relationship between \( \text{pH} \), \( \text{pOH} \), and \( pK_w \) is given by \( \text{pH} + \text{pOH} = pK_w \). At \( 25^{\circ} \text{C} \), \( pK_w = -\log(10^{-14}) = 14 \). This statement correctly represents acid-base chemistry relationships.

Key Concepts

Dissociation Constant

Understanding the dissociation constant for water is often pivotal in grasping key concepts in acid-base chemistry. For water, this is often represented by the balance between molecules of water (\[ H_2O \]) and the ions they dissociate into, namely hydrogen ions (\[ H^+ \]) and hydroxide ions (\[ OH^- \]).
\[ H_2O \rightleftharpoons H^+ + OH^- \]
The equilibrium constant for this dissociation is known as the dissociation constant (\( K_d \)), which showcases the extent to which water molecules split into ions. In the context of water, the dissociation constant reflects the capacity of water to generate ionic species under given conditions.

Kw Value

The ionic product of water, often symbolized as \( K_w \), is a critical parameter in chemistry.
It represents the equilibrium constant for the self-ionization of water:
\[ K_w = [H^+][OH^-] \]
At room temperature, typically around \( 25^{\circ} C \), the value of \( K_w \) is \( 10^{-14} \). This implies that in pure water, the concentrations of both hydrogen and hydroxide ions are each \( 10^{-7} \) M. The consistency of this value highlights the delicate balance in neutral water and is dependent largely on temperature.

Temperature Effect on Kw

The value of \( K_w \) is not static but varies with temperature. As temperature increases, \( K_w \) also rises. This occurs because higher thermal energy encourages more molecular movement, leading to an increased rate of water dissociation.

When water boils at \( 100^{\circ} C \), the \( K_w \) value is noted to be higher than \( 10^{-14} \). This increase implies the presence of more hydrogen and hydroxide ions at elevated temperatures, showing that hotter water is slightly more acidic and basic simultaneously.

pH and pOH Relationship

The relationship between \( pH \) and \( pOH \) is fundamental in understanding the nature of aqueous solutions. In pure water or neutral solutions, the sum of \( pH \) and \( pOH \) always equals \( pK_w \).

At \( 25^{\circ} C \), this value is \( 14 \), corresponding to the \( K_w \) value of \( 10^{-14} \). Thus, when you know the \( pH \), the \( pOH \) can easily be determined by subtracting the \( pH \) from 14, and vice versa. This relationship is vital for quickly determining the acidity or basicity of a solution.
\[ pH + pOH = pK_w = 14 \]