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 \()>\mathrm{K}_{w}\) (ionic product of water) (b) \(\mathrm{K}_{\mathrm{w}}\) of boiling water is greater than \(10^{-14}\). (c) Ionic product of water at \(25^{\circ} \mathrm{C}\) is \(10^{-14}\) (d) \(\mathrm{pH}+\mathrm{pOH}=\mathrm{pK}_{\mathrm{w}}\).

Step-by-Step Solution

Answer

Statements (b), (c), and (d) are correct.

Step 1: Understanding Ionic Product of Water

The ionic product of water ( abla kw) represents the equilibrium constant for the self-ionization of water. At 25°C, abla kw is given by abla kw = [H^+] [OH^-] = 10^{-14}.

Step 2: Analyze Statement (a)

Statement (a) claims the dissociation constant ( abla K) of water is greater than the ionic product ( abla kw). This is incorrect at 25°C, as abla kw defines the dissociation of water in equilibrium with abla K_w.

Step 3: Analyze Statement (b)

Statement (b) states that abla kw of boiling water is greater than 10^{-14}. At elevated temperatures, the tendency of water to ionize increases, thus abla kw increases as the temperature rises.

Step 4: Analyze Statement (c)

Statement (c) correctly claims the ionic product of water at 25°C is 10^{-14}. This is the standard value at this temperature in pure water.

Step 5: Analyze Statement (d)

Statement (d) asserts that abla pH + abla pOH = abla pK_w. By definition, abla pK_w = -log( abla kw), which equals 14 at 25°C, so this equation holds true.

Key Concepts

Dissociation Constant

The dissociation constant, often represented as \( K_d \) or simply \( K \), is a crucial concept in understanding how molecules break into ions in a solution. For water, this constant delineates the extent to which water molecules dissociate into hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\). It provides a snapshot of chemical equilibrium. When discussing pure water at \(25^{\circ}C\), the ionic product \( K_w \) is also a measure of this equilibrium, represented by \( K_w = [H^+][OH^-] = 10^{-14} \). However, \( K_d \) is often not greater than \( K_w \) since \( K_w \) inherently includes \( K_d \) in its definition. It's important to distinguish between these terms to accurately describe the equilibrium and tendencies of different chemical species in solution.

Self-Ionization of Water

Water is fascinating in its ability to self-ionize, meaning it can split into its constituent ions even in the absence of other dissolved substances. This constant conversion is represented by the expression \( 2H_2O \leftrightarrow H_3O^+ + OH^- \) or more commonly simplified as \( H_2O \leftrightarrow H^+ + OH^- \). This reaction is very subtle, with only a minute fraction of water dissociating at any given time, but it’s fundamental to the chemistry of water.
- The self-ionization of water is the underlying phenomenon dictating the formation of \( H^+ \) and \( OH^- \) ions.- It significantly influences water's pH and pOH values, framing them around neutral levels at standard conditions.
Understanding self-ionization helps comprehend the behavior of water in various chemical reactions, and it serves as a basis for calculating pH levels across different solutions.

Temperature Dependence of Ionic Product

The ionic product of water, \( K_w \), isn't fixed; it fluctuates with temperature. At standard room temperature (\(25^{\circ}C\)), \( K_w = 10^{-14} \). However, as temperature rises, more thermal energy is available to facilitate the dissociation process, hence \( K_w \) increases.
- At boiling temperatures, \( K_w \) exceeds \( 10^{-14} \), implying a higher concentration of \( H^+ \) and \( OH^- \) ions.- This is significant for reactions sensitive to pH changes when temperatures deviate from the standard.
Such variations must be considered in practical applications involving temperature fluctuations, as they can lead to significant changes in acidity and alkalinity, directly impacting chemical reaction dynamics.

pH and pOH Relationship

The relationship between pH and pOH is a fundamental concept in chemistry, especially in solutions management. At 25°C, the sum of pH and pOH is 14, mathematically expressed as \( pH + pOH = 14 \). This stems from the logarithmic scale applied to ion concentrations and their corresponding change with \( K_w \).
- \( pH \) measures the concentration of hydrogen ions \([H^+]\) while \( pOH \) accounts for hydroxide ions \([OH^-]\).- When a solution is neutral, \( pH = 7 \) is equivalent to \( pOH = 7 \).
Recognizing this relationship allows chemists to deduce one value from the other, given \( K_w \) at a particular temperature. It underpins many practical applications, including determining substance corrosivity, biological compatibility, and more.