Problem 115 - Chemistry The Central Science In Si Units

Question

The \(\mathrm{p} K_{\mathrm{b}}\) of water is (a) 1 (b) 7 (c) 14 (d) not defined (e) none of the above

Step-by-Step Solution

Answer

The pKb of water is not defined.

Step 1: Understand the Concept of pKb

The pKb is a measure of the strength of a base and is defined as the negative logarithm of the base dissociation constant (Kb). It is given by the formula: \( ext{p}K_b = - ext{log}_{10}(K_b) \). In the context of water, we need to understand its property as a base.

Step 2: Consider Water as a Base

Water is often considered neutral in pH terms because it can act both as an acid and a base (amphoteric nature). However, in the context of pKb, we need to determine whether its base dissociation constant \( K_b \) can be defined.

Step 3: Conceptualize Water's Base Constant

Since water can act as a base, its reaction with an acid can be described as \( ext{H}_2 ext{O} + ext{HA} ightarrow ext{OH}^- + ext{H}_2 ext{A}^+ \). However, water in pure form does not predominantly exist as a base compared to stronger bases. Thus, assigning a meaningful base dissociation constant \( K_b \) solely to water is inappropriate.

Step 4: Conclusion

Given its neutral nature, water does not have a distinct base dissociation constant \( K_b \) like conventional bases. Therefore, the concept of pKb is not applicable for water.

Key Concepts

Base Dissociation Constant

The base dissociation constant, often denoted as \( K_b \), is a vital concept in understanding the strength of a base in a chemical reaction. The \( K_b \) value quantifies the degree to which a base can accept a proton (H⁺) in an aqueous solution. This constant helps in comparing the strengths of various bases. The formula used to calculate \( K_b \) is similar to the equilibrium constant for acids, but it is specifically for bases.The equation is typically given as:

• \( K_b = \frac{[OH^-][B^+]}{[B]} \)

In this equation, \([OH^-]\) denotes the concentration of hydroxide ions, \([B^+]\) is the concentration of the base in its protonated form, and \([B]\) indicates the concentration of the base. When it comes to determining the strength of a base, a larger \( K_b \) value signifies a stronger base that ionizes more completely in solution. However, unlike strong bases, weak bases have smaller \( K_b \) values and thus do not dissociate as fully.

Amphoteric Nature

Water's amphoteric nature is one of its most intriguing qualities. An amphoteric substance is one that can exhibit dual chemical behavior, acting both as an acid and a base. Water perfectly exemplifies this property. In an acidic reaction, water can donate a proton, functioning as an acid. Conversely, when in contact with a base, water can accept a proton, exhibiting its basic nature.The classic examples of water's behavior include:

• As an acid: \( H_2O + NH_3 \rightarrow OH^- + NH_4^+ \)
• As a base: \( H_2O + HCl \rightarrow H_3O^+ + Cl^- \)

These reactions highlight water's flexibility to play multiple roles in chemical processes. Despite its amphoteric nature, in the context of dissociation constants such as \( K_b \) or \( K_a \), water typically functions as a neutral entity due to its balanced ability to donate and accept protons.

Neutrality of Water

The neutrality of water is a fundamental concept, often highlighted in chemistry. Pure water possesses a neutral pH of 7. This pH level means that the concentration of hydrogen ions \([H^+]\) is equal to that of hydroxide ions \([OH^-]\) in pure water at 25°C. This balanced ion presence signifies neutrality on the pH scale, which ranges from 0 to 14.The neutrality of water is explained by the self-ionization process:

• \( 2H_2O \rightleftharpoons H_3O^+ + OH^- \)

In this reversible reaction, two water molecules generate hydronium ions and hydroxide ions in equal measure. Because of this self-ionization, water doesn't exhibit strong acidic or basic characteristics in its pure form. This neutrality is why defining a \( K_b \) solely for water is challenging and unnecessary, as water doesn't behave as a typical base or acid compared to stronger substances. Understanding water's neutral nature helps in appreciating its stability and importance in various chemical and biological systems.