Problem 14 - A Complete Resource Book in Chemistry for JEE Main

Question

The \(\mathrm{pH}\) of pure water at \(80^{\circ} \mathrm{C}\) will be \((\) a) \(=7\) (b) \(<7\) (c) \(>7\) (d) none of these

Step-by-Step Solution

Answer

(b) <7

Step 1: Understanding Pure Water Neutrality

Pure water is considered neutral. At any temperature, when pure water is neutral, the concentration of hydrogen ions \([H^+]\) equals the concentration of hydroxide ions \([OH^-]\). This means the product \([H^+][OH^-]\) equals the ionic product of water \(K_w\).

Step 2: Ionic Product of Water

The ionic product of water \(K_w\) is dependent on temperature. At \(25^{\circ} \mathrm{C}\), \(K_w = 1.0 \times 10^{-14}\). However, as temperature increases, \(K_w\) increases; at \(80^{\circ} \mathrm{C}, K_w\) is higher than \(1.0 \times 10^{-14}\).

Step 3: Calculating \(\mathrm{pH}\) of Pure Water at Increased Temperature

The \(\mathrm{pH}\) is calculated by the formula \(\mathrm{pH} = -\log[H^+]\). Since \(K_w\) is higher at \(80^{\circ} \mathrm{C}\), \([H^+][OH^-] = K_w\) leads to higher \([H^+]\) than at \(25^{\circ} \mathrm{C}\), making the \(\mathrm{pH}\) less than 7.

Key Concepts

Ionic Product of Water

The ionic product of water, often represented as \( K_w \), is a fundamental concept in chemistry, describing the self-ionization of water. At room temperature \((25^{\circ} \mathrm{C})\), water slightly ionizes into equal concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\). The product of these ion concentrations is constant and is defined as \( K_w \). This is illustrated by the equation:

\[ [H^+][OH^-] = K_w \]

For water at \(25^{\circ} \mathrm{C}\), \( K_w = 1.0 \times 10^{-14} \). It is important to note that \( K_w \) changes with temperature, and this change is crucial for understanding water's acidity at different conditions. When \( K_w \) increases, it indicates a greater degree of ionization, resulting in more acid and base ions in the solution, although in equal amounts for pure water.

Temperature Dependence of Kw

The value of \( K_w \) is highly affected by temperature. As temperature increases, the ionic product of water \( K_w \) also increases. This is because increased thermal energy encourages more water molecules to ionize. At higher temperatures such as \(80^{\circ} \mathrm{C}\), the increased \( K_w \) suggests more hydrogen ions and hydroxide ions in the solution.

• Higher \( K_w \) means increased ionization.
• More hydrogen and hydroxide ions are produced as temperature rises.

This concept is crucial for understanding the behavior of water at different temperatures, which ultimately affects its \( \text{pH} \). When studying \( \text{pH} \) alterations due to temperature changes, it's important to consider the corresponding adjustments in \( K_w \).

Neutrality of Pure Water

Even though the \( \text{pH} \) of pure water changes with temperature, it remains neutral as long as the concentrations of \( [H^+] \) and \( [OH^-] \) are equal. Neutrality in pure water is characterized by this balance. However, the numeric pH value that signifies neutrality shifts due to temperature-induced changes in \( K_w \).

At room temperature, neutrality is typically pegged at \( \text{pH} = 7 \). However, this shifts below 7 at higher temperatures, such as \(80^{\circ} \mathrm{C}\), where a higher concentration of ions (due to increased \( K_w \)) results in a lower \( \text{pH} \) value. Despite the numerical change, pure water at this temperature is still neutral as long as the ion concentrations are equal.

• The concept of neutrality is tied to the equality of \( [H^+] \) and \( [OH^-] \), not the actual \( \text{pH} \) value.
• Temperature changes affect \( \text{pH} \) but not the inherent neutrality.

Understanding this can help clarify misconceptions about \( \text{pH} \).