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

The pH of pure water at \(80^{\circ} \mathrm{C}\) is (b) \(<7\).

Step 1: Understand the Relationship between Temperature and Kw

The ion product of water, often denoted as \(K_w\), changes with temperature. At \(25^{\circ} C\), the \(K_w\) is \(1.0 \times 10^{-14}\). However, at higher temperatures such as \(80^{\circ} C\), \(K_w\) increases, indicating more ionization of water molecules, which affects the \(\text{pH}\).

Step 2: Define pH in Terms of Kw

The \(\text{pH}\) is defined as \( -\log[H^+] \). In pure water, \([H^+] = [OH^-]\), so \(K_w = [H^+][OH^-] = [H^+]^2\.\) Therefore, \([H^+] = \sqrt{K_w}\). As \(K_w\) increases with temperature, the concentration \([H^+]\) also increases.

Step 3: Determine the Resulting pH Value

As \([H^+]\) increases while \(K_w\) increases, the \(\text{pH}\) (which equals \(-\log[H^+]\)) decreases. Therefore, the \(\text{pH}\) of pure water at \(80^{\circ} C\) will be less than 7, indicating that water becomes more acidic in terms of numerical pH scale at increased temperatures.

Step 4: Choose the Correct Option

Given that the \(\text{pH}\) decreases with increased temperature, pure water at \(80^{\circ} C\) will have a \(\text{pH}\) less than 7. Thus, the correct option is (b) \(<7\).

Key Concepts

Temperature Effect on \(K_w\)

Water's ionization product, denoted as \(K_w\), is highly dependent on temperature.
At \(25^{\circ} C\), \(K_w\) is commonly known to be \(1.0 \times 10^{-14}\).
As the water temperature rises, such as at \(80^{\circ} C\), \(K_w\) increases, and this alteration is crucial in understanding how variations in temperature affect water's properties.
This increase in \(K_w\) implies more ionization of water, meaning more molecules break up into ions.
A higher \(K_w\) shows increased ionization, which has a direct impact on the calculation and understanding of pH changes when water is heated. Essentially:

• Higher temperature \(\rightarrow\) higher \(K_w\)
• More ionization \(\rightarrow\) greater presence of \([H^+]\) and \([OH^-]\) ions

These dynamic changes help explain the variations in pH with temperature shifts in water.

Ionization of Water

The process of ionization in water refers to water molecules dissociating into hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\).
At room temperature, water is partially ionized, maintaining a balance in its neutral state.
When we discuss ionization at varying temperatures, such as \(80^{\circ} C\), we observe an increase in the number of ions present.
The ionization equation for water is:\[H_2O(l) \leftrightarrows H^+(aq) + OH^-(aq)\]With increased temperature, the equilibrium shifts to favor more ionization, meaning that there are more \([H^+]\) and \([OH^-]\) ions in the water.
Key insights:

• Increase in temperature spikes the ionization process
• Explains increased values of \([H^+]\) and \(K_w\) at higher temperatures

This helps students understand why the \(pH\) scale, typically at \(7\) for pure water at room temperature, shifts at higher temperatures.

Relationship between \(K_w\) and pH

The pH is a logarithmic scale used to express the acidity or basicity of a solution, calculated using the formula \(\text{pH} = -\log[H^+]\).
In pure water, the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) are equal.
The equation \(K_w = [H^+][OH^-] = [H^+]^2\) confirms this balance.
When \(K_w\) increases, due to factors like rising temperature, the concentration \([H^+]\) will increase as well. This affects the pH value:

• As \([H^+]\) rises, the pH value lowers
• A higher \(K_w\) at increased temperatures indicates that pure water becomes more 'acidic' in numerical terms

Thus, even though chemically water remains neutral, its pH value tends to decline below \(7\) at higher temperatures.
Understanding this intricate relationship helps in predicting the behavior of water's pH in various thermal conditions.