Problem 20 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following statement is correct? (a) Bronsted-Lowry theory could not explain the acidic nature of \(\mathrm{BCl}_{3}\) (b) the \(\mathrm{pH}\) of \(0.01 \mathrm{M} \mathrm{NaOH}\) solution is 2 (c) the ionic product of water at \(25^{\circ} \mathrm{C}\) is \(10^{-10} \mathrm{~mol}^{2} \mathrm{~L}^{-2}\) (d) the \(\mathrm{pH}\) of a solution can be calculated using the equation \(\mathrm{pH}=\log \left[\mathrm{H}^{+}\right]\)

Step-by-Step Solution

Answer

Option (a) is correct: Bronsted-Lowry theory could not explain the acidic nature of \(\mathrm{BCl}_3\).

Step 1: Analyze Option (a)

The Bronsted-Lowry theory defines acids as proton donors and bases as proton acceptors. \(\mathrm{BCl}_3\) does not donate protons; it accepts electron pairs, acting as a Lewis acid rather than a Bronsted-Lowry acid. Thus, the Bronsted-Lowry theory indeed fails to explain the acidic nature of \(\mathrm{BCl}_3\). Therefore, option (a) is correct.

Step 2: Evaluate Option (b)

The \(\mathrm{pH}\) of a solution is calculated using the formula \(\mathrm{pH} = -\log{[\mathrm{H}^+]}\). For a \(0.01 \mathrm{M}\) \(\mathrm{NaOH}\) solution, which is a strong base, \([\mathrm{OH}^-] = 0.01\,\mathrm{M}\). The \([\mathrm{H}^+] \) can be calculated from \(\mathrm{Kw} = [\mathrm{H}^+][\mathrm{OH}^-] = 10^{-14}\). Thus, \(\mathrm{pH} = 12\), not 2. Option (b) is incorrect.

Step 3: Check Option (c)

The ionic product of water at \(25^{\circ}\mathrm{C}\), \(\mathrm{Kw}\), is always \([\mathrm{H}^+][\mathrm{OH}^-] = 10^{-14}\,\mathrm{mol}^2\,\mathrm{L}^{-2}\). Therefore, option (c), which states \(10^{-10}\,\mathrm{mol}^2\,\mathrm{L}^{-2}\), is incorrect.

Step 4: Verify Option (d)

The \(\mathrm{pH}\) of a solution can be calculated using \(\mathrm{pH} = -\log{[\mathrm{H}^+]}\), not \(\log{[\mathrm{H}^+]}\). So option (d) is incorrect.

Step 5: Conclusion: Determine Correct Statement

After analyzing each statement, option (a) is the only correct statement, as the Bronsted-Lowry theory does not account for the acidic nature of \(\mathrm{BCl}_3\).

Key Concepts

Lewis Acid

In the context of acid-base chemistry, a Lewis acid stands out due to its unique way of interacting with other substances. Unlike Bronsted-Lowry acids, which donate protons, Lewis acids accept electron pairs. This makes them pivotal in many chemical reactions, particularly where electron-rich molecules are involved.

• A common characteristic of Lewis acids is their electron deficiency, which drives them to seek electron pairs from other substances to achieve stability.
• For example, \( \mathrm{BCl}_3 \) is a well-known Lewis acid because it can accept an electron pair into its boron atom's vacant p-orbital.
• Understanding this concept is essential, as it broadens the definition of acids beyond merely proton donors.

The failure of the Bronsted-Lowry theory to recognize \( \mathrm{BCl}_3 \) as an acid stems from its strict criterion of proton donation, which is not required in Lewis' broader definition.

pH Calculation

Calculating the \( \text{pH} \) of a solution is fundamental in understanding its acidity or basicity. The \( \text{pH} \) is determined by the concentration of hydrogen ions \( \left[\text{H}^{+}\right]\) in a solution.

To find the \( \text{pH} \), you use the formula: \[\text{pH} = -\log{[\text{H}^+]}\]

• This formula implies that the concentration of H ions is expressed in a logarithmic scale, making the \( \text{pH} \) a representation of this concentration in a more manageable number.
• This is critical as small changes in the concentration of \( \left[\text{H}^{+}\right]\) result in significant changes in \( \text{pH} \).

Specifically, when calculating the \( \text{pH} \) of bases like \( \text{NaOH} \), you first find the hydrogen ion concentration using the ionic product of water and then apply the formula. This correct understanding is essential since misconceptions can lead to errors, such as believing a basic solution like \( 0.01 \text{ M NaOH} \) has a low \( \text{pH} \).

Ionic Product of Water

The ionic product of water, \( \text{Kw} \), is a constant at a given temperature. It defines the auto-ionization of water into hydrogen and hydroxide ions.At \( 25^{\circ} \text{C}, \text{Kw} \) is represented as: \[[\text{H}^+][\text{OH}^-] = 10^{-14} \, \text{mol}^2 \, \text{L}^{-2}\]

• This equation is pivotal in predicting the concentration of ions in pure water and also in solutions, being fundamental to acid-base calculations.
• Knowing this constant helps in calculating \( \text{pH} \) when either the hydrogen ion or hydroxide ion concentration is known.

Many misconceptions arise from incorrectly remembering this value, leading to mistakes such as thinking it is \( 10^{-10} \, \text{mol}^2 \, \text{L}^{-2} \). Always remember that in any aqueous solution at \( 25^{\circ} \text{C}, \text{Kw} \) maintains this value, making it a cornerstone of chemical calculations.

Acid-Base Chemistry

Acid-base chemistry is an integral part of understanding chemical reactions and processes. Both Bronsted-Lowry and Lewis theories expand on what constitutes an acid or base.

• The Bronsted-Lowry theory defines acids and bases in terms of their ability to donate and accept protons, respectively.
• Conversely, the Lewis theory expands the definition to encompass the exchange of electron pairs.
• While Bronsted-Lowry acids donate protons, Lewis acids accept electron pairs, providing a more comprehensive framework for understanding how molecules interact.

This breadth in definition reveals the versatility of acids and bases in both theoretical and practical chemical processes. Grasping these theories is critical for predicting reaction outcomes, particularly in organic and inorganic chemistry, where different acids and bases play fundamental roles. Understanding both perspectives allows for a deeper insight into chemical behavior, broadening the potential applications and manipulations in various scientific fields.