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

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

Step 1: Analyzing Statement (a)

The Bronsted-Lowry theory defines acids as proton donors. \( \mathrm{BCl}_3 \) does not donate a proton; instead, it accepts an electron pair due to its electron deficiency. Therefore, Bronsted-Lowry theory cannot explain the acidity of \( \mathrm{BCl}_3 \). So statement (a) is correct.

Step 2: Analyzing Statement (b)

The \( \mathrm{pH} \) of a \(0.01\, \mathrm{M}\) \( \mathrm{NaOH} \) solution can be calculated by first determining the \( \mathrm{pOH} \). \( \mathrm{pOH} = -\log[\mathrm{OH}^-] \), so \( \mathrm{pOH} = -\log(0.01) = 2 \). Since \( \mathrm{pH} + \mathrm{pOH} = 14 \), \( \mathrm{pH} = 14 - 2 = 12 \). Statement (b) is incorrect.

Step 3: Analyzing Statement (c)

The ionic product of water \( \mathrm{K_w} \) at \(25^{\circ} \mathrm{C} \) is typically \(1.0 \times 10^{-14} \, \mathrm{mol}^2 \, \mathrm{L}^{-2}\). Therefore, \(10^{-10} \, \mathrm{mol}^2 \, \mathrm{L}^{-2}\) is incorrect for the ionic product of water. Statement (c) is incorrect.

Step 4: Analyzing Statement (d)

The correct equation to find the \( \mathrm{pH} \) of a solution is \( \mathrm{pH} = -\log[\mathrm{H}^+] \). Therefore, statement (d) is incorrect.

Key Concepts

Bronsted-Lowry Theory

The Bronsted-Lowry theory is a fundamental concept in acid-base chemistry. It defines acids and bases based on their ability to donate or accept a proton (H").
According to this theory:

• An acid is a proton donor - it donates an H".
• A base is a proton acceptor - it receives an H".

One significant advantage of the Bronsted-Lowry theory is its applicability to reactions without water. Instead of limiting acids and bases to aqueous solutions, it includes any chemical species that can donate or accept protons.
This theory, however, does not address substances that are not involved in proton transfer, such as boron trichloride (BCl₃).
BCl₃ is known to be acidic because it accepts an electron pair, rather than donating a proton.
This is why the Bronsted-Lowry theory cannot fully describe the acidic nature of BCl₃, which is more accurately explained by the Lewis acid-base theory.

pH Calculation

pH calculation is crucial for understanding the acidity or basicity of a solution. The pH scale ranges from 0 to 14, with pH 7 being neutral, values below 7 acidic, and above 7 basic.
The formula to calculate the pH of a solution is:

• \( \mathrm{pH} = -\log [\mathrm{H}^+] \)

The concentration of \( [\mathrm{H}^+] \) ions is used in the logarithmic calculation to determine the pH. For example, in calculating the pH of a 0.01 M NaOH solution, we start by finding the pOH first.
Since NaOH is a strong base, it dissociates completely, giving a hydroxide ion concentration [OH⁻] of 0.01 M.
The pOH is calculated as:

• \( \mathrm{pOH} = -\log [\mathrm{OH}^-] \), which equals \( \mathrm{pOH} = 2 \)

Given that \( \mathrm{pH} + \mathrm{pOH} = 14 \), the pH equals 12.
It's crucial to remember that negative logarithms can result in a bit of a mind-bender conceptually, which makes understanding the idea behind pH calculations vital.

Ionic Product of Water

The ionic product of water, represented by \( K_w \), is a key concept in acid-base chemistry. It signifies the equilibrium constant for the ionization of water, describing the self-ionization property.
In pure water, at 25°C, the reaction is expressed as:

• \( 2 \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^- \)

The equilibrium expression can be written as:

• \( K_w = [\mathrm{H}^+][\mathrm{OH}^-] \)

At 25°C, \( K_w \) is \( 1.0 \times 10^{-14} \, \text{mol}^2\, \text{L}^{-2} \).
When calculating the pH or pOH of a solution, this value is a constant used to express the relationship between hydrogen ions \( [\mathrm{H}^+] \) and hydroxide ions \( [\mathrm{OH}^-] \).
Any significant deviation from this value at standard conditions indicates unique solute effects or temperature changes.

Boron Trichloride (BCl3)

Boron trifluoride, or \( BCl_3 \), is an intriguing compound in the study of acid-base chemistry. Its behavior does not conform to the classical Bronsted-Lowry definition, where an acid is defined as a proton donor.
\( BCl_3 \) acts as a Lewis acid, which is defined as an electron pair acceptor.

• In \( BCl_3 \), the boron atom lacks a full octet, making it electron-deficient, which explains its ability to accept an electron pair from a donor molecule, such as water or ammonia.
• This electron-pair acceptance leads to reactions, forming adducts, that do not involve the transfer of protons, distinguishing it from typical Bronsted-Lowry reactions.

The understanding that \( BCl_3 \) is a Lewis acid emphasizes the differences and overlaps between the Lewis and Bronsted-Lowry acid-base theories.
Lewis theory broadens the definition of acids and bases beyond proton transfer, accommodating compounds like \( BCl_3 \) and providing a more inclusive insight into chemical reactivity.