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

Statement (a) is correct.

Step 1: Understand the Bronsted-Lowry Theory

The Bronsted-Lowry theory defines acids as proton donors and bases as proton acceptors. According to this theory, molecules that do not donate protons, like \( \mathrm{BCl}_3 \), cannot be considered acids under this definition. Therefore, statement (a) is correct since \( \mathrm{BCl}_3 \) does not fit the Bronsted-Lowry definition.

Step 2: Calculate the pH of NaOH

\( \mathrm{NaOH} \) is a strong base, completely dissociating into \( \mathrm{OH}^{-} \) ions in water. For a \( 0.01 \mathrm{M} \) solution, \( [\mathrm{OH}^{-}]=0.01 \mathrm{M} \). Using the relation \( \mathrm{pOH}=-\log 0.01=2 \). Thus, \( \mathrm{pH} = 14 - \mathrm{pOH} = 12 \). Therefore, statement (b) is incorrect.

Step 3: Check Ionic Product of Water

The ionic product of water at \( 25^{\circ} \mathrm{C} \) is actually \( 10^{-14} \mathrm{~mol}^{2} \mathrm{~L}^{-2} \), which is a well-known constant at this temperature. Therefore, statement (c) is incorrect.

Step 4: Verify pH Equation

The correct formula to calculate \( \mathrm{pH} \) is \( \mathrm{pH} = -\log[\mathrm{H}^+] \), which indicates statement (d) is incorrect as it misses the negative sign.

Key Concepts

Acid-Base Reactions

In the realm of chemistry, acid-base reactions play an essential role. Understanding these reactions is crucial for identifying the nature of substances and predicting their behavior in various environments. The Bronsted-Lowry Theory is one of the foundational principles in this area. **Understanding Bronsted-Lowry Theory** According to the Bronsted-Lowry Theory, acids are substances that donate protons (hydrogen ions, \( \mathrm{H}^+ \)), while bases are substances that accept protons. This concept allows us to understand the interaction between acids and bases in a solution where they exchange protons.**Application in Identifying Acids and Bases** For example, substances like \( \mathrm{BCl}_3 \) are not acids under this theory because they do not donate protons. This is contrary to substances like hydrochloric acid (\( \mathrm{HCl} \)), which readily donates protons and thus is classified as an acid in the Bronsted-Lowry sense.By applying the Bronsted-Lowry Theory, we can determine whether a substance acts as an acid or base in a given reaction system. It provides a broader understanding beyond simple definitions, accommodating a range of chemical behaviors.

pH Calculation

Calculating the \( \mathrm{pH} \) of solutions is vital for understanding their acidity or basicity. This measure tells us how acidic or basic a solution is on a scale, generally ranging from 0 to 14.**Basics of Calculating pH** The \( \mathrm{pH} \) is calculated using the equation \( \mathrm{pH} = -\log [\mathrm{H}^+] \). Here, \( [\mathrm{H}^+] \) is the concentration of hydrogen ions in the solution. A lower \( \mathrm{pH} \) value indicates a more acidic solution, while a higher \( \mathrm{pH} \) value indicates a more basic or alkaline solution.**Example with NaOH** Sodium hydroxide (\( \mathrm{NaOH} \)) is a strong base and dissociates completely in water to produce \( \mathrm{OH}^- \) ions. In a \( 0.01 \mathrm{M} \) NaOH solution, the concentration of \( \mathrm{OH}^- \) ions is \( 0.01 \mathrm{M} \), making the \( \mathrm{pOH} \) 2, using \( \mathrm{pOH} = -\log [\mathrm{OH}^-] \). Since \( \mathrm{pH} + \mathrm{pOH} = 14 \), the \( \mathrm{pH} \) of the solution is \( 14 - 2 = 12 \), indicating a basic solution.Accurate \( \mathrm{pH} \) calculation is imperative for understanding solution chemistry and conducting experiments properly.

Ionic Product of Water

Water is a unique substance, and its ability to dissociate into ions is characterized by the ionic product. Appreciating this concept is critical for understanding many chemical reactions in aqueous solutions.**What Is the Ionic Product of Water?** The ionic product of water (\(K_w\)) is the product of the concentrations of hydrogen ions \([\mathrm{H}^+]\) and hydroxide ions \([\mathrm{OH}^-]\) in pure water. At \( 25^{\circ} \mathrm{C} \), this constant is \( 10^{-14} \mathrm{~mol}^2 \mathrm{~L}^{-2} \). This means that in pure water, the concentrations of \( \mathrm{H}^+ \) and \( \mathrm{OH}^- \) are both \( 10^{-7} \mathrm{M} \).**Significance in Chemistry** Understanding \(K_w\) is important for calculating pH and pOH values of substances in water. It also explains why water is neutral at \( 25^{\circ} \mathrm{C} \) because the concentrations of \( \mathrm{H}^+ \) and \( \mathrm{OH}^- \) are equal.The ionic product helps chemists predict the behavior of acids and bases in water. It's essential for ensuring that reactions are controlled and precise, which is foundational for successful chemical practices.