Problem 62 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statement is correct? 1\. The \(\mathrm{pH}\) of \(1.0 \times 10^{-8} \mathrm{M}\) solution of \(\mathrm{HCl}\) is 8 2\. The conjugate base of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)is \(\mathrm{HPO}_{4}^{2-}\) 3\. Autoprotolysis constant of water increases with temperature 4\. When a solution of a weak monoprotic acid is titrated against a strong base at half neutralization point, \(\mathrm{pH}=(1 / 2) \mathrm{pKa}\). (a) 2,3 (b) \(1,2,3\) (c) 3,4 (d) \(2,3,4\)

Step-by-Step Solution

Answer

Correct answer: (a) 2, 3

Step 1: Analyze statement 1

The \(\text{pH}\) of a very dilute solution of HCl at concentration \(1.0 \times 10^{-8} \ \text{M}\) is not 8. Since the concentration is extremely low, the effect of water ionization (which gives a \([\text{H}^+])\) of \(1.0 \times 10^{-7} \ \text{mol/L}\) should be considered, leading to \(\text{pH}\) close to 7, not 8.

Step 2: Analyze statement 2

The conjugate base of \(\text{H}_2 \text{PO}_4^-\) indeed is \(\text{HPO}_4^{2-}\). The reaction can be represented by \(\text{H}_2 \text{PO}_4^- \rightleftharpoons \text{HPO}_4^{2-} + \text{H}^+\), showing the removal of a proton from the acid.

Step 3: Analyze statement 3

The autoprotolysis constant of water \(K_w\) is known to increase with temperature. This makes statement 3 correct. As temperature increases, water ionizes more, leading to an increase in \(K_w\).

Step 4: Analyze statement 4

At the half-neutralization point of a weak monoprotic acid titrated against a strong base, the \(\text{pH} \) of the solution is equal to the \(\text{pKa}\) of the acid, not half the \(\text{pKa}\). Therefore, statement 4 is incorrect.

Step 5: Conclusion

The correct statements are 2 and 3 which correspond to option (a) 2, 3.

Key Concepts

pH and pKa relationship

To understand the pH and pKa relationship, it's essential to think about how acids dissociate in water. The pH measures how acidic or basic a solution is, with lower values indicating more acidic properties. On the other hand, the pKa value is a specific constant for each acid, representing the pH at which half of the acid molecules are dissociated.

A critical point to remember is the half-neutralization stage of a weak acid titration. At this stage, the amounts of the acid and its conjugate base are equal, and the pH of the solution equals the pKa of the acid. This is because the acid is half dissociated – a perfect balance for calculating these values. It's an important concept for understanding buffer solutions.

In our original problem, the statement intended to explore this relationship incorrectly stated that pH equals half the pKa at the half-neutralization point. Actually, it should have said that pH equals pKa at this point. This distinction is crucial for correctly interpreting acid-base equilibria.

Autoprotolysis constant

The autoprotolysis constant of water, commonly denoted by \( K_w \), refers to the equilibrium constant for the ionization of water into hydroxide \( \text{OH}^- \) and hydronium \( \text{H}_3\text{O}^+ \) ions. At 25°C, \( K_w \) is typically \( 1.0 \times 10^{-14} \). However, as temperature increases, the ability of water to ionize also increases, hence the autoprotolysis constant experiences an increase.

This relationship between temperature and \( K_w \) is vital in various chemical processes, especially those operating at different temperatures. We must account for this variance since it impacts the calculation of pH in temperature-variable environments. In our exercise, this was another focus.
Remember, a higher \( K_w \) means more ionization, which in turn suggests an increasing ability of water to conduct electricity due to more ions being present. This is a helpful concept for understanding how temperature can affect chemical reactions involving water.

Conjugate acid-base pairs

Conjugate acid-base pairs are at the heart of the Bronsted-Lowry theory of acids and bases. According to this theory, an acid donates a proton, becoming its conjugate base, while a base accepts a proton, becoming its conjugate acid.

For example, considering a reaction where \( \text{H}_2 \text{PO}_4^- \) loses a proton, it forms \( \text{HPO}_4^{2-} \), making \( \text{HPO}_4^{2-} \) the conjugate base of \( \text{H}_2 \text{PO}_4^- \). This reaction exemplifies the systematic nature of conjugate acid-base pairs, where each acid-base transformation is reversible and involves the exchange of protons.

Knowing these pairs is crucial in predicting the direction of acid-base reactions and understanding titration curves. It helps in visualizing the dynamic equilibrium states in such reactions, making it an indispensable concept in acid-base chemistry.