JEE Chemistry 2023 Question with Solution

Given: Four statements about pH, conjugate base, $K_w$, and weak acid-strong base titration are to be checked.

Find: Which statements are correct and the corresponding correct option.

Statement (A): For very dilute $1 \times 10^{-8}\,\mathrm{M}$ HCl, the contribution of $\mathrm{H^+}$ from water auto-ionisation cannot be neglected. Therefore, the pH is less than $7$, not $8$. So statement (A) is incorrect.

Statement (B): The conjugate base is formed by removal of one proton. When $\mathrm{H_2PO_4^-}$ loses one $\mathrm{H^+}$ ion, it forms $\mathrm{HPO_4^{2-}}$. So statement (B) is correct.

Statement (C): Ionisation of water is an endothermic process. Therefore, with increase in temperature, the extent of ionisation increases and hence $K_w$ increases. So statement (C) is correct.

Statement (D): At half neutralisation point of a weak acid-strong base titration, the concentration of acid equals that of its conjugate base, and the correct relation is

$$\mathrm{pH} = pK_a$$

not

$$\mathrm{pH} = \dfrac{1}{2}pK_a$$

So statement (D) is incorrect.

Therefore, only statements (B) and (C) are correct. The correct option is C.

Given: The task is to identify the correct set of statements.

Find: The option that contains only true statements.

A quick elimination works here:

• Statement (A) is false because extremely dilute HCl does not give pH $8$; water auto-ionisation must be considered.
• Statement (D) is false because at half-neutralisation for a weak acid and strong base titration,

$$\mathrm{pH} = pK_a$$

This immediately removes any option containing (A) or (D).

Among the given options, only (B), (C) survives. Hence, the correct option is C.