Problem 197 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements are correct? (a) The conjugate base of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)is \(\mathrm{HPO}_{4}^{2-}\). (b) \(\mathrm{pH}\) of \(1.0 \times 10^{-8} \mathrm{M}\) aqueous solution of \(\mathrm{HCl}\) is 8 . (c) When a weak monoprotic acid solution is treated with a strong base, at half neutralization point, \(\mathrm{pH}=\frac{1}{2} \mathrm{pK}_{\mathrm{a}}\) (d) The autoprotolysis constant of water increases with temperature.

Step-by-Step Solution

Answer

Statements (a) and (d) are correct.

Step 1: Understanding Conjugate Bases

To find the conjugate base of an acid, remove one hydrogen (H) and decrease the charge by one unit. The chemical species \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) has a hydrogen removed to become \(\mathrm{HPO}_{4}^{2-}\), making statement (a) correct.

Step 2: Calculating pH of Dilute Strong Acid Solution

For \(1.0 \times 10^{-8} \mathrm{M}\) \(\mathrm{HCl}\), which is a strong acid, the pH calculation considers the effect of water. Given this concentration is lower than that of pure water, we calculate pH as 7 (neutral water) slightly decreased considering the presence of \(\mathrm{HCl}\), making pH close to 7, but not 8. Therefore, statement (b) is incorrect.

Step 3: Analyzing the Half Neutralization Point of Weak Acids

At the half neutralization point of a weak acid, the concentration of the acid equals the concentration of its conjugate base, hence \(\mathrm{pH} = \mathrm{pK}_{\mathrm{a}}\), not \(\frac{1}{2}\mathrm{pK}_{\mathrm{a}}\). Thus, statement (c) is incorrect.

Step 4: Understanding Autoprotolysis Constant of Water

The autoprotolysis constant \(Kw\) of water is known to increase with temperature because more water molecules can dissociate into \(\mathrm{H^{+}}\) and \(\mathrm{OH^{-}}\) ions. Therefore, statement (d) is correct.

Key Concepts

pH calculation

Understanding how to calculate the pH of a solution is crucial when dealing with acids and bases. The pH measures the hydrogen ion concentration in a solution, usually expressed on a scale from 0 to 14. For a strong acid like \(\text{HCl}\), the pH is calculated using the formula:

• \(\text{pH} = -\log[\text{H}^+]\)

However, when the concentration of \(\text{HCl}\) is \(1.0 \times 10^{-8} \text{ M}\), it's below the ion product of water (\[10^{-7} \ ext{ M}\]) which contributes additional hydronium ions that must be considered.
This makes the system slightly acidic, and the pH will be less than 7, not 8.
Thus, when calculating such low concentrations, it's essential to account for the dissociation of water itself along with the added acid.

Half neutralization point

The half neutralization point is a critical concept in acid-base titrations, especially when dealing with weak acids and strong bases. At this point, half of the weak acid has been neutralized to form its conjugate base.

• This means the concentration of the acid equals the concentration of its conjugate base.

A key outcome of this is that the \(\text{pH}\) at this point is equal to the \(\mathrm{pK}_{\mathrm{a}}\) of the acid, not half of \(\mathrm{pK}_{\mathrm{a}}\).
Therefore,

• \(\text{pH} = \mathrm{pK}_{\mathrm{a}}\)

This relationship underlines the buffering region of the titration curve, where the pH changes minimally with the addition of small amounts of acid or base.
Understanding this makes the titration process easier and provides insights into the acid's strength and behavior.

Water autoprotolysis constant

The autoprotolysis constant, \(K_w\), of water is a vital parameter in understanding water’s slight ionization into hydronium and hydroxide ions.
The familiar formula is \(K_w = [\text{H}^+][\text{OH}^-]\) at 25°C, where \(K_w = 1.0 \times 10^{-14}\).
However, it's essential to note that \(K_w\) is temperature dependent.

• As temperature increases, more water molecules have enough energy to dissociate, leading to an increase in \(K_w\).

Thus, at higher temperatures, water becomes a slightly better conductor of electricity due to increased ionization.
This phenomenon is crucial in chemical reactions and biological processes, where a small change in temperature can significantly affect the reaction rate and equilibrium. Understanding how temperature affects \(K_w\) is important for accurately predicting the behavior of aqueous solutions.