Question

Which of the following statement is correct? 1\. The 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) \(2,3,4\)

Short answer

The correct statements are 2 and 3, so option (a) 2,3 is correct.

Step-by-step solution

Understanding the pH of Dilute HCl Solution

A 1.0 × 10^{-8} M solution of HCl is extremely dilute, comparable to the concentration of H+ ions in pure water (10^{-7} M), making this approximation invalid for pH calculation. Both ions from HCl and water contribute to the H+, making the pH value not accurately 8, which should be below 7 due to extra ions from the acid.

Identify the Conjugate Base of Dihydrogen Phosphate

The conjugate base of an acid is formed when it loses a proton (H+). Hence, the conjugate base of H2PO4^- is HPO4^{2-}, which is formed by the removal of one proton.

Effect of Temperature on Water's Autoprotolysis Constant

The autoprotolysis constant of water (Kw) generally increases with temperature. As temperature rises, the ionization of water increases, producing more H+ and OH- ions, which results in a larger Kw.

pH at Half Equivalence Point in Weak Acid-Strong Base Titration

For a weak acid HA being titrated with a strong base, at the half-equivalence point, the concentration of HA equals the concentration of its conjugate base A-. Thus, the pH equals pKa, not (1/2) pKa, making the given statement false.

Key concepts

pH Calculation

The calculation of pH is a fundamental concept in acid-base chemistry. **pH** is a measure of the acidity or alkalinity of a solution, and is defined as the negative logarithm (base 10) of the hydrogen ion concentration: \[ \text{pH} = -\log[\mathrm{H}^+] \]For a highly dilute solution, like a \(1.0 \times 10^{-8} \mathrm{M}\) solution of \(\mathrm{HCl}\), calculating the pH isn't as straightforward as simply plugging the concentration into the formula. Since this concentration is near the level of \(\mathrm{H}^+\) ions naturally present in pure water (\(10^{-7} \mathrm{M}\)), both the acids' and water's contribution to \(\mathrm{H}^+\) needs to be considered.

• This often means the pH is lower than 7, reflecting a more acidic solution due to the extra H+ ions.

Understanding this principle is crucial, as incorrect approximations can lead to significant miscalculations, particularly in dilute solutions.

Conjugate Base

The concept of conjugate bases is especially significant in buffering solutions and acid-base reactions. A conjugate base is what remains after an acid donates a proton (\(\mathrm{H}^+\)). For example, the conjugate base of \(\mathrm{H}_2\mathrm{PO}_4^-\) is \(\mathrm{HPO}_4^{2-}\), which is formed when one proton is lost.

• This loss of a proton doesn't always mean a decrease in acidity immediately; rather, it shows a step in the transition between acid and base forms.
• Recognizing conjugate acid-base pairs is key to predicting the behavior of solutions and their pH changes when mixed.

These pairs are part of the Bronsted-Lowry acid-base theory, underscoring the dual nature of substances to act as both acids and bases under certain conditions.

Autoprotolysis Constant

The autoprotolysis constant, denoted as \(K_w\), is an equilibrium constant for the self-ionization of water:
\[ \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}^+ + \mathrm{OH}^- \] Typically, \(K_w\) is approximately \(1.0 \times 10^{-14}\) at 25°C. However, this value is temperature-dependent. As temperature increases, \(K_w\) also increases because more water molecules ionize, which leads to more \(\mathrm{H}^+\) and \(\mathrm{OH}^-\) ions.

• This change in \(K_w\) with temperature means that neutral water (pH = 7) will not always have a pH of precisely 7 when the temperature is different from 25°C.

This behavior is an essential consideration when working with pH-sensitive processes ranging from biological systems to chemical manufacturing.

Titration

Titration is a technique used to determine the concentration of an unknown solution by adding a solution of known concentration. In acid-base titrations, one often encounters a point known as the **half-equivalence point**. This is the stage in the titration of a weak acid with a strong base when half of the acid has been neutralized by the base.

• At the half-equivalence point, the concentration of the weak acid (HA) is equal to its conjugate base (A-).
• This makes the solution a buffer and the pH of the solution equals the \(\mathrm{pKa}\) of the weak acid, not \((1/2)\mathrm{pKa}\) as sometimes mistaken."

This relationship is crucial for practical applications, where titration serves as a method for analyzing the components of an unknown solution's composition more precisely.