Problem 203 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are wrong statements? (a) \(\mathrm{K}_{\mathrm{i}}\) is always constant and equal to \(10^{-14}\) (b) \(\mathrm{pH}+\mathrm{pOH}=\mathrm{pK}_{w}\) at all temperature (c) Salts of strong acid and strong base undergo hydrolysis (d) Addition of \(\mathrm{CH}_{3} \mathrm{COONa}\) to acetic acid solution decreases the \(\mathrm{pH}\) of solution of acetic acid.

Step-by-Step Solution

Answer

All statements (a), (b), (c), and (d) are incorrect.

Step 1: Analyze Statement (a)

Statement (a) claims that \( K_i \) is always constant and equal to \( 10^{-14} \). This is incorrect because \( K_i \) is not a standard notation and might be confusing with \( K_w \), the ionic product of water, which varies with temperature and is approximately \( 1.0 \times 10^{-14} \) at 25°C.

Step 2: Analyze Statement (b)

Statement (b) refers to the equation \( \mathrm{pH} + \mathrm{pOH} = \mathrm{pK}_w \) at all temperatures. The correct version of this equation is \( \mathrm{pH} + \mathrm{pOH} = 14 \) at 25°C (standard conditions). The sum of \( \mathrm{pH} \) and \( \mathrm{pOH} \) can vary with temperature since \( \mathrm{pK}_w = -\log K_w \). Thus, statement (b) is incorrect.

Step 3: Analyze Statement (c)

Salts formed from strong acids and strong bases do not undergo hydrolysis; they dissociate completely in water, producing neutral solutions. Statement (c) incorrectly suggests that these salts do undergo hydrolysis, so it is incorrect.

Step 4: Analyze Statement (d)

Acetic acid is a weak acid, and \( \mathrm{CH}_3\mathrm{COONa} \) is its sodium salt, which when added increases the solution's pH due to the common ion effect. This statement suggests the opposite, making statement (d) incorrect.

Key Concepts

pH and pOH

The concept of pH and pOH is crucial in understanding the acidity and basicity of solutions. - **pH**: It is the measure of the hydrogen ion concentration \([\text{H}^+]\) in a solution. It is calculated using the formula \(\text{pH} = -\log_{10}[\text{H}^+]\). A low pH value (below 7) indicates an acidic solution, while a high pH value (above 7) indicates a basic solution.- **pOH**: It complements the pH scale, measuring the hydroxide ion \([\text{OH}^-]\) concentration. It can be calculated using the formula \(\text{pOH} = -\log_{10}[\text{OH}^-]\). One of the essential relationships in chemistry is that for any aqueous solution at 25°C, the sum of pH and pOH equals 14.0, given by \(\text{pH} + \text{pOH} = 14\). This sum can change with temperature, as the ionic product of water \(K_w\) also varies with temperature. Understanding these concepts helps in predicting the behavior of solutions and in chemical reactions.

Ionic Product of Water (Kw)

The ionic product of water, often denoted as \(K_w\), is a fundamental concept in acid-base equilibrium. It refers to the equilibrium constant for the self-ionization of water:\[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \]At 25°C, the value of \(K_w\) is approximately \(1.0 \times 10^{-14}\). This means that even pure water has both hydrogen ions and hydroxide ions present, albeit in very small concentrations.- **Temperature Dependence**: Unlike common misconceptions, \(K_w\) is not a fixed value across all temperatures. It increases as the temperature rises, which causes the equilibrium concentrations of \([\text{H}^+]\) and \([\text{OH}^-]\) to increase as well.Understanding \(K_w\) is vital for mathematical calculations involving pH and pOH as they relate back to this constant through the relation \(\text{pH} + \text{pOH} = -\log K_w\). Recognizing how changes in temperature affect \(K_w\) can help predict how pH levels might shift in different environments.

Hydrolysis of Salts

Hydrolysis refers to the reaction between water and the salt, resulting in the formation of an acid and a base. Whether or not a salt undergoes hydrolysis depends on the nature of the acid and base from which it is derived:- **Salts from Strong Acid and Strong Base**: These salts (e.g., NaCl, produced from HCl and NaOH) typically do not undergo hydrolysis. They dissociate completely, and the solution remains neutral.- **Salts from Weak Acid or Weak Base**: Salts like \(\text{Na}_2\text{CO}_3\) can undergo hydrolysis. If derived from a weak acid, the base characteristics might dominate, making the solution basic.An interesting factor is the **common ion effect**, where adding a salt can affect the pH by shifting the equilibrium. For instance, adding sodium acetate \(\text{CH}_3\text{COONa}\) to acetic acid increases the pH, due to suppression of ionization of the acid by the acetate ions.