Problem 134 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following solution(s) have \(\mathrm{pH}\) between 6 and \(7 ?\) 1\. \(2 \times 10^{-6} \mathrm{M} \mathrm{NaOH}\) 2\. \(2 \times 10^{-6} \mathrm{M} \mathrm{HCl}\) 3\. \(10^{-8} \mathrm{M} \mathrm{HCl}\) 4\. \(10^{-13} \mathrm{M} \mathrm{NaOH}\) (a) 1,2 (b) 2,3 (c) 3,4 (d) \(2,3,4\)

Step-by-Step Solution

Answer

Solutions 3 and 4 have a pH between 6 and 7.

Step 1: Calculate pH of NaOH Solutions

For solutions containing NaOH, calculate the pOH first using the formula \(\text{pOH} = -\log[\text{OH}^-]\). Then, use \(\text{pH} = 14 - \text{pOH}\). 1. \([\text{OH}^-] = 2 \times 10^{-6} \text{ M}\), \(\text{pOH} = -\log(2 \times 10^{-6}) = 5.70\), \(\text{pH} = 14 - 5.70 = 8.30\).4. \([\text{OH}^-] = 10^{-13} \text{ M}\), \(\text{pOH} = -\log(10^{-13}) = 13\), \(\text{pH} = 14 - 13 = 1.00\).

Step 2: Calculate pH of HCl Solutions

For solutions containing HCl, calculate the pH directly using the formula \(\text{pH} = -\log[\text{H}^+]\).2. \([\text{H}^+] = 2 \times 10^{-6} \text{ M}\), \(\text{pH} = -\log(2 \times 10^{-6}) = 5.70\). Note that the pH is less than 6.3. \([\text{H}^+] = 10^{-8} \text{ M}\). Normally this would suggest a pH of 8, but since this is a very dilute solution (approaching the concentration of pure water, which is \(10^{-7} \text{ M}\)), the actual pH is closer to 7. Adjust for autoionization of water: \([\text{H}^+] + [\text{OH}^-] = 10^{-7}\text{ M}\), so \(\text{pH} \approx 7.00\).

Key Concepts

Acid-Base Solutions

Understanding acid-base solutions is vital for grasping pH calculations. These solutions are characterized by the presence of either hydrogen ions

• Acidic solutions have excess \([ ext{H}^+]\) leading to a lower pH.
• Basic solutions contain hydroxide ions \([ ext{OH}^-]\), resulting in a higher pH.
• A neutral solution, like pure water, has an equal concentration of hydrogen and hydroxide ions, typically at a pH of 7.

Knowing the concentration of these ions helps calculate the solution's pH. For acids like HCl, the \([ ext{H}^+]\) concentration is directly related to pH. For bases like NaOH, you first find the pOH from the \([ ext{OH}^-]\) concentration and use it to find the pH, since \( ext{pH} = 14 - ext{pOH}\).
This relationship aids in identifying the nature of the solution as acidic or basic, influencing its pH and behavior in chemical reactions.

Autoionization of Water

Autoionization of water is a phenomenon where water molecules dissociate into hydrogen and hydroxide ions.Br>

• This dissociation is at equilibrium, usually expressed as: \[2 ext{H}_2 ext{O} ightleftharpoons ext{H}_3 ext{O}^+ + ext{OH}^-\]
• The equilibrium constant \([K_w]\) for this reaction is \(1.0 imes 10^{-14}\) at 25°C.

Under these conditions, both \([ ext{H}^+]\) and \([ ext{OH}^-]\) are \(10^{-7}\) M, making pure water neutral at pH 7.
Autoionization significantly affects the calculations in extremely dilute solutions like \(10^{-8}\) M HCl.
In such cases, the ion concentrations approach the level in pure water, necessitating adjustments to calculate pH correctly.This understanding is essential for accurate pH measurement in various solutions.

pOH and pH Relationship

The connection between pOH and pH is foundational in chemistry, hinging on the concept of the ion product of water \(K_w\) which is \(1.0 imes 10^{-14}\).

• For any aqueous solution, \(K_w = [ ext{H}^+][ ext{OH}^-] = 10^{-14}\) mol² L⁻².
• You calculate pOH using \(\text{pOH} = -\log [\text{OH}^-]\).
• Then, relate pOH to pH through the formula \(\text{pH} + \text{pOH} = 14\).

This means if \([ ext{OH}^-]\) increases (making the solution more basic), pH increases as pOH decreases.
Conversely, more hydrogen ions (acidic) increase the pOH and lower the pH.
Mastering this relationship is crucial for deriving pH from ion concentrations, especially in basic solutions like NaOH.

Dilute Solutions

Dilute solutions present unique challenges in calculating pH due to low concentrations of acid or base, often comparable to pure water.For instance, in very dilute solutions such as \(10^{-8}\) M HCl, simply calculating pH using standard methods doesn't give accurate results.
When a solution's concentration is near \(10^{-7}\) M, it gets close to the natural autoionization level of water.

• The calculated \(\text{pH}\) should account for contributions from water’s hydrogen ion concentration.
• In such a scenario, you need to adjust the pH calculation because \([ ext{H}^+] + [ ext{OH}^-] \approx 10^{-7}\) may apply.

Understanding this balance ensures correct pH determination in dilute environments, crucial for precise chemical analysis and reactions.