Problem 19 - A Complete Resource Book in Chemistry for JEE Main

Question

The \(\mathrm{pH}\) of \(\mathrm{N} / 10 \mathrm{HCl}\) is (a) 3 (b) 4 (c) 2 (d) 1

Step-by-Step Solution

Answer

The pH of \( N/10 \text{ HCl} \) is 1.

Step 1: Understand the Formula for pH Calculation

The pH of a solution is calculated using the formula: \( \text{pH} = -\log[\text{H}^+] \). Here, \([\text{H}^+]\) is the concentration of hydrogen ions in the solution.

Step 2: Determine the Concentration of HCl

The solution given is \( N/10 \text{ HCl} \), which means the concentration is 0.1 N, i.e., \( [\text{H}^+] = 0.1 \, \text{molar} \) since HCl is a strong acid and dissociates completely in water, supplying \( [\text{H}^+] = 0.1 \, \text{mol/L} \).

Step 3: Calculate the pH Value

Substitute the hydrogen ion concentration into the pH formula: \( \text{pH} = -\log[0.1] = -(-1) = 1 \) because \( \log(0.1) = -1 \).

Step 4: Verify and Conclude the Answer

Double-check calculations to ensure accuracy. Since \( \text{pH} = 1 \) for \( N/10 \text{ HCl} \), the answer is 1.

Key Concepts

Hydrogen Ion Concentration

In chemistry, understanding hydrogen ion concentration is crucial to determining the pH of a solution. The concentration of hydrogen ions ( [H^+] ) indicates how acidic a solution is. High concentrations of hydrogen ions mean increased acidity and thus lower pH values. For any solution, especially strong acids like hydrochloric acid (HCl), knowing the concentration helps us predict its behavior in reactions and its corrosive properties.

Hydrogen ions are simply protons, and when in water, they bond readily with water molecules forming hydronium ions (H₃O⁺). In practice, however, we often just denote them as hydrogen ions for simplicity.
- Always expressed in terms of molarity (mol/L). - Determines the acidity; higher [H^+] = lower pH. - Critical component in calculating pH levels.

Strong Acids

Strong acids, such as hydrochloric acid (HCl), are a well-known category of acids characterized by their complete ionization in water. This means that in a solution, they dissociate fully into hydrogen ions ( H^+ ) and their accompanying anions.

Features of Strong Acids:

• Complete dissociation in water
• High conductance due to free-moving ions
• Predictable [H^+] concentration equivalent to the molarity of the acid

It’s this complete dissociation that makes calculating the [H^+] for strong acids straightforward. For example, in a solution of 0.1 mol/L HCl, the concentration of hydrogen ions ( [H^+] ) is also 0.1 mol/L. This consistent relationship simplifies our pH calculations and predictions about the acid’s behavior.

Logarithmic Calculations

When calculating pH, we employ logarithms to simplify the expression of hydrogen ion concentrations, which are often very small numbers. The term pH itself is defined as the negative logarithm of the hydrogen ion concentration: \[pH = -\log [H^+]\]

This logarithmic calculation is not only a compact way to represent a range of ion concentrations but also reflects the exponential nature of acid and base strengths.
- The pH scale is logarithmic. A change of one pH unit reflects a tenfold change in [H^+].- A lower pH means greater hydrogen ion concentration (more acidic).- For calculations: \[\log(0.1) = -1\, \text{so} \,-\log(0.1) = 1\]By understanding this relationship, students can manipulate the formula to find pH values in various scenarios quickly. The logarithmic nature of the pH scale accentuates the differences in acidity or basicity that might seem minimal on a linear scale.