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 is 1, so the correct option is (d) 1.

Step 1: Understand the Problem

We are asked to find the pH of a solution labeled as \( \mathrm{N} / 10 \mathrm{HCl} \). This indicates a normality of \( \frac{1}{10} \) or \( 0.1 \) normal (N) hydrochloric acid (HCl) solution.

Step 2: Recall the Definition of pH

The pH of a solution is determined by the formula \( \mathrm{pH} = -\log_{10}[\mathrm{H}^+] \), where \([\mathrm{H}^+]\) is the concentration of hydrogen ions in moles per liter (Molarity). For strong acids like HCl, the normality and molarity are equivalent, so the concentration of \( [\mathrm{H}^+] \) is \( 0.1 \) M.

Step 3: Calculate the pH

Using the formula \( \mathrm{pH} = -\log_{10}[\mathrm{H}^+] \) with \( [\mathrm{H}^+] = 0.1 \), calculate the pH as follows: \[\mathrm{pH} = -\log_{10}(0.1) = 1.\]

Step 4: Consideration of Options

With a calculated pH of 1, compare it to the given options: (a) 3, (b) 4, (c) 2, (d) 1. The correct answer is option (d) 1, as this matches the calculated value.

Key Concepts

Normality and Molarity

Normality and molarity both measure the concentration of a solution, but they cater to slightly different scenarios. Normality (N) is a measure of concentration equivalent to molarity, but it accounts for the number of reactive units in a solution. Molarity (M), on the other hand, is the number of moles of solute per liter of solution. For acids like  **Normality (N)**: Normality accounts for the number of hydrogen ions a solution can provide. It is particularly useful in reactions like acid-base titrations where the reactive ions need to be explicitly considered.
 **Molarity (M)**: Simply focuses on the amount of solute per liter. In the case of strong acids like HCl, each molecule dissociates completely in water, making normality equal to molarity. For example, a 0.1 N HCl solution is also 0.1 M because one mole of HCl yields one mole of H⁺ ions.
Understanding both concepts helps in accurately describing the concentration in various chemical contexts.

Strong Acids

Strong acids have distinctive properties when they dissolve in water. They dissociate completely into their constituent ions. This means that in a solution of a strong acid like hydrochloric acid (HCl), essentially all acid molecules release hydrogen ions.  **Complete Dissociation**: For instance, HCl in water separates into H⁺ and Cl⁻ ions, maximizing the concentration of hydrogen ions.
 **Correlation with pH**: Because strong acids yield high hydrogen ion concentrations, they result in low pH values. For a 0.1 M solution of HCl, which is also its normality, the pH is calculated as \(\text{pH} = -\log_{10}(0.1) = 1\). By fully understanding these principles, we can accurately determine the acidic strength and pH of strong acids in solution.

Hydrogen Ion Concentration

Hydrogen ion concentration is fundamental to calculating the pH of any solution. It directly indicates the acidity or basicity of the solution, determining how molecules interact in solutions.  **Relation to pH**: The pH is a measure on a scale from 0 to 14, illustrating the concentration of H⁺ ions. Lower values indicate higher acidity, while higher numbers signify basicity.
 **Significance in Strong Acids**: With strong acids like HCl, the normality represents the concentration of H⁺ ions. A 0.1 M solution of HCl means the hydrogen ion concentration is 0.1 M because each HCl molecule donates a single hydrogen ion.
 **Calculating pH**: Using the relationship \(\text{pH} = -\log_{10}([ ext{H}^+])\), we find that a hydrogen ion concentration of 0.1 M corresponds to a pH of 1. Understanding and calculating hydrogen ion concentration is crucial for predicting the behavior of acidic solutions.