Question

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

Short answer

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

Step-by-step solution

Understanding the Problem

To find the pH of the given solution, we need to understand that the pH is calculated by taking the negative logarithm (base 10) of the hydrogen ion concentration. Specifically, \(\mathrm{pH} = -\log[H^+]\), where \([H^+]\) represents the concentration of hydrogen ions in the solution.

Determine Hydrogen Ion Concentration

A \(\mathrm{N} / 10\) solution refers to a normal solution that is a tenth of the normality. Since hydrochloric acid (HCl) is a strong acid and dissociates completely in water, the hydrogen ion concentration in an \(\mathrm{N} / 10\) HCl solution is equivalent to its normality, or \(\frac{1}{10} \, ext{N} = 0.1\, \mathrm{mol/L}.\)

Calculate the pH

Using the formula \(\mathrm{pH} = -\log[H^+]\), substitute the hydrogen ion concentration \(0.1\). The pH is calculated as follows:\(\mathrm{pH} = -\log(0.1) = 1\).

Key concepts

Understanding Hydrogen Ion Concentration

In chemistry, hydrogen ion concentration refers to the number of hydrogen ions ([H⁺]) in a solution. This is crucial in determining the pH, which is a measure of the acidity or basicity of a solution.
- A lower pH indicates a higher concentration of hydrogen ions, meaning the solution is more acidic.
- Conversely, a higher pH means lower hydrogen ion concentration, indicating a more basic solution.
In a strong acid like hydrochloric acid (HCl), the acid dissociates completely in water, releasing hydrogen ions. Therefore, the concentration of these ions in the solution is direct and straightforward to calculate. For example, in a 0.1 mol/L (N/10) HCl solution, the hydrogen ion concentration is exactly 0.1 mol/L.

Defining Normality in Solutions

Normality is a measure of concentration equivalent to the gram equivalent weight of a solute per liter of solution. It is particularly useful for reactions involving the transfer of electrons or protons.
- Normality takes into account not just the concentration of a substance, but its reactivity, making it a useful measure for acid-base reactions where hydrogen ions are involved.
- In the case of acids and bases, normality can be related directly to hydrogen or hydroxide ion concentration.
For instance, a normal solution would have a normality of 1N, meaning one mole of reactive hydrogen ions per liter. A 0.1N (N/10) solution of HCl refers to one-tenth the normal strength, indicating a lesser, but still complete, dissociation of hydrogen ions.

Strong Acid Dissociation Explained

Strong acids like hydrochloric acid (HCl) dissociate fully in an aqueous solution, meaning they entirely separate into their constituent ions.
- This complete dissociation means every molecule of HCl splits into hydrogen ions (H⁺) and chloride ions (Cl^-) when dissolved in water.
- Because of this, the concentration of HCl is directly equal to the concentration of hydrogen ions in the solution.
This property is critical for calculating pH. Knowing that a 0.1N HCl solution will fully dissociate allows us to assume the hydrogen ion concentration is also 0.1 mol/L, and thereby, directly compute the pH.

Utilizing the Logarithmic Function for pH Calculation

The pH scale is logarithmic, which means it represents hydrogen ion concentration using powers of ten. This scale ranges from 0 to 14, where each unit change represents a tenfold change in hydrogen ion concentration.
- To calculate pH, we use the formula: \[\mathrm{pH} = -\log[H^+]\]
- The negative symbol is used because pH decreases as hydrogen ion concentration increases.
In our specific example, for a hydrogen ion concentration of 0.1 mol/L, the calculation goes as follows:
- Substitute the value into the pH formula: \[\mathrm{pH} = -\log(0.1)\]
- The result of this logarithmic calculation is a pH of 1, confirming the solution’s highly acidic nature since it's a strong acid.