Problem 10 - Chemistry in 30 days

Question

An acid solution of \(\mathrm{pH} 6\) is diluted hundred times. The \(\mathrm{pH}\) of the solution becomes (a) 6 (b) \(6.95\) (c) 4 (d) 8

Step-by-Step Solution

Answer

The pH becomes 8 (option d).

Step 1: Understand the pH Definition

The pH of a solution is determined by the concentration of hydrogen ions ({H^+}) in the solution. The formula is given by:\[\mathrm{pH} = -\log_{10}[H^+]\]This means that for each unit change in pH, the concentration of hydrogen ions changes by a factor of 10.

Step 2: Calculate Initial Hydrogen Ion Concentration

For an acid solution with a \(\mathrm{pH} = 6\), the concentration of hydrogen ions is calculated as:\[[H^+] = 10^{-6} \text{ M}\]

Step 3: Consider the Effect of Dilution on \([H^+]\)

Diluting the solution by a factor of 100 means the concentration of hydrogen ions is reduced to one hundredth of its initial concentration. Therefore:\[[H^+]_{\text{new}} = \frac{10^{-6}}{100} = 10^{-8} \text{ M}\]

Step 4: Calculate New pH After Dilution

Calculate the new pH using the new hydrogen ion concentration:\[\mathrm{pH_{new}} = -\log_{10}(10^{-8}) = 8\]

Step 5: Evaluate the Answer

Since the calculation yields \(\mathrm{pH} = 8\), option (d) is the correct answer.

Key Concepts

Hydrogen Ion Concentration

Understanding hydrogen ion concentration is fundamental in grasping how acidity works in a solution. The concentration of hydrogen ions, denoted as \[H^+\], indicates how acidic or basic a solution is. The formula that connects hydrogen ion concentration to the pH value is \[-\log_{10}[H^+]\].
In simple terms, pH measures how many hydrogen ions are present. A low \[H^+\] concentration means the solution is less acidic, while a high concentration signifies more acidity.
Here's a helpful tip:

• Each whole pH unit represents a tenfold difference in \[H^+\] concentration. For instance, a change from pH 5 to pH 6 means the hydrogen ion concentration has decreased tenfold.

This logarithmic scale is important because it simplifies expressing concentrations over several orders of magnitude in a readable way. Remember, smaller pH means more acid, thereby a higher \[H^+\] concentration.

Effect of Dilution on pH

Dilution is a common laboratory process where the concentration of a substance is reduced by adding more solvent, usually water.
The effect of dilution on the pH of a solution hinges on how much the hydrogen ion concentration decreases with dilution.
In our exercise example, diluting an acid solution (pH 6) by a factor of 100 affects the hydrogen ion concentration significantly. Calculations show that such dilution decreases \[H^+]\] concentration from \([H^+] = 10^{-6}\) to \([H^+] = 10^{-8}\).
This process of dilution makes the acidic solution less acidic, consequently increasing the pH value. Generally, dilution of an acid reduces its \[H^+]\] concentration, leading to a rise in the pH number. This behavior is crucial to understand in applications where precise control of acidity or alkalinity is required.

pH Scale

The pH scale is an essential tool in chemistry, ranging from 0 to 14. It's used to indicate how acidic or basic a solution is, based on the concentration of hydrogen ions present.
A pH value can be interpreted as follows:

• pH less than 7: Solutions are acidic, with more hydrogen ions.
• pH equal to 7: Solutions are neutral, typical of pure water.
• pH greater than 7: Solutions are basic or alkaline, having fewer hydrogen ions.

Each unit change in pH reflects a tenfold change in hydrogen ion concentration, due to the logarithmic nature of the scale. Understanding the pH scale helps in determining the nature and intensity of a solution's acidity or basicity.
In our exercise, the initial pH of 6 indicates a weak acidic solution. After dilution, resulting in a pH of 8, the solution becomes weakly basic. This shift shows the effectiveness of the pH scale in illustrating the dramatic change in acidity levels due to dilution.