By what factor does [H⁺] change for a pH change of (a) 2.00 units? (b) 0.50 units?

Verified step by step guidance

1. pH is a measure of the hydrogen ion concentration in a solution, given by the formula: \( \text{pH} = -\log[\text{H}^+] \).
2. A change in pH of 2.00 units means the pH has either increased or decreased by 2.00.
3. If the pH decreases by 2.00 units, the concentration of \( \text{H}^+ \) ions increases. Conversely, if the pH increases by 2.00 units, the concentration of \( \text{H}^+ \) ions decreases.
4. The relationship between pH change and \( \text{H}^+ \) concentration change is logarithmic. A change of 1 pH unit corresponds to a tenfold change in \( \text{H}^+ \) concentration.
5. Therefore, a change of 2.00 pH units corresponds to a change in \( \text{H}^+ \) concentration by a factor of \( 10^2 \).

Key Concepts

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, below 7 is acidic, and above 7 is basic. Each unit change in pH represents a tenfold change in hydrogen ion concentration, meaning that a decrease in pH indicates an increase in acidity.

Hydrogen Ion Concentration

Hydrogen ion concentration, denoted as [H+], is a measure of the amount of hydrogen ions present in a solution. It is directly related to pH, where a lower pH corresponds to a higher concentration of H+. For example, a change of 2.00 units in pH results in a change in [H+] by a factor of 10^2, or 100 times.

Logarithmic Relationship

The relationship between pH and hydrogen ion concentration is logarithmic, meaning that pH is the negative logarithm of the hydrogen ion concentration: pH = -log[H+]. This implies that small changes in pH can lead to significant changes in [H+], which is crucial for understanding how acidity affects chemical reactions and biological processes.