Question

Calculation of Hydrogen Ion Concentration from \(\mathrm{pH}\) What is the \(\mathrm{H}^{+}\)concentration of a solution with \(\mathrm{pH}\) of a. \(3.82\); b. \(6.52\); c. \(11.11\) ?

Short answer

a. \(1.51 \times 10^{-4}\, \text{mol/L}\); b. \(3.02 \times 10^{-7}\, \text{mol/L}\); c. \(7.76 \times 10^{-12}\, \text{mol/L}\).

Step-by-step solution

Understanding the Concept of pH

The pH of a solution is a measure of its acidity or alkalinity, which is defined as the negative logarithm of the hydrogen ion concentration. Mathematically, it is expressed as: \[pH = -\log[\text{H}^{+}] \]where \([\text{H}^{+}]\) represents the concentration of hydrogen ions in moles per liter (mol/L). This relationship will help us find the \([\text{H}^{+}]\) from a given pH.

Rearranging the pH Formula

Using the equation: \[pH = -\log[\text{H}^{+}] \]we need to solve for \([\text{H}^{+}]\). To do this, we rearrange the formula to isolate \([\text{H}^{+}]\). This involves taking the antilog (or inverse logarithm) of both sides of the equation:\[[\text{H}^{+}] = 10^{-\text{pH}}\]This equation allows us to calculate the hydrogen ion concentration from a given pH.

Calculating [H+] for pH = 3.82

Substitute \(\text{pH} = 3.82\) into the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-3.82}\]Using a calculator, we find:\[[\text{H}^{+}] \approx 1.51 \times 10^{-4} \text{ mol/L}\]This is the hydrogen ion concentration for a solution with a pH of 3.82.

Calculating [H+] for pH = 6.52

Substitute \(\text{pH} = 6.52\) into the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-6.52}\]Using a calculator, we find:\[[\text{H}^{+}] \approx 3.02 \times 10^{-7} \text{ mol/L}\]This is the hydrogen ion concentration for a solution with a pH of 6.52.

Calculating [H+] for pH = 11.11

Substitute \(\text{pH} = 11.11\) into the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-11.11}\]Using a calculator, we find:\[[\text{H}^{+}] \approx 7.76 \times 10^{-12} \text{ mol/L}\]This is the hydrogen ion concentration for a solution with a pH of 11.11.

Key concepts

Understanding Hydrogen Ion Concentration

The term "hydrogen ion concentration" refers to the amount of hydrogen ions (H⁺) present in a solution. These ions are a key player in determining the solution's acidity. The concentration of hydrogen ions is expressed in moles per liter (mol/L).
- A high concentration of hydrogen ions usually indicates an acidic solution, whereas a low concentration signifies a basic or alkaline solution.
To compute hydrogen ion concentration from pH, we rely on the formula:\[[H^{+}] = 10^{-pH}\]This formula allows us to take the negative exponent of the pH value to determine the exact concentration of hydrogen ions. This method is essential when assessing the nature of a substance, especially in chemical reactions and environmental science.

The Role of Inverse Logarithm in pH Calculation

Inverse logarithm might sound complicated, but it simply reverses the logarithmic function. In the context of pH calculation, pH is originally defined by the equation:\[pH = -\log{[H^{+}]}\]To find the hydrogen ion concentration from a given pH, we apply the inverse of this logarithm. This process involves rearranging the pH equation to solve for H⁺. Instead of thinking in terms of base-ten logarithms directly, we can consider the inversion as the reverse—the antilog. The equation is then transformed as:\[[H^{+}] = 10^{-pH}\]The inverse logarithm thus helps convert a pH value into a tangible measure of hydrogen concentration. Understanding this reversal is crucial for quick and accurate chemical analyses.

Balancing Acidity and Alkalinity

Acidity and alkalinity describe the overall character of a solution based on its hydrogen ion concentration. The pH scale—ranging from 0 to 14—is our best friend for determining this balance:
- A pH less than 7 signals an acidic solution. - A pH of 7 means the solution is neutral, like pure water. - A pH greater than 7 indicates an alkaline (basic) solution.
Each unit change in pH represents a tenfold change in hydrogen ion concentration. This factor highlights the logarithmic nature of the scale, where small numerical changes equate to significant shifts in acidity or alkalinity.
Understanding acidity and alkalinity is vital in diverse fields, from biology to industrial applications, as it dictates the behavior of substances and their interactions in various environments.