One of the most acidic lakes in the United States is Little Echo Pond in the Adirondacks in New York. Recently, this lake had a pH of 4.2, well below the recommended pH of 6.5.
a. What are the [H₃O⁺] and [OH^-] of Little Echo Pond?

Verified step by step guidance

1. Step 1: Recall the relationship between pH and [H₃O⁺]. The formula to calculate [H₃O⁺] from pH is: \([H₃O^+] = 10^{-\text{pH}}\). Substitute the given pH value of 4.2 into this formula.
2. Step 2: Calculate \([H₃O^+]\) using the formula \([H₃O^+] = 10^{-4.2}\). This will give the concentration of hydronium ions in moles per liter (M).
3. Step 3: Use the relationship between \([H₃O^+]\) and \([OH^-]\) in water, which is governed by the ion product constant for water, \(K_w = [H₃O^+][OH^-] = 1.0 \times 10^{-14}\) at 25°C. Rearrange this equation to solve for \([OH^-]\): \([OH^-] = \frac{K_w}{[H₃O^+]}\).
4. Step 4: Substitute the value of \([H₃O^+]\) calculated in Step 2 and \(K_w = 1.0 \times 10^{-14}\) into the formula \([OH^-] = \frac{K_w}{[H₃O^+]}\) to find the concentration of hydroxide ions.
5. Step 5: Verify your results by checking that the product of \([H₃O^+]\) and \([OH^-]\) equals \(1.0 \times 10^{-14}\), ensuring consistency with the ion product constant for water.

Key Concepts

pH Scale

The pH scale measures the acidity or alkalinity of a solution, ranging from 0 to 14. A pH of 7 is neutral, while values below 7 indicate acidity and above 7 indicate alkalinity. Each unit change in pH represents a tenfold change in hydrogen ion concentration, making it crucial for understanding the chemical properties of water bodies like Little Echo Pond.

Hydronium and Hydroxide Ion Concentrations

In aqueous solutions, the concentration of hydronium ions [H₃O⁺] and hydroxide ions [OH⁻] are inversely related. The product of these concentrations is constant at 25°C, represented by the equation [H₃O⁺] × [OH⁻] = 1.0 × 10⁻¹⁴. This relationship is essential for calculating the concentrations of these ions in acidic or basic solutions.

Acid-Base Chemistry

Acid-base chemistry involves the study of substances that can donate protons (acids) or accept protons (bases). In the context of Little Echo Pond, the low pH indicates a high concentration of hydronium ions, suggesting that the lake is acidic. Understanding these concepts helps in analyzing the ecological impacts of such acidity on aquatic life.