Problem 20 - Algebra 2

Question

The acidity of water determines the toxic effects of runoff into streams from industrial or agricultural areas. A pH range of 6.0 to 9.0 appears to provide protection for freshwater fish. What is this range in terms of the water's hydrogen ion concentration?

Step-by-Step Solution

Answer

The hydrogen ion concentration range is from \(1.0 \times 10^{-9}\) to \(1.0 \times 10^{-6}\) moles per liter.

Step 1: Understanding pH

The pH of a solution is a measure of its acidity or alkalinity, defined as the negative logarithm (base 10) of the hydrogen ion concentration. The formula is \( pH = -\log[H^+] \), where \([H^+]\) represents the hydrogen ion concentration.

Step 2: Solving for Hydrogen Ion Concentration

To find the hydrogen ion concentration from a given pH, we use the formula \([H^+] = 10^{-pH}\). It's useful to calculate it for both ends of the pH range, i.e., 6.0 and 9.0.

Step 3: Calculating Lower Limit

For the lower limit of the pH range (6.0), the hydrogen ion concentration is \([H^+] = 10^{-6.0}\). Calculating gives \([H^+] = 1.0 \times 10^{-6}\) moles per liter.

Step 4: Calculating Upper Limit

For the upper limit of the pH range (9.0), the hydrogen ion concentration is \([H^+] = 10^{-9.0}\). Calculating gives \([H^+] = 1.0 \times 10^{-9}\) moles per liter.

Step 5: Range of Hydrogen Ion Concentration

Therefore, the hydrogen ion concentration range that provides protection for freshwater fish is from \(1.0 \times 10^{-9}\) to \(1.0 \times 10^{-6}\) moles per liter.

Key Concepts

Hydrogen Ion Concentration and pH

When we talk about the hydrogen ion concentration, we're referring to how many hydrogen ions are present in a solution. This is important because it's directly linked to pH, which determines how acidic or alkaline a solution is. The pH scale is a handy tool for measuring this. It ranges from 0 to 14, where a low pH signifies high acidity (more hydrogen ions), and a higher pH represents low acidity or higher alkalinity (fewer hydrogen ions).

There's a specific formula we use to convert pH into hydrogen ion concentration: \[ [H^+] = 10^{-pH} \]. This tells us that the concentration decreases as the pH increases. For instance, water with a pH of 6 has a hydrogen ion concentration of \(1.0 \times 10^{-6}\) moles per liter, while water with a pH of 9 has a concentration of \(1.0 \times 10^{-9}\) moles per liter. Understanding this relationship is crucial, especially when evaluating environmental conditions like water quality.

Understanding Acidity and Alkalinity

Acidity and alkalinity are like two sides of a coin that define the chemical nature of a solution. Acidity is connected with the presence of hydrogen ions \(H^+\), while alkalinity relates to hydroxide ions \(OH^-\). Limits like a pH of 7 are neutral, meaning the amount of \(H^+\) and \(OH^-\) ions are balanced. When the pH drops below 7, solutions become more acidic, and above 7, they become more alkaline.

Acidic solutions (e.g., lemon juice with a pH around 2) have higher hydrogen ion concentrations. Meanwhile, alkaline solutions (e.g., baking soda with a pH around 9) have more hydroxide ions and fewer hydrogen ions. This balance is essential for many biological and chemical processes. Whether you're ensuring plants grow or fish thrive, maintaining an appropriate pH is key.

Environmental Impact on Aquatic Life

The pH level of natural water bodies has significant effects on aquatic organisms. Freshwater fish and other aquatic life are sensitive to changes in acidity and alkalinity. A pH range of 6.0 to 9.0 is generally safe for them. When the pH of water falls outside this range, it can lead to harmful conditions.

• Too acidic: Increased acidity (pH < 6.0) can damage fish gills and disrupt respiratory functions. It may also affect egg hatching rates.
• Too alkaline: On the other hand, excessively alkaline water (pH > 9.0) can lead to similar issues, suppressing fish's immune responses and causing stress.

Human activities such as industrial discharge and agricultural runoff can alter these pH levels. It's crucial to monitor and manage these impacts to preserve aquatic ecosystems. Proper understanding and interventions can protect the delicate balance necessary for aquatic life's survival.