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The pH scale: Acidity of a solution is determined by the concentration \(H\) of hydrogen ions in the solution (measured in moles per liter of solution). Chemists use the negative of the logarithm of the concentration of hydrogen ions to define the \(\mathrm{pH}\) scale: $$ \mathrm{pH}=-\log H . $$ Lower pH values indicate a more acidic solution. a. Normal rain has a pH value of 5.6. Rain in the eastern United States often has a pH level of \(3.8\). How much more acidic is this than normal rain? b. If the \(\mathrm{pH}\) of water in a lake falls below a value of 5 , fish often fail to reproduce. How much more acidic is this than normal water with a \(\mathrm{pH}\) of \(5.6 ?\)

Step by step solution

01

Understanding the pH Scale Formula

The pH scale is defined by the formula \( \text{pH} = -\log H \), where \( H \) is the concentration of hydrogen ions. A lower pH means a higher concentration of hydrogen ions, which indicates higher acidity.

02

Calculating Hydrogen Ion Concentration for Normal Rain

Normal rain has a pH of 5.6. Using the pH formula, the hydrogen ion concentration \( H \) can be calculated as follows: \[ H = 10^{-\text{pH}} = 10^{-5.6} \].

03

Calculating Hydrogen Ion Concentration for Eastern U.S. Rain

Rain in the eastern U.S. has a pH of 3.8. The hydrogen ion concentration for this rain is calculated as: \[ H = 10^{-3.8} \].

04

Comparing Acidity Between Normal and Eastern U.S. Rain

The acidity difference is determined by comparing the hydrogen ion concentrations: \[ \text{Difference in acidity} = \frac{10^{-3.8}}{10^{-5.6}} \]. Calculate this to determine how many times more acidic the eastern U.S. rain is compared to normal rain.

05

Calculating Hydrogen Ion Concentration for Normal Lake Water

Normal lake water has a pH of 5.6. The hydrogen ion concentration \( H \) is: \[ H = 10^{-5.6} \].

06

Calculating Hydrogen Ion Concentration for Lake Water Below pH 5

If lake water has a pH of 5, its hydrogen ion concentration is: \[ H = 10^{-5} \].

07

Comparing Acidity Between Normal Lake Water and Acidic Lake Water

The difference in acidity is: \[ \text{Difference in acidity} = \frac{10^{-5}}{10^{-5.6}} \]. This calculates how many times more acidic the lake water is when its pH falls below 5 compared to normal lake water.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Acidity

Acidity is a fundamental concept in chemistry, essentially indicating how acidic or basic a substance is. A solution's acidity is commonly measured using the pH scale, where each pH value represents how concentrated the hydrogen ions (\(H^+\)) are in the solution. Here are some key ideas to remember about acidity and the pH scale:

• A low pH indicates high acidity.
• High concentrations of hydrogen ions correspond to a low pH value.
• Neutral pH is 7, values below 7 are acidic, and values above 7 are basic.

When a solution has a pH of 5.6, it is less acidic than a solution with a pH of 3.8. This is because a lower pH value like 3.8 signals a greater presence of hydrogen ions compared to a pH of 5.6.
Understanding these differences is crucial for comparing acidity in different environments, such as between normal rain and acidic rain.

The Logarithmic Scale and Its Role

The pH scale is based on a logarithmic scale, which means that each integer change on the scale represents a tenfold change in acidity.
Why do chemists use this scale? The main reason is because hydrogen ion concentrations can vary over a huge range, and a logarithmic scale helps simplify those numbers.

• The formula for pH is \(\text{pH} = -\log H\), where \(H\) represents the hydrogen ion concentration.
• For example, having a pH of 3.8 suggests a concentration of\(10^{-3.8}\)
• A pH of 5.6 means a concentration of\(10^{-5.6}\)

This difference shows how much more acidic one solution is compared to another. In our example, when comparing rain in the eastern United States with normal rain, you notice a tenfold increase in concentrations for each step down the pH scale.

Hydrogen Ion Concentration's Role

Hydrogen ion concentration is at the heart of the pH scale. The concentration of these ions determines how acidic a solution is. Chemists use it to quantify the acid in various solutions, much like different ecosystems affected by varying acidity levels.

• Higher hydrogen ion concentration equals a lower pH and more acidic solution.
• To find these concentrations, you use the formula \(H = 10^{-\text{pH}}\).
• For example, at pH 5.6, \(H = 10^{-5.6}\)
• At pH 3.8, \(H = 10^{-3.8}\)

By knowing these concentrations, you can determine how conditions like acidic waters can impact environments and organisms. Understanding these concepts is particularly important for monitoring pollution and its effects on habitats such as lakes and rivers.