Problem 59 - Chemistry: An Atoms-Focused Approach

Question

Acid Rain I \(A\) weather system moving through the American Midwest produced rain with an average pH of 5.02. By the time the system reached New England, the rain it produced had an average pH of 4.66. How much more acidic was the rain falling in New England?

Step-by-Step Solution

Answer

Answer: The rain in New England was approximately 1.3 times more acidic than the rain in the American Midwest.

Step 1: Convert pH values to hydrogen ion concentrations

Use the formula \([\text{H}^+] = 10^{-\text{pH}}\) to calculate the hydrogen ion concentration \([\text{H}^+]\) for each region: For the American Midwest (pH 5.02): \([\text{H}^+]_\text{Midwest} = 10^{-5.02}\) For New England (pH 4.66): \([\text{H}^+]_\text{NewEngland} = 10^{-4.66}\)

Step 2: Calculate the difference in hydrogen ion concentrations

Subtract the Midwest's hydrogen ion concentration from New England's concentration to find the difference: \([\text{H}^+]_\text{difference} = [\text{H}^+]_\text{NewEngland} - [\text{H}^+]_\text{Midwest}\)

Step 3: Determine how many times more acidic the rain was

Divide the difference in hydrogen ion concentrations by the Midwest's hydrogen ion concentration: \(\text{Acidity factor} = \frac{[\text{H}^+]_\text{difference}}{[\text{H}^+]_\text{Midwest}}\)

Step 4: Calculate the values and compare

Using the values we calculated, find the numerical values for the hydrogen ion concentrations and the acidity factor: \([\text{H}^+]_\text{Midwest} = 10^{-5.02} \approx 9.54 \times 10^{-6}\) \([\text{H}^+]_\text{NewEngland} = 10^{-4.66} \approx 2.19 \times 10^{-5}\) \([\text{H}^+]_\text{difference} = 2.19 \times 10^{-5} - 9.54 \times 10^{-6} \approx 1.24 \times 10^{-5}\) \(\text{Acidity factor} = \frac{1.24 \times 10^{-5}}{9.54 \times 10^{-6}} \approx 1.3\) The rain in New England was approximately 1.3 times more acidic than the rain in the American Midwest.

Key Concepts

pH scale

The pH scale is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with 7 considered neutral. Values below 7 indicate acidity while values above 7 indicate alkalinity. The scale is logarithmic, meaning each whole number decrease on the pH scale represents a tenfold increase in acidity. For example, a pH of 5 is ten times more acidic than a pH of 6.

In the case of rainwater, a lower pH signifies more acidic rain. When we consider acid rain, small changes in pH numbers can reflect significant changes in acidity. This is because of the logarithmic nature of the scale. Rain with a pH of 5.02, compared to a pH of 4.66, shows that the latter contains more hydrogen ions, making it more acidic.

Hydrogen Ion Concentration

Hydrogen ion concentration \(\left[ \text{H}^+ \right]\) is a crucial measure of acidity. The pH is directly related to hydrogen ion concentration with the formula \(\left[ \text{H}^+ \right] = 10^{-\text{pH}}\). The lower the pH, the higher the hydrogen ion concentration.

• For the Midwest with a pH of 5.02, the hydrogen ion concentration is \([\text{H}^+]_{\text{Midwest}} = 10^{-5.02}\).
• For New England's rain with a pH of 4.66, \(\left[ \text{H}^+ \right]_{\text{NewEngland}} = 10^{-4.66}\).

Calculating these concentrations shows us that New England's rain has a significantly higher hydrogen ion presence, explaining its lower pH value. Understanding hydrogen ion concentration helps in assessing the acidity and potential impacts of acid rain on the environment.

Acidity Factor

The acidity factor helps quantify how much more acidic one solution is compared to another. It is determined by comparing the hydrogen ion concentrations between two samples.

• Calculate the difference: Find \(\left[ \text{H}^+ \right]_{\text{difference}} = \left[ \text{H}^+ \right]_{\text{NewEngland}} - \left[ \text{H}^+ \right]_{\text{Midwest}}\).
• Divide by the original concentration to find how many times more acidic one sample is compared to the other: \left( \text{Acidity factor} = \frac{\left[ \text{H}^+ \right]_{\text{difference}}}{\left[ \text{H}^+ \right]_{\text{Midwest}}} \right)\.

In this specific scenario, the rain in New England has an acidity factor of approximately 1.3. This indicates New England's rain was 1.3 times more acidic than the rain in the Midwest. Understanding the acidity factor is essential in environmental chemistry for assessing the severity of acid rain events.