Question

Acid rain over the Great Lakes has a \(\mathrm{pH}\) of about \(4.5 .\) Calculate the \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) of this rain and compare that value to the \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) of rain over the West Coast that has a pH of 5.4. How many times more concentrated is the acid in rain over the Great Lakes?

Short answer

The hydronium ion concentration in the Great Lakes rain is \(10^{-4.5} \) M and \(10^{-5.4} \) M in the West Coast rain. Therefore, the acid in rain over the Great Lakes is approximately 8 times more concentrated than that of the West Coast.

Step-by-step solution

Understand pH and Concentration Relation

The pH of a solution is the negative logarithm (base 10) of the hydrogen ion concentration. Mathematically, we write this as \(\mathrm{pH} = -\log[\mathrm{H}_3\mathrm{O}^+]\). To find the concentration of hydrogen ions \(\left[\mathrm{H}_3\mathrm{O}^+\right]\), we need to take the antilog (inverse logarithm) of the negative pH value.

Calculate Concentration for Great Lakes Rain

For the rain over the Great Lakes with a pH of 4.5, use the pH equation to find \(\left[\mathrm{H}_3\mathrm{O}^+\right]\): \(\left[\mathrm{H}_3\mathrm{O}^+\right] = 10^{-\mathrm{pH}} = 10^{-4.5}\). This gives us the concentration of hydronium ions in moles per liter.

Calculate Concentration for West Coast Rain

For the rain over the West Coast with a pH of 5.4, repeat the process: \(\left[\mathrm{H}_3\mathrm{O}^+\right] = 10^{-\mathrm{pH}} = 10^{-5.4}\). Calculate the concentration of hydronium ions for this pH value.

Compare the Concentrations

Divide the concentration of hydronium ions of Great Lakes rain by that of West Coast rain to find how many times more concentrated the acid is: \(\frac{\mathrm{Concentration}_{\mathrm{Great Lakes}}}{\mathrm{Concentration}_{\mathrm{West Coast}}} = \frac{10^{-4.5}}{10^{-5.4}}\).

Key concepts

pH Scale

The pH scale is an index measuring the acidity or alkalinity of a solution. It ranges from 0 to 14, with 7 being neutral, values below 7 indicating acidity, and values above 7 indicating alkalinity. Solutions with a lower pH have a higher concentration of hydronium ions \(\left[\mathrm{H}_3\mathrm{O}^+\right]\), making them more acidic. As an example, lemon juice has a pH around 2, highly acidic, while household ammonia has a pH around 11, making it basic.

The importance of the pH scale extends to various fields, from chemistry to environmental science, as seen in the analysis of acid rain. Acid rain with a pH of 4.5 is significantly more acidic than one with a pH of 5.4, because the pH scale is logarithmic - each whole pH value below 7 is ten times more acidic than the next higher value.

Hydronium Ion Concentration

Hydronium ion concentration \(\left[\mathrm{H}_3\mathrm{O}^+\right]\) represents the amount of hydronium ions in a liter of solution. It is the key determinant of a solution's acidity. As the concentration of these ions increases, the acidity of the solution increases as well.

For instance, in the comparison of rainwater from two regions, the hydronium ion concentration directly influences the degree of harm the acid rain can inflict on ecosystems. High concentrations of \(\left[\mathrm{H}_3\mathrm{O}^+\right]\) can lead to detrimental effects on marine and plant life, highlighting the relevance of accurately determining this parameter in environmental chemistry.

[H3O+] Calculation

To calculate the concentration of hydronium ions \(\left[\mathrm{H}_3\mathrm{O}^+\right]\) from pH, one must apply the inverse logarithmic relationship. This calculation involves finding the antilog, or the inverse log, of the negative pH value. A pH of 4.5, as in the Great Lakes rain, is converted using the equation: \[\left[\mathrm{H}_3\mathrm{O}^+\right] = 10^{-\mathrm{pH}} = 10^{-4.5}\].

Performing this calculation yields the exact concentration in moles per liter, which is essential for quantifying the severity of acid rain or the strength of any acidic solution, providing critical data for various practical applications, including water treatment and environmental conservation efforts.

Logarithm and pH Relationship

The relationship between logarithms and pH is foundational to understanding the chemistry of solutions. pH is the negative logarithm (base 10) of the hydronium ion concentration, mathematically expressed as \(\mathrm{pH} = -\log[\mathrm{H}_3\mathrm{O}^+]\). This logarithmic relationship means that a one-unit change in pH corresponds to a ten-fold change in hydronium ion concentration.

As a consequence, even a slight variation in pH can result in a significant change in acidity, which is paramount when considering the impact on living organisms and the environment, such as assessing the effects of acid rain on ecosystems. Understanding this relationship helps in making sense of the acidity levels inferred by pH values and is crucial in fields like environmental science, agriculture, and medicine.