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Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 4 - Inverse, Exponential, and Logarithmic FunctionsProblem 37
Chapter 5, Problem 37

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. 2.49×\(\times\)10-5

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1
Recall that the pH of a solution is calculated using the formula \(\mathrm{pH} = -\log_{10} [\mathrm{H_3O^+}]\), where \([\mathrm{H_3O^+}]\) is the hydronium ion concentration.
Substitute the given hydronium ion concentration \(2.49 \times 10^{-5}\) into the pH formula: \(\mathrm{pH} = -\log_{10} (2.49 \times 10^{-5})\).
Use logarithm properties to simplify the expression: \(\mathrm{pH} = - (\log_{10} 2.49 + \log_{10} 10^{-5})\).
Calculate the logarithms separately (without final numeric evaluation here): \(\log_{10} 2.49\) and \(\log_{10} 10^{-5} = -5\).
Determine the pH value from the above steps and then compare it to the typical pH ranges for rich fen, poor fen, and bog to classify the wetland type.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH and Hydronium Ion Concentration

pH is a measure of acidity calculated as the negative logarithm of the hydronium ion concentration (pH = -log[H3O+]). Understanding how to convert hydronium ion concentration to pH is essential for classifying water types based on acidity.

Classification of Wetlands by pH

Wetlands such as rich fens, poor fens, and bogs are classified based on their pH levels. Rich fens are typically neutral to slightly alkaline, poor fens are mildly acidic, and bogs are strongly acidic. Knowing these pH ranges helps identify the wetland type.

Logarithmic Calculations

Calculating pH from hydronium ion concentration requires understanding logarithms, specifically how to apply the negative base-10 logarithm to very small numbers. This skill is crucial for accurately determining the acidity of the sample.
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