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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 41
Chapter 5, Problem 41

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×\(\times\)10-7

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Identify the relationship between hydronium ion concentration \([H_3O^+]\) and pH using the formula \(pH = -\log_{10}([H_3O^+])\).
Calculate the pH by substituting the given hydronium ion concentration \(2.49 \times 10^{-7}\) into the formula: \(pH = -\log_{10}(2.49 \times 10^{-7})\).
Use logarithm properties to simplify the calculation: \(pH = - (\log_{10}(2.49) + \log_{10}(10^{-7}))\).
Evaluate the logarithms separately: \(\log_{10}(2.49)\) and \(\log_{10}(10^{-7}) = -7\), then combine to find the pH value.
Compare the calculated pH to the typical pH ranges for wetlands: rich fen (pH 6.5 to 8), poor fen (pH 5 to 6.5), and bog (pH less than 5) 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 the acidity or basicity of a solution, 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 slightly acidic, and bogs are strongly acidic. Knowing these pH ranges helps identify the wetland type from the pH value.

Logarithmic Calculations

Calculating pH from hydronium ion concentration requires understanding logarithms, specifically how to apply the negative base-10 logarithm to a given concentration. This skill is fundamental in chemistry and environmental science for interpreting ion concentrations.
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