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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 35
Chapter 5, Problem 35

Find the [H3O+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. beer, 4.8

Verified step by step guidance
1
Recall the relationship between pH and hydronium ion concentration \([H_3O^+]\) is given by the formula: \([H_3O^+] = 10^{-\text{pH}}\).
Substitute the given pH value into the formula: \([H_3O^+] = 10^{-4.8}\).
Calculate the exponent part first, which means finding the value of \(10^{-4.8}\) (you can use a calculator for this step).
Express the result in scientific notation, which means writing it in the form \(a \times 10^{b}\) where \(1 \leq a < 10\) and \(b\) is an integer.
Round the coefficient \(a\) to the nearest tenth as requested to complete the answer.

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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 Relationship

pH is a measure of the acidity of a solution and is defined as the negative logarithm (base 10) of the hydronium ion concentration, [H₃O⁺]. The formula is pH = -log[H₃O⁺]. To find [H₃O⁺] from pH, use the inverse relationship: [H₃O⁺] = 10^(-pH).
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Scientific Notation

Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of ten, such as 3.2 × 10⁻⁵. It is useful for representing very large or very small numbers clearly and concisely, which is common in chemistry for concentrations like [H₃O⁺].
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Rounding to the Nearest Tenth in Scientific Notation

When rounding numbers in scientific notation, focus on the first decimal place of the coefficient (the number between 1 and 10). For example, 1.234 × 10⁻⁵ rounded to the nearest tenth is 1.2 × 10⁻⁵. This ensures answers are precise yet simple.
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