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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 33
Chapter 5, Problem 33

Find the [H3O+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. soda pop, 2.7

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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: \([H_3O^+] = 10^{-2.7}\).
Calculate the exponent part first, which means finding the value of \(10^{-2.7}\) (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 a × 10^b. 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 writing answers in scientific notation, rounding to the nearest tenth means adjusting the decimal part of the coefficient to one decimal place. For example, 2.68 × 10^-3 rounded to the nearest tenth is 2.7 × 10^-3, ensuring clarity and consistency in reporting results.
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