For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). limes, 1.6*10^-2

Verified step by step guidance

1. Recall the formula to find pH from the hydronium ion concentration \([\mathrm{H_3O^+}]\): \(pH = -\log_{10}([\mathrm{H_3O^+}])\).
2. Identify the given hydronium ion concentration: \([\mathrm{H_3O^+}] = 1.6 \times 10^{-2}\).
3. Substitute the given concentration into the pH formula: \(pH = -\log_{10}(1.6 \times 10^{-2})\).
4. Use logarithm properties to simplify the expression: \(pH = - (\log_{10}(1.6) + \log_{10}(10^{-2}))\).
5. Calculate the logarithms separately (without final numeric evaluation here): \(pH = - (\log_{10}(1.6) - 2)\), then combine the terms to find the pH value.

Key Concepts

pH and Hydronium Ion Concentration

pH is a measure of the acidity of a solution and is calculated as the negative logarithm (base 10) of the hydronium ion concentration, [H3O+]. The formula is pH = -log[H3O+]. A higher hydronium ion concentration corresponds to a lower pH, indicating a more acidic solution.

Logarithms and Their Properties

Logarithms are the inverse operations of exponentiation. Understanding how to calculate and interpret logarithms, especially base 10 logs, is essential for converting hydronium ion concentrations into pH values. For example, log(1.6 × 10^-2) can be split into log(1.6) + log(10^-2).

Rounding and Significant Figures

When reporting pH values, it is important to round the result to the specified precision, here to the nearest tenth. This ensures clarity and consistency in communication. Proper rounding involves looking at the digit beyond the desired decimal place to decide whether to round up or down.