Calculate [H₃O⁺] and [OH^–] for each solution at 25 °C. b. pH = 11.23 c. pH = 2.87

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Start by recalling the relationship between pH and [H3O+]: \( \text{pH} = -\log[\text{H}_3\text{O}^+] \).

Rearrange the equation to solve for [H3O+]: \( [\text{H}_3\text{O}^+] = 10^{-\text{pH}} \).

Substitute the given pH value into the equation to find [H3O+].

Use the water dissociation constant at 25 °C, \( K_w = 1.0 \times 10^{-14} \), to find [OH-] using the relationship \( [\text{H}_3\text{O}^+] \times [\text{OH}^-] = K_w \).

Rearrange the equation to solve for [OH-]: \( [\text{OH}^-] = \frac{K_w}{[\text{H}_3\text{O}^+]} \) and substitute the value of [H3O+] to find [OH-].

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Key Concepts

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

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is considered neutral, while values below 7 indicate acidity and values above 7 indicate basicity. The pH is defined as the negative logarithm of the hydrogen ion concentration, [H+], in a solution, which is crucial for determining the concentration of hydronium ions, [H3O+].

Ion Product of Water (Kw)

The ion product of water, Kw, is the equilibrium constant for the self-ionization of water, defined as Kw = [H3O+][OH-] = 1.0 x 10^-14 at 25 °C. This relationship allows us to calculate the concentration of hydroxide ions, [OH-], when the concentration of hydronium ions, [H3O+], is known, and vice versa. Understanding Kw is essential for solving problems involving pH and pOH.

Hydronium and Hydroxide Ion Concentrations

In aqueous solutions, the concentrations of hydronium ions, [H3O+], and hydroxide ions, [OH-], are inversely related due to the ion product of water. For a basic solution, like one with a pH of 11.23, [H3O+] will be lower than 1.0 x 10^-7 M, while [OH-] will be higher than 1.0 x 10^-7 M. Calculating these concentrations is essential for understanding the solution's properties and behavior.

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Textbook Question

Like all equilibrium constants, the value of K_w depends on temperature. At body temperature (37 °C), K_w = 2.4×10^–14. What are the [H₃O⁺] and pH of pure water at body temperature?

Pick the stronger base from each pair. c. F^– or ClO^–

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Textbook Question

Calculate [H₃O⁺] and [OH^–] for each solution at 25 °C. a. pH = 8.55

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Textbook Question