Calculate [H 3 O + ] and [OH – ] for each solution at 25 °C. b. pH = 11.23 c. pH = 2.87

Hello. In this problem, we are asked to determine the values of the hydro nea mine and hydroxide ion concentrations for a solution with a ph of 8.92 at 25 degrees Celsius, we call at 25 degrees Celsius. The Ph plus the P O H is equal to 14. So our P O H then is equal to 14 minus the PH Which is equal to 8.92. So our POH is 5.08. We can find the hydrogen ion concentration By taking 10 to the -4. So this is then 10 to the negative 8.92 Which works out to 1.2 times 10 to the -9 moller. And then our hydroxide ion concentration is equal to 10 to the negative P O H. So this is equal to 10 to the negative 5.08, Which is equal to 8.3 times 10 to the -6 smaller. So we could also do a check on our work 25°C. Then iron product constant of water should be equal to one times 10 to the minus 14. So we can plug in what we found and verify then that the hydro mine and hydroxide ion concentration are 1.2 times 10 minus nine moller and 8. times 10 to minus six Mohler. Respectfully. Thanks for watching. Hope this helps.

Ch.17 - Acids and Bases

Tro - Chemistry: A Molecular Approach 6th Edition

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Ch.17 - Acids and Bases

Problem 53b,c

Chapter 17, Problem 53b,c

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

Verified step by step guidance

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.