/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 Calculate the concentration of a... [FREE SOLUTION] | 91影视

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Calculate the concentration of an aqueous solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) that has a \(\mathrm{pH}\) of \(10.05 .\)

Short Answer

Expert verified
The concentration of the aqueous solution of Ca(OH)鈧 with a pH of 10.05 is approximately \( 5.6 \times 10^{-5} \) M.

Step by step solution

01

Determine pOH from pH

To find the concentration of OH鈦 ions in the solution, it is necessary to convert the given pH value into the pOH value. This can be done using the following relationship: pH + pOH = 14 Substitute the given pH value: 10.05 + pOH = 14 Now, solve for pOH: pOH = 14 - 10.05 pOH = 3.95
02

Calculate the concentration of OH鈦 ions

The pOH value represents the negative base-10 logarithm of the concentration of OH鈦 ions. To find the concentration of OH鈦 ions, use the following equation: pOH = -log鈧揫OH鈦籡 We can convert the pOH value to the concentration of OH鈦 ions using the following formula: [OH鈦籡 = 10^{-pOH} Now, substitute the pOH value: [OH鈦籡 = 10^{-3.95} [OH鈦籡 鈮 1.12 脳 10^-4 M
03

Calculate the concentration of Ca(OH)鈧

Since each calcium hydroxide (Ca(OH)鈧) dissociates into two hydroxide ions (OH鈦), the stoichiometry of the reaction is as follows: Ca(OH)鈧 鈫 Ca虏鈦 + 2OH鈦 So, for every one Ca(OH)鈧 dissolved, two OH鈦 ions are produced. To find the concentration of Ca(OH)鈧, divide the concentration of OH鈦 by the stoichiometric coefficient (2): [Ca(OH)鈧俔 = [OH鈦籡/2 Now, substitute the concentration of OH鈦 ions: [Ca(OH)鈧俔 = (1.12 脳 10^-4 M)/2 [Ca(OH)鈧俔 鈮 5.6 脳 10^-5 M The concentration of the aqueous solution of Ca(OH)鈧 with a pH of 10.05 is approximately 5.6 脳 10鈦烩伒 M.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

pH Calculation
Understanding how to determine the pH of a solution is crucial in many areas of chemistry and biology. In this exercise, the focus is on understanding the relation between pH and pOH. - **pH** is a measure of how acidic or basic a solution is. It is based on the concentration of hydrogen ions (\(\text{H}^+\)). A lower pH means more acidic, and a higher pH means more basic.- The formula, \(\text{pH} + \text{pOH} = 14\), relates pH and pOH, which helps us find the concentration of hydroxide ions (\(\text{OH}^-\).Given a pH value, as in this problem, we can find the pOH by re-arranging this formula:1. **Substitute the pH into the formula**: For a solution with a pH of 10.05, we have: - 10.05 + pOH = 14 2. **Solve for pOH**: Subtract the pH from 14 to find the pOH: - pOH = 14 - 10.05 = 3.95 This calculation is the first step in determining the concentration of hydroxide ions in the solution.
OH鈦 Ion Concentration
Calculating the concentration of hydroxide ions (\([\text{OH}^-]\)) is essential for understanding the basicity of a solution. Once you have the pOH from the previous step:- The pOH is related to the concentration of OH鈦 ions through a logarithmic relation: - \(\text{pOH} = -\log_{10}{[\text{OH}^-]}\)To find the concentration, you need to reverse this relationship by using antilogarithms:1. **Use the antilog equation**: Rearrange to solve for \([\text{OH}^-]\): - \([\text{OH}^-] = 10^{-\text{pOH}}\)2. **Substitute the pOH value**: For pOH of 3.95: - \([\text{OH}^-] = 10^{-3.95} \approx 1.12 \times 10^{-4} \text{ M}\)This represents the molarity of hydroxide ions in your solution, a crucial step in determining how basic the solution is.
Stoichiometry
Stoichiometry helps you understand the relationships between reactants and products in a chemical reaction. For the case of calcium hydroxide, \(\text{Ca(OH)}_2\), each unit dissociates into one calcium ion (\(\text{Ca}^{2+}\)) and two hydroxide ions (\(\text{2OH}^-\)).- **Dissociation reaction**: - \(\text{Ca(OH)}_2 \rightarrow \text{Ca}^{2+} + 2\text{OH}^-\)Given the concentration of \([\text{OH}^-] = 1.12 \times 10^{-4} \text{ M}\), you can find the concentration of \(\text{Ca(OH)}_2\):1. **Use stoichiometry**: For each molecule of \(\text{Ca(OH)}_2\), two hydroxide ions are produced. - Therefore, the concentration of \(\text{Ca(OH)}_2\) is half the concentration of \([\text{OH}^-]\).2. **Calculate concentration**: - \([\text{Ca(OH)}_2] = \frac{1.12 \times 10^{-4} \text{ M}}{2} \approx 5.6 \times 10^{-5} \text{ M}\)Knowing the concentration of \(\text{Ca(OH)}_2\) allows you to further explore the properties of the solution, such as assessing its capacity to neutralize acids.

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Most popular questions from this chapter

Write the chemical equation and the \(K_{a}\) expression for the acid dissociation of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\), (b) \(\mathrm{HCO}_{3}^{-}\).

Predict the products of the following acid-base reactions, and predict whether the equilibrium lies to the left or to the right of the equation: (a) \(\mathrm{NH}_{4}{ }^{+}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons\) (b) \(\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons\) (c) \(\mathrm{HCO}_{3}^{-}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons\)

The active ingredient in aspirin is acetylsalicylic acid \(\left(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\right),\) a monoprotic acid with \(K_{a}=3.3 \times 10^{-4}\) at \(25^{\circ} \mathrm{C}\). What is the \(\mathrm{pH}\) of a solution obtained by dissolving two extra-strength aspirin tablets, containing \(500 \mathrm{mg}\) of acetylsalicylic acid each, in \(250 \mathrm{~mL}\) of water?

Calculate the \(\mathrm{pH}\) of each of the following strong acid solutions: (a) \(0.0167 \mathrm{M} \mathrm{HNO}_{3},\) (b) \(0.225 \mathrm{~g}\) of \(\mathrm{HClO}_{3}\) in \(2.00 \mathrm{~L}\) of solution, (c) \(15.00 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\) diluted to \(0.500 \mathrm{~L}, (\mathrm{~d})\) a mixture formed by adding \(50.0 \mathrm{~mL}\) of \(0.020 \mathrm{M} \mathrm{HCl}\) to \(125 \mathrm{~mL}\) of \(0.010 \mathrm{M} \mathrm{HI}\)

Predict whether aqueous solutions of the following compounds are acidic, basic, or neutral: (a) \(\mathrm{NH}_{4} \mathrm{Br}\), (b) \(\mathrm{FeCl}_{3},(\mathrm{c})\) \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) (d) \(\mathrm{KClO}_{4},\) (e) \(\mathrm{NaHC}_{2} \mathrm{O}_{4}\)

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