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Calculate the percent dissociation of the acid in each of the following solutions. a. 0.50\(M\) acetic acid b. 0.050\(M\) acetic acid c. 0.0050\(M\) acetic acid d. Use Le Ch芒telier's principle to explain why percent dissociation increases as the concentration of a weak acid decreases. e. Even though the percent dissociation increases from solutions a to \(c,\) the \(\left[\mathrm{H}^{+}\right]\) decreases. Explain.

Short Answer

Expert verified
The percent dissociation of acetic acid increases as its concentration decreases: a. 0.50 M: 1.08%, b. 0.050 M: 3.82%, and c. 0.0050 M: 12.03%. This is because, according to Le Ch芒telier's principle, the system shifts to increase dissociation as the concentration of the weak acid decreases. However, the concentration of H鈦 decreases from solutions a to c because there is less acetic acid available to dissociate into H鈦 ions, even though the percent dissociation increases.

Step by step solution

01

Write the chemical equation for acetic acid's dissociation in water

The chemical equation for acetic acid (CH鈧僀OOH) dissociation in water can be represented as: CH鈧僀OOH (aq) + H鈧侽 (l) 鈬 CH鈧僀OO鈦 (aq) + H鈧僌鈦 (aq) Since the autoionization of water is not significant in this case, we can rewrite the equation as: CH鈧僀OOH (aq) 鈬 CH鈧僀OO鈦 (aq) + H鈦 (aq)
02

Write the equilibrium expression and the given acidity constant value

Write the equilibrium expression for the reaction: \[ K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]} \] The acidity constant value for acetic acid is \(K_a = 1.8 \times 10^{-5}\).
03

Calculate the concentration of the dissociated species

Let x be the concentration of H鈦 (and also CH鈧僀OO鈦) at equilibrium. Then, the equilibrium concentrations will be: [CH鈧僀OOH] = initial concentration - x [CH鈧僀OO鈦籡 = x [H鈦篯 = x The equilibrium expression will become: \[ K_a = \frac{x^2}{[CH_3COOH]_0 - x} \] We'll use this equation to calculate the equilibrium concentration, x, of H鈦 for each given acetic acid concentration. #a. 0.50 M acetic acid: \[ 1.8 \times 10^{-5} = \frac{x^2}{0.50 - x} \] #b. 0.050 M acetic acid: \[1.8 \times 10^{-5} = \frac{x^2}{0.050 - x} \] #c. 0.0050 M acetic acid: \[ 1.8 \times 10^{-5} = \frac{x^2}{0.0050 - x} \] By solving these equations for x, we can find the equilibrium concentration of H鈦 for each solution.
04

Calculate the percent dissociation

Using the calculated equilibrium concentrations, we can find the percent dissociation for each solution: Percent dissociation = \(\frac{[H^+]}{[CH_3COOH]_0}\) 脳 100% Calculate the percent dissociation for each initial concentration of acetic acid.
05

Explain the relationship between the percent dissociation and acid concentration using Le Ch芒telier's principle

Le Ch芒telier's principle states that when a system at equilibrium is subjected to a change in concentration, the system will shift to minimize the change and reestablish equilibrium. As the concentration of a weak acid decreases, the system will shift to increase the dissociation of the weak acid. Therefore, the percent dissociation increases when the concentration of the weak acid decreases.
06

Explain why the concentration of H+ decreases from solutions a to c even though the percent dissociation increases

Although the percent dissociation increases as the concentration of acetic acid decreases, the total concentration of H+ in the solution decreases because there is less acetic acid available to dissociate into H+ ions. So even with a higher percent dissociation, the overall concentration of H+ ions in the solution is lower due to the lesser concentration of acetic acid.

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Key Concepts

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

Acetic Acid
Acetic acid is a well-known weak acid with the chemical formula CH鈧僀OOH. It is the component of vinegar that gives it the characteristic sour taste and pungent smell. In its pure form, acetic acid is a clear and corrosive liquid. In aqueous solutions, acetic acid can donate a proton (H鈦) to water to form acetate ions (CH鈧僀OO鈦) and hydronium ions (H鈧僌鈦). However, since it is a weak acid, it does not completely dissociate in water. This partial dissociation can be represented by the equilibrium equation.

When working with acetic acid in solutions, particularly in the context of chemical equilibrium, the important thing to consider is its dissociation behavior. Acetic acid's dissociation is governed by the acid dissociation constant, denoted as K鈧, which for acetic acid is 1.8 脳 10鈦烩伒 at room temperature. The value of K鈧 helps us understand the extent to which the acid dissociates in water, indicating its strength relative to other acids.
Chemical Equilibrium
Chemical equilibrium refers to the state in which the forward and reverse reactions occur at the same rate, meaning the concentrations of reactants and products remain constant over time. For the dissociation of acetic acid, this equilibrium can be represented by the chemical equation:

CH鈧僀OOH (aq) 鈬 CH鈧僀OO鈦 (aq) + H鈦 (aq).

At equilibrium, the rate at which acetic acid molecules dissociate into acetate ions and hydrogen ions is balanced by the rate at which these ions recombine to form acetic acid. The equilibrium expression for this process is given by the ratio: \[ K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]} \]
This expression is crucial for calculating the concentrations of the involved species at equilibrium. The system's response to any changes in concentration, temperature, or pressure is governed by this equilibrium. The principle of equilibrium forms the basis for understanding chemical reactions and processes in solutions.
Le Ch芒telier's Principle
Le Ch芒telier's Principle is a fundamental concept for predicting how an equilibrium system responds to changes. If a dynamic equilibrium is disrupted by changing the conditions, the system will adjust to restore a new equilibrium by counteracting the change. When applied to the dissociation of weak acids like acetic acid, this principle helps explain how a decrease in the concentration of the acid leads to increased percent dissociation.

Here's how it works: If the concentration of CH鈧僀OOH is decreased, the system shifts to produce more H鈦 and CH鈧僀OO鈦 ions to counteract the reduction in concentration. As a result, the percent dissociation of the acid increases, compensating for the lower initial concentration. This behavior illustrates how equilibrium systems are self-regulating, striving to restore balance when faced with external changes. Le Ch芒telier鈥檚 Principle is an instrumental tool in understanding and predicting the outcomes of chemical changes.
Weak Acid Dissociation
Weak acid dissociation is characterized by the incomplete ionization of the acid in water. Unlike strong acids, which completely dissociate, weak acids like acetic acid only partially ionize, establishing a chemical equilibrium between the undissociated acid and the ions produced. The degree of dissociation is determined by the acid dissociation constant (K鈧).

For acetic acid, we calculate the percent dissociation as: \[ \text{Percent dissociation} = \left( \frac{[H^+]}{[CH_3COOH]_0} \right) \times 100\% \] This expresses how much of the initial acetic acid concentration has dissociated into ions.

Even though the percent dissociation increases as the concentration of acetic acid decreases, the concentration of hydrogen ions ([H鈦篯) may still decline. This is because there is initially less acid available to dissociate into ions. These patterns showcase the delicate balance maintained by weak acids in solution and illustrate key elements of chemical equilibrium.

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Most popular questions from this chapter

A solution contains a mixture of acids: 0.50\(M\) HA \(\left(K_{\mathrm{a}}=1.0\right.\) \(\times 10^{-3} ), 0.20 M \mathrm{HB}\left(K_{\mathrm{a}}=1.0 \times 10^{-10}\right),\) and 0.10 \(\mathrm{MHC}\left(K_{\mathrm{a}}=\right.\) \(1.0 \times 10^{-12} ) .\) Calculate the \(\left[\mathrm{H}^{+}\right]\) in this solution.

Place the species in each of the following groups in order of increasing base strength. Give your reasoning in each case. a. \(\mathrm{IO}_{3}^{-}, \mathrm{BrO}_{3}^{-}\) b. \(\mathrm{NO}_{2}^{-}, \mathrm{NO}_{3}^{-}\) c. \(\mathrm{OCl}^{-}, \mathrm{OI}^{-}\)

Given that the \(K_{\mathrm{a}}\) value for acetic acid is \(1.8 \times 10^{-5}\) and the \(K_{\mathrm{a}}\) value for hypochlorous acid is \(3.5 \times 10^{-8},\) which is the stronger base, \(\mathrm{OCl}^{-}\) or \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-} ?\)

Monochloroacetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{2} \mathrm{ClO}_{2},\) is a skin irritant that is used in "chemical peels" intended to remove the top layer of dead skin from the face and ultimately improve the complexion. The value of \(K_{\mathrm{a}}\) for monochloroacetic acid is \(1.35 \times 10^{-3}\) Calculate the pH of a \(0.10-M\) solution of monochloroacetic acid.

Place the species in each of the following groups in order of increasing acid strength. a. \(\mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2} \mathrm{S}, \mathrm{H}_{2} \mathrm{Se}\) (bond energies: \(\mathrm{H}-\mathrm{O}, 467 \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{H}-\mathrm{S}, 363 \mathrm{kJ} / \mathrm{mol} ; \mathrm{H}-\mathrm{Se}, 276 \mathrm{kJ} / \mathrm{mol} )\) b. \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}, \mathrm{FCH}_{2} \mathrm{CO}_{2} \mathrm{H}, \mathrm{F}_{2} \mathrm{CHCO}_{2} \mathrm{H}, \mathrm{F}_{3} \mathrm{CCO}_{2} \mathrm{H}\) c. \(\mathrm{NH}_{4}^{+}, \mathrm{HONH}_{3}^{+}\) d. \(\mathrm{NH}_{4}^{+}, \mathrm{PH}_{4}^{+}\) (bond energies: \(\mathrm{N}-\mathrm{H}, 391 \mathrm{kJ} / \mathrm{mol} ; \mathrm{P}-\mathrm{H},\) 322 \(\mathrm{kJ} / \mathrm{mol} )\) Give reasons for the orders you chose.

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