Problem 8 - Chemistry An Atoms First Approach

Question

Consider a solution prepared by mixing a weak acid HA, HCl, and NaA. Which of the following statements best describes what happens? a. The \(\mathrm{H}^{+}\) from the HCl reacts completely with the \(\mathrm{A}^{-}\) from the NaA. Then the HA dissociates somewhat. b. The \(\mathrm{H}^{+}\) from the HCl reacts somewhat with the \(\mathrm{A}^{-}\) from the NaA to make HA, while the HA is dissociating. Eventually you have equal amounts of everything. c. The \(\mathrm{H}^{+}\) from the HCl reacts somewhat with the \(\mathrm{A}^{-}\) from the NaA to make HA while the HA is dissociating. Eventually all the reactions have equal rates. d. The \(\mathrm{H}^{+}\) from the HCl reacts completely with the \(\mathrm{A}^{-}\) from the NaA. Then the HA dissociates somewhat until "too much" \(\mathrm{H}^{+}\) and \(\mathrm{A}^{-}\) are formed, so the \(\mathrm{H}^{+}\) and \(\mathrm{A}^{-}\) react to form HA, and so on. Eventually equilibrium is reached. Justify your choice, and for choices you did not pick, explain what is wrong with them.

Step-by-Step Solution

Answer

The correct statement is (c): The H⁺ from HCl reacts somewhat with the A⁻ from NaA to make HA while the HA is dissociating. Eventually, all the reactions have equal rates. This is because both reactions (H⁺ from HCl reacting with A⁻, and the dissociation of HA) occur simultaneously and support each other until equilibrium is reached. Statements a, b, and d are incorrect as they do not accurately describe the behavior of the acids and their impact on the system's equilibrium.

Step 1: Understanding the provided statements and the behavior of acids, bases, and salts in solution

Before analyzing each statement, it is important to understand some basic concepts: 1. In a solution containing a weak acid HA, the primary reaction is: HA ↔ H⁺ + A⁻ (Where ↔ indicates that the reaction is in equilibrium) 2. HCl is a strong acid, which will completely dissociate in solution: HCl → H⁺ + Cl⁻ (Where → indicates a complete reaction) 3. NaA is a salt containing the conjugate base A⁻. In solution, the salt will dissociate as well: NaA → Na⁺ + A⁻ With these reactions in mind, we can now analyze the given statements and determine which one is correct.

Step 2: Analyzing statements a, b, c, and d

a. This statement says that H⁺ from HCl will react completely with A⁻ from NaA, and then HA will dissociate. This scenario is incorrect, because H⁺ ions from HCl and HA will compete for the A⁻ ions from NaA. The reaction will continue until equilibrium is reached. b. This statement suggests that H⁺ from HCl will react with A⁻ from NaA to form equal amounts of HA, H⁺, and A⁻. This is incorrect, as the reaction will not result in equal amounts of each species. The ratio of the species in the solution at equilibrium will depend on the equilibrium constant of the weak acid and the initial concentrations of all species. c. This statement explains that both HA dissociation and H⁺ from HCl reacting with A⁻ from NaA happen at the same time, and eventually, all reactions have equal rates. This is the correct statement because in a mixture of strong and weak acids, both reactions will support each other until equilibrium is reached. d. According to this statement, H⁺ from HCl reacts completely with A⁻ from NaA, then HA dissociates until "too much" H⁺ and A⁻ are formed, and H⁺ and A⁻ react to form HA again. This statement is incorrect because it oversimplifies the actual process happening in the solution. The H⁺ from HCl and the dissociation of HA will influence the reaction at the same time until equilibrium is reached.

Step 3: Conclusion

The correct statement is (c). The H⁺ from HCl reacts somewhat with the A⁻ from NaA to make HA while the HA is dissociating. Eventually, all the reactions have equal rates. Statements a, b, and d are incorrect because they do not correctly describe the behavior of the acids and their impact on the equilibrium of the system.

Key Concepts

Weak Acids

Weak acids are fascinating because they don't completely break apart in solution. This means they dissociate partially, establishing an equilibrium between the undissociated acid \( HA \) and its ions \( H^+ \) and \( A^- \).
Key characteristics of weak acids include:

• Partial dissociation in water, creating a dynamic equilibrium state.
• Presence of both the whole acid molecule and its ionized form in the solution.
• Sensitivity to changes in the concentration of ions, which can shift the position of equilibrium.

This behavior can be mathematically captured by the acid dissociation constant \( K_a \), which tells us the strength of the weak acid in terms of its dissociation tendency. Understanding weak acids is crucial because even in low concentrations, they can significantly affect the pH of a solution.

Strong Acids

Strong acids differ from weak acids by completely dissociating into their ions in solution. For instance, hydrochloric acid \( HCl \) dissociates entirely into \( H^+ \) and \( Cl^- \) ions.
Important properties of strong acids:

• They fully dissociate, so there's no equilibrium established with undecomposed molecules in solution.
• They typically result in a lower pH due to the high concentration of \( H^+ \) ions.
• Alteration of the reaction environment significantly, as they do not re-form the original acid molecule once dissociated.

In contrast to weak acids, strong acids display predictable behavior in reactions because they always yield ions in proportion to the initial concentration of the acid.

Reaction Equilibrium

In the context of acids and bases, reaction equilibrium refers to a balanced state where the rates of the forward and backward reactions are equal. At equilibrium, the concentrations of reactants and products remain constant over time.
Here's what to remember about reaction equilibrium:

• Established in weak acid solutions where both the acid and its ions coexist.
• Strong acids, once dissociated, do not establish an equilibrium as they do not reform molecules.
• The equilibrium position can shift with changes in concentration, pressure, or temperature, altering how much of the acid remains undissociated.

Therefore, understanding equilibrium is crucial for predicting how acids interact in a mixture, such as in our exercise where both a strong \( HCl \) and weak acid \( HA \) influence the system.

Conjugate Base

When a weak acid like \( HA \) donates a proton \( H^+ \), it forms its conjugate base, \( A^- \). This base is an essential player in the dynamics of acid-base equilibria.
Considerations about conjugate bases include:

• The conjugate base \( A^- \) has a noticeable presence in weak acid solutions, affecting the equilibrium state.
• In our example exercise, the presence of \( A^- \) helps stabilize the equilibrium by reacting with the \( H^+ \) from the dissociation of \( HA \).
• The strength of \( A^- \) as a base is inversely related to the strength of its parent acid. Thus, a weak acid has a relatively stronger conjugate base.

Understanding conjugate bases is vital for predicting the behavior of an acid in a reaction, especially in mixed solutions!

Dissociation

Dissociation is the process by which molecules split into smaller particles, such as ions. In the acid-base context, dissociation involves acids releasing \( H^+ \) ions into a solution.
Key insights about dissociation include:

• Strong acids dissociate completely, contributing to high \( H^+ \) concentration.
• Weak acids dissociate only partially, creating a balance between undissociated molecules and ions.
• The degree of dissociation is vital in determining the pH of a solution and its reactivity with other species, like conjugate bases in our reference exercise.

Grasping the concept of dissociation helps in anticipating how acids will behave in solution, facilitating the prediction of equilibrium shifts and interactions with other dissolved substances.