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Magazine Chapter 16: Problem 64
Calculate the percent dissociation of \(0.10 \mathrm{M}\) hydrazoic acid \(\left(\mathrm{HN}_{3}, K_{\mathrm{a}}=1.9 \times 10^{-5}\right) .\) Recalculate the percent dissociation of \(0.10 \mathrm{M} \mathrm{HN}_{3}\) in the presence of \(0.10 \mathrm{M} \mathrm{HCl}\), and explain the change.
Short Answer
Expert verified
Percent dissociation without HCl is approximately 1.378%. With 0.10 M HCl, dissociation is negligible due to the common ion effect.
Step by step solution
01
Understand the Concept of Percent Dissociation
Percent dissociation refers to the percentage of the initial concentration of a weak acid that dissociates into its ions in solution. For a weak acid HA, dissociation in water is given by the equation: \( \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- \).
02
Set Up the Initial Expression for Dissociation
For the initial concentration of hydrazoic acid \( [\text{HN}_3] = 0.10 \; \text{M} \), we set up an equilibrium expression: \( [\text{HN}_3] \rightleftharpoons [\text{H}^+] + [\text{N}_3^-] \). The change in concentration at equilibrium is given by \( x \), where \( x \) is the concentration of ions formed.
03
Write the Equilibrium Expression
Using the given \( K_a \), the equilibrium expression for dissociation is:\[ K_a = \frac{[\text{H}^+][\text{N}_3^-]}{[\text{HN}_3]} = 1.9 \times 10^{-5} \]Substitute the equilibrium concentrations: \[ K_a = \frac{x^2}{0.10 - x} \]
04
Approximate and Solve for x
Since \( K_a \) is small, assume \( x \ll 0.10 \), so \( 0.10 - x \approx 0.10 \). Thus, the equation simplifies to:\[ x^2 = (0.10)(1.9 \times 10^{-5}) \]Solve for \( x \):\[ x = \sqrt{1.9 \times 10^{-6}} \approx 1.378 \times 10^{-3} \; \text{M} \]
05
Calculate Percent Dissociation
Percent dissociation is calculated as:\[ \text{Percent Dissociation} = \left( \frac{x}{0.10} \right) \times 100 \approx 1.378 \% \]
06
Recalculate Percent Dissociation with HCl
In the presence of \(0.10 \; \text{M} \; \text{HCl}\), \([\text{H}^+]\) from \text{HCl} is added to the mixture. Total \([\text{H}^+]\) is approximately \(0.10 \; \text{M}\). Since \([\text{H}^+]\) from \text{HCl} is much larger than \(x\), additional dissociation of \text{HN}_3 is negligible, leading to minimal further dissociation.
07
Explain the Change in Percent Dissociation
The percent dissociation of \( \text{HN}_3 \) decreases significantly in the presence of \( \text{HCl} \) due to the common ion effect. The initial concentration of \( [\text{H}^+] \) is already high in the solution due to \( \text{HCl} \), thus suppressing the further dissociation of weak acid \( \text{HN}_3 \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Common Ion Effect
The common ion effect occurs when a solution containing a weak acid is mixed with a strong acid or salt that shares a common ion. This effect reduces the dissociation of the weak acid. In our example, adding HCl to the hydrazoic acid solution introduces more H鈦� ions, which are common between both acids.
This additional concentration of H鈦� ions shifts the equilibrium position to favor the undissociated form of hydrazoic acid (HN鈧�).
This happens because, according to Le Chatelier's Principle, the system will adjust to minimize the disturbance (additional H鈦�). As a result, less HN鈧� dissociates, and the dissociation percentage decreases.
This additional concentration of H鈦� ions shifts the equilibrium position to favor the undissociated form of hydrazoic acid (HN鈧�).
This happens because, according to Le Chatelier's Principle, the system will adjust to minimize the disturbance (additional H鈦�). As a result, less HN鈧� dissociates, and the dissociation percentage decreases.
- Reduces the ionization of the weak acid.
- Adds a common ion, increasing the concentration of H鈦�.
- Shifts equilibrium towards the non-dissociated acid.
Weak Acid Dissociation
Weak acids like hydrazoic acid (
HN鈧�) only partially dissociate in solutions. Unlike strong acids, which fully dissociate, weak acids reach an equilibrium between the dissociated ions and the undissociated molecules.
For hydrazoic acid, the dissociation can be represented as:
HN鈧� 鈫� H鈦� + N鈧冣伝.
This means that not all of the acid molecules release H鈦� ions into the solution.
The extent of dissociation is crucial to understand as it affects calculations like percent dissociation. In the absence of other influencing factors, this dissociation is determined by the inherent acid strength, captured by its acid dissociation constant (K鈧�).
For hydrazoic acid, the dissociation can be represented as:
HN鈧� 鈫� H鈦� + N鈧冣伝.
This means that not all of the acid molecules release H鈦� ions into the solution.
The extent of dissociation is crucial to understand as it affects calculations like percent dissociation. In the absence of other influencing factors, this dissociation is determined by the inherent acid strength, captured by its acid dissociation constant (K鈧�).
- Partial dissociation of weak acids.
- Equilibrium between dissociated and undissociated forms.
Equilibrium Expression
The equilibrium expression is crucial in understanding how concentration changes affect the dissociation process in weak acids.
For hydrazoic acid, the equilibrium expression is:\[ K_a = \frac{[\text{H}^+][\text{N}_3^-]}{[\text{HN}_3]} \]
This formula relates the concentrations of ions produced to the original acid concentration.
In calculations, this expression helps evaluate how changes in conditions, like adding a common ion, shift the equilibrium.
By understanding how to substitute values for concentrations at equilibrium, you can solve for unknowns like the concentration of hydrogen ions ([H鈦篯).
For hydrazoic acid, the equilibrium expression is:\[ K_a = \frac{[\text{H}^+][\text{N}_3^-]}{[\text{HN}_3]} \]
This formula relates the concentrations of ions produced to the original acid concentration.
In calculations, this expression helps evaluate how changes in conditions, like adding a common ion, shift the equilibrium.
By understanding how to substitute values for concentrations at equilibrium, you can solve for unknowns like the concentration of hydrogen ions ([H鈦篯).
- Relates ion concentrations to original acid amount.
- Essential for calculating dissociation ratios.
- Helps predict behavior under different conditions.
Acid Dissociation Constant (Ka)
The acid dissociation constant (K鈧�) is a key metric that defines the strength of a weak acid. It quantifies the extent to which an acid dissociates in solution. A smaller K鈧� value indicates that the acid only partially dissociates, typical of weak acids like hydrazoic acid.
In our example, the given K鈧� is \(1.9 \times 10^{-5}\). This shows that hydrazoic acid is a weak acid since this value is small.
The K鈧� value allows us to set up the equilibrium expression and solve for the changes in concentrations at equilibrium.
In our example, the given K鈧� is \(1.9 \times 10^{-5}\). This shows that hydrazoic acid is a weak acid since this value is small.
The K鈧� value allows us to set up the equilibrium expression and solve for the changes in concentrations at equilibrium.
- Defines the dissociation level of an acid.
- Smaller values indicate weaker acids.
- Essential for equilibrium calculations.
