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Chapter 14: Problem 3

Sketch two graphs: (a) percent dissociation for weak acid HA versus the initial concentration of \(\mathrm{HA}\left([\mathrm{HA}]_{0}\right)\) and \((\mathrm{b}) \mathrm{H}^{+}\) concentration versus [HA lo- Explain both.

Short Answer

Expert verified
In conclusion, when sketching the two graphs: 1. Graph (a) Percent dissociation vs. [HA]鈧�: The curve starts high at lower concentrations and then gradually decreases as the initial concentration of the weak acid, [HA]鈧� increases. This shows that as the initial concentration increases, the percent dissociation decreases. 2. Graph (b) H鈦� concentration vs. [HA]鈧�: The curve shows an increasing trend, starting at low concentrations of H鈦� at low initial concentrations and then gradually increasing with increasing initial concentrations. However, the slope of the curve decreases because of the square root term in the relationship, \([H^{+}] \approx \sqrt{K_{a} \times [HA]_{0}}\).

Step by step solution

01

Understanding Weak Acid Dissociation

Weak acids partially dissociate in water, which means that they do not donate all their protons (H鈦� ions) to the solution. The equilibrium constant for this dissociation, Ka, is used to describe the extent of the dissociation. We can represent the dissociation of a weak acid HA as follows: \[HA \rightleftharpoons H^{+} + A^{-}\] The Ka expression for this dissociation is: \[K_{a} = \frac{[H^{+}][A^{-}]}{[HA]}\]
02

Calculating Percent Dissociation

Percent dissociation is the ratio of the dissociated acid concentration to the total initial acid concentration, expressed as a percentage. To calculate this, we divide the concentration of dissociated weak acid [HA] by the initial concentration [HA]鈧�: \[\text{Percent dissociation} = \frac{[HA]}{[HA]_{0}} \times 100\%\]
03

Relationship Between Percent Dissociation and Initial Concentration

As the initial concentration [HA]鈧� of the weak acid increases, the percent dissociation decreases. This happens because a greater amount of the weak acid remains undissociated and does not contribute to the proton concentration. Sketch a graph with percent dissociation on the y-axis and [HA]鈧� on the x-axis. The curve should start high at lower concentrations and then decrease gradually as the [HA]鈧� increases.
04

Calculating H鈦� Concentration

To calculate the H鈦� concentration, we can use the Ka expression mentioned in step 1 and the initial concentration of the weak acid, [HA]鈧�. The relationship can be approximated as follows: \[[H^{+}] \approx \sqrt{K_{a} \times [HA]_{0}}\] The H鈦� concentration increases with an increase in the initial concentration of the weak acid, [HA]鈧�, but the rate of increase is slower due to the square root term.
05

Sketching the Graph of H鈦� Concentration Versus Initial Concentration

To sketch the graph of H鈦� concentration versus [HA]鈧�, plot the H鈦� concentration on the y-axis and the initial concentration of the weak acid [HA]鈧� on the x-axis. The curve should have an increasing trend, starting at low concentrations of H鈦� at low initial concentrations and then gradually increasing with increasing initial concentrations. However, the slope of the curve will be decreasing because of the square root term in the relationship. In conclusion, the first graph (a) illustrates the relationship between the percent dissociation of a weak acid and its initial concentration, showing a decreasing trend as [HA]鈧� increases. The second graph (b) demonstrates the relationship between the H鈦� concentration and the initial concentration of the weak acid, displaying an increasing trend but with a decreasing slope as the initial concentration increases. Both graphs provide insight into how the dissociation of a weak acid is affected by its initial concentration.

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Key Concepts

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

Percent Dissociation
Percent dissociation is an important concept when studying weak acids. It tells us the fraction of the acid that has actually dissociated into ions compared to its initial amount. The term 'percent' means we express this ratio as a percentage, which helps in understanding just how much of the acid has transformed.

To find the percent dissociation, we use the formula:
  • Divide the concentration of the dissociated form of the acid, denoted [HA], by the initial concentration [HA]鈧�.
  • Then multiply this ratio by 100 to convert it into a percentage.
The overall expression looks like this: \[\text{Percent dissociation} = \frac{[HA]}{[HA]_{0}} \times 100\%\] It鈥檚 important to note that as the initial concentration [HA]鈧� increases, the percent dissociation usually decreases. This is because a larger amount of acid remains in its undissociated form. The graph sketching percent dissociation versus initial concentration highlights this point, showing a downward curve as [HA]鈧� gets larger.
Equilibrium Constant
The equilibrium constant, represented by \(K_a\), is a measure used to express the extent of dissociation of a weak acid. Unlike strong acids, weak acids do not dissociate completely. The equilibrium constant helps us understand how far they have gone towards completing dissociation.

For a weak acid dissociating as \[HA \rightleftharpoons H^{+} + A^{-}\] The equilibrium constant \(K_a\) can be given by the expression:\[K_{a} = \frac{[H^{+}][A^{-}]}{[HA]}\] Here,
  • [H鈦篯 and [A鈦籡 are the concentrations of the ions formed.
  • [HA] is the concentration of the undissociated acid remaining in the solution.
The equilibrium constant allows chemists to qualitatively compare the strengths of different weak acids. A larger \(K_a\) value indicates a stronger weak acid that dissociates more, while a smaller value suggests a weaker tendency to dissociate.
Initial Concentration
Initial concentration refers to the starting amount of a substance before any reaction takes place. For weak acids, initial concentration [HA]鈧� plays a crucial role in determining how much of the acid dissociates into H鈦� ions and its conjugate base, A鈦�.

Consider the equation:\[[H^{+}] \approx \sqrt{K_{a} \times [HA]_{0}}\] This approximation highlights the relationship between the initial concentration and the resulting concentration of hydrogen ions. As you can see, the hydrogen ion concentration is directly related to both \(K_a\) and [HA]鈧�. But because of the square root, even if [HA]鈧� increases, the rise in H鈦� concentration is slower.

When sketching graphs:
  • For percent dissociation 鈥� it decreases with increasing initial concentration.
  • For H鈦� concentration 鈥� it increases, but not as sharply because of the square root effect.
Such insights are vital for predicting the behavior of weak acids in solutions, especially in chemistry and biology where pH levels are critical.

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