Question

Arrange the following \(0.10 M\) solutions in order from most acidic to most basic. See Appendix 5 for \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) values. \(\mathrm{CaBr}_{2}, \quad \mathrm{KNO}_{2}, \quad \mathrm{HClO}_{4}, \quad \mathrm{HNO}_{2}, \quad \mathrm{HONH}_{3} \mathrm{ClO}_{4}\).

Short answer

The order of the given solutions from most acidic to most basic is: \(\mathrm{HClO}_4\), \(\mathrm{HNO}_2\), \(\mathrm{HONH}_3 \mathrm{ClO}_4\), \(\mathrm{CaBr}_2\), \(\mathrm{KNO}_2\).

Step-by-step solution

Identify acidic and basic compounds

We have to identify the acidic and basic nature of each compound: 1. CaBr2: Neutral 2. KNO2: Basic 3. HClO4: Acidic (strong acid) 4. HNO2: Acidic (weak acid) 5. HONH3ClO4: Acidic (weak base + strong acid)

Comparing acidic strengths

We need to compare the acidic strengths of HClO4, HNO2, and HONH3ClO4. We know that HClO4 is a strong acid, so it will have the lowest pH compared to the weak acidic solutions. Comparison of weak acids HNO2 and HONH3ClO4 can be done based on the Ka values: - HNO2: Ka = \(5.1 \times 10^{-4}\) - HONH3ClO4: Ka (NH4+) = \(5.6 \times 10^{-10}\) HNO2 has a higher Ka value (larger acidic dissociation constant); thus, it is more acidic than HONH3ClO4.

Comparing basic strengths

Now, we will compare the basic strengths of KNO2 and CaBr2. Since CaBr2 is neutral and KNO2 is a basic solution, KNO2 will be more basic.

Arrange solutions

Arrange the solutions from most acidic to most basic based on the comparisons of their acidic and basic strengths: 1. HClO4 (strong acid) 2. HNO2 (weak acid with higher Ka) 3. HONH3ClO4 (weak acid with lower Ka) 4. CaBr2 (neutral) 5. KNO2 (basic) Therefore, the order from most acidic to most basic is: \(\mathrm{HClO}_4\), \(\mathrm{HNO}_2\), \(\mathrm{HONH}_3 \mathrm{ClO}_4\), \(\mathrm{CaBr}_2\), \(\mathrm{KNO}_2\).

Key concepts

Acid Strength

Acid strength refers to the ability of an acid to donate protons (H⁺ ions) in a solution. The strength of an acid depends significantly on its dissociation in water. Strong acids like perchloric acid (HClO₄) dissociate completely in aqueous solutions. This means they release all available protons, resulting in a high concentration of H⁺ ions.

In contrast, weak acids like nitrous acid (HNO₂) and hydroxylammonium perchlorate (HONH₃ClO₄) only partially dissociate in solution. As a result, only some of their protons are donated, leading to a lower concentration of H⁺ ions compared to strong acids. The acid dissociation constant ( Ka ) is a useful metric in determining acid strength. A larger Ka value indicates a stronger acid. Therefore, HNO₂ with a Ka of 5.1 × 10⁻⁴ is more acidic than HONH₃ClO₄, which has a lower Ka value.

Base Strength

Base strength is a measure of a base's ability to accept protons (H⁺ ions). Just as with acids, base strength can vary widely. Bases can be categorized into strong and weak, based on their ionization extent in solution.

For example, potassium nitrite ( KNO₂ ) is considered a basic solution largely because it can dissociate in water to produce nitrite ions ( NO₂⁻ ). These ions can accept protons, making the solution basic. It's important to note that the strength of a base is typically quantified by its base dissociation constant ( Kb ). A higher Kb value generally indicates a stronger base, capable of accepting more protons. However, in this solution set, we don't calculate Kb but instead look at the neutral or basic characteristics of the substances to rank them.

Dissociation Constant

The dissociation constant ( K ) is a crucial factor in understanding both acid and base strengths. For acids, the acid dissociation constant ( Ka ) measures the degree to which an acid can donate protons in solution. A higher Ka value signifies a strong acid, while a lower Ka indicates a weaker acid.

Conversely, the base dissociation constant ( Kb ) evaluates a base's ability to accept protons. Greater Kb values denote stronger bases. Both Ka and Kb are fundamental in chemistry for predicting how a substance behaves in solution. By knowing these constants, it becomes easier to predict the relative acidity or basicity of a compound and arrange different substances according to their acid or base strengths in a solution.

Neutral Solutions

Neutral solutions have a balance between the concentration of hydrogen ions ( H⁺ ) and hydroxide ions ( OH⁻ ). Water is the classic example of a neutral solution, with a pH of 7 under standard conditions. When discussing compounds such as calcium bromide ( CaBr₂ ), it is essential to recognize it as effectively neutral in an aqueous solution.

In this context, since CaBr₂ does not contribute additional H⁺ or OH⁻ ions beyond what is naturally present in water, it does not alter the pH. Therefore, its effect on acidity or basicity is negligible, and it acts as a reference point between more acidic or basic solutions. Understanding neutral solutions is key when comparing a series of solutions based on their tendency to alter the environment towards acidity or basicity.