Problem 114 - Chemistry An Atoms First Approach

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. $$\mathrm{CaBr}_{2}, \quad \mathrm{KNO}_{2}, \quad \mathrm{HClO}_{4}, \quad \mathrm{HNO}_{2}, \quad \mathrm{HONH}_{3} \mathrm{ClO}_{4}$$

Step-by-Step Solution

Answer

The order of the given solutions from most acidic to most basic is: \(\mathrm{HClO}_{4}\), \(\mathrm{HNO}_{2}\), \(\mathrm{CaBr}_{2}\), \(\mathrm{HONH}_{3}\mathrm{ClO}_{4}\), and \(\mathrm{KNO}_{2}\).

Step 1: Identify the Type of Solution

First, we need to identify whether each given solution is acidic or basic. 1. \(\mathrm{CaBr}_{2}\) - It is a salt of weak base (\(\mathrm{Br^-}\)) and strong acid (\(\mathrm{Ca^{2+}}\)), so it will be acidic. 2. \(\mathrm{KNO}_{2}\) - It is a salt of weak acid (\(\mathrm{HNO}_{2}\)) and strong base (\(\mathrm{K^+}\)), so it will be basic. 3. \(\mathrm{HClO}_{4}\) - It is a strong acid, so it will be acidic. 4. \(\mathrm{HNO}_{2}\) - It is a weak acid, so it will be acidic. 5. \(\mathrm{HONH}_{3} \mathrm{ClO}_{4}\) - It is a salt of strong acid (\(\mathrm{HClO}_{4}\)) and weak base (\(\mathrm{HONH}_{3}\)), so it will be acidic. Now we know that out of these 5 given solutions, 4 are acidic and 1 is basic.

Step 2: Compare Ka Values for Acidic Solutions

Now, let's compare \(K_{\mathrm{a}}\) values for the acidic solutions using Appendix 5. 1. \(\mathrm{CaBr}_{2}\) - \(K_{\mathrm{a}}\) not required directly, as Br is a weak base, and it will produce an acidic solution. 2. \(\mathrm{HClO}_{4}\) - \(K_{\mathrm{a}} > 1\) 3. \(\mathrm{HNO}_{2}\) - \(K_{\mathrm{a}} = 4.5 \times 10^{-4}\) 4. \(\mathrm{HONH}_{3} \mathrm{ClO}_{4}\) - \(K_{\mathrm{a}}\) not required directly, as HONH3 is a weak base, and it will produce an acidic solution. Out of these acidic solutions, \(\mathrm{HClO}_{4}\) has the highest \(K_{\mathrm{a}}\) value, followed by \(\mathrm{HNO}_{2}\).

Step 3: Compare Kb Values for Basic Solutions

Now, let's compare \(K_{\mathrm{b}}\) values for the basic solution using Appendix 5. 1. \(\mathrm{KNO}_{2}\) - \(K_{\mathrm{b}} = 2.4 \times 10^{-2}\) Since we have only one basic solution, we don't need to compare it with others; we just need to place it properly in the final order.

Step 4: Arrange the Solutions in the Order of Acidity

Based on the above analysis, we can arrange the given solutions in the following order, from most acidic to most basic: 1. \(\mathrm{HClO}_{4}\) (strong acid) 2. \(\mathrm{HNO}_{2}\) (weak acid) 3. \(\mathrm{CaBr}_{2}\) (acidic due to \(\mathrm{Br^-}\), a weak base) 4. \(\mathrm{HONH}_{3}\mathrm{ClO}_{4}\) (acidic due to \(\mathrm{HONH}_{3}\), a weak base) 5. \(\mathrm{KNO}_{2}\) (basic, due to \(\mathrm{NO}_{2^-}\), a weak acid)

Key Concepts

pH scale

Understanding the pH scale is crucial in acid-base chemistry. The pH scale measures how acidic or basic a solution is, ranging from 0 to 14. A

• pH less than 7 indicates an acidic solution.
• pH of 7 is neutral, like pure water.
• pH greater than 7 indicates a basic solution.

The concentration of hydrogen ions \( \left( \text{H}^+ \right) \) in a solution determines its pH. The formula to calculate pH is \[\text{pH} = -\log[\text{H}^+]\]A strong acid will have a high concentration of \( \text{H}^+ \,\) thus a low pH, often closer to 0. Conversely, a strong base has fewer \( \text{H}^+ \ \,\) which means a higher pH near 14.
Acids and bases can affect pH differently. Strong acids and bases dissociate completely, changing the pH more drastically than weak acids and bases, which only partially dissociate.

Ka and Kb values

The values of \( K_a \) and \( K_b \) help us understand the strength of acids and bases. They are equilibrium constants for the ionization reactions of weak acids and bases.

• \( K_a \) is the acid dissociation constant.
• \( K_b \) is the base dissociation constant.

\[ K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \] \[ K_b = \frac{[\text{OH}^-][\text{B}^+]}{[\text{BOH}]} \]
A larger \( K_a \) or \( K_b \) indicates a stronger acid or base, respectively. In the exercise, \( \text{HClO}_4 \) has a very high \( K_a \,\) confirming it's a strong acid. \(\text{HNO}_2\) with a lesser \( K_a \,\) is a weaker acid. For basic solutions, like \( \text{KNO}_2 \,\) \( K_b \) shows student how basic the solution really is. These values directly affect the pH of the solution, where a higher \( K_a \) implies more \( \text{H}^+ \) ions, leading to a lower pH for acids.

strong and weak acids and bases

Understanding the distinction between strong and weak acids and bases is pivotal in chemistry. Strong acids, like \( \text{HClO}_4 \,\) dissociate completely in water, releasing a high concentration of \( \text{H}^+ \) ions.

• Examples of strong acids include \( \text{HCl} \,\) \( \text{HNO}_3 \).
• Strong bases, like \( \text{NaOH} \,\) dissociate entirely too, releasing \( \text{OH}^- \,\) ions.

Weak acids, such as \( \text{HNO}_2 \,\) partially dissociate in water, which means not all available \( \text{H}^+ \,\) ions are released. Weak bases, including ammonia (\[ \text{NH}_3 \]), also only partially ionize, producing fewer \( \text{OH}^- \) ions.