Question

Acid-base reactions usually go to completion. Confirm this statement by calculating the equilibrium constant for each of the following cases: (a) A strong acid reacting with a strong base. (b) A strong acid reacting with a weak base \(\left(\mathrm{NH}_{3}\right) .(\mathrm{c})\) A weak acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) reacting with a strong base. (d) A weak acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) reacting with a weak base \(\left(\mathrm{NH}_{3}\right)\). (Hint: Strong acids exist as \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions and strong bases exist as \(\mathrm{OH}^{-}\) ions in solution. You need to look up \(K_{\mathrm{a}}, K_{\mathrm{b}}\), and \(K_{\mathrm{w}}\).)

Short answer

Strong acid-base reactions have large equilibrium constants, confirming near-completion reactions. Weak acid-base reactions have smaller constants, indicating less complete reactions.

Step-by-step solution

Introduction to the Equilibrium Constant

When a chemical reaction reaches equilibrium, the equilibrium constant (K) reflects the ratio of the concentrations of products to reactants at equilibrium. For an acid-base reaction, the equilibrium constant indicates how far the reaction proceeds towards formation of products.

Strong Acid and Strong Base Reaction

For reactions involving a strong acid and strong base, such as HCl + NaOH, both substances completely dissociate in water:\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]Since both species ionize completely, the equilibrium constant for the reaction to form water is very large, often exceeding \(10^{7}\), indicating the reaction proceeds nearly to completion.

Strong Acid and Weak Base Reaction

Consider the reaction between HCl (a strong acid) and NH₃ (a weak base):\[ \text{NH}_3 + \text{H}_3\text{O}^+ \rightarrow \text{NH}_4^+ + \text{H}_2\text{O} \]The equilibrium constant \(K_c\) for this reaction can be found by using\[ K_c = \frac{K_w}{K_b(\text{NH}_3)} \]Given that \(K_w = 1 \times 10^{-14}\) and \(K_b \text{(NH}_3\text{)} \approx 1.8 \times 10^{-5}\), \(K_c \approx 5.6 \times 10^{8}\), which is very large, indicating completion.

Weak Acid and Strong Base Reaction

In the case of CH₃COOH (a weak acid) reacting with NaOH (a strong base):\[ \text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \]The equilibrium constant \(K_c\) is given by\[ K_c = \frac{K_w}{K_a(\text{CH}_3\text{COOH})} \]With \(K_a \approx 1.8 \times 10^{-5}\), \(K_c \approx 5.6 \times 10^{9}\), indicating that the reaction nearly goes to completion.

Weak Acid and Weak Base Reaction

For the reaction between CH₃COOH and NH₃:\[ \text{CH}_3\text{COOH} + \text{NH}_3 \rightarrow \text{CH}_3\text{COO}^- + \text{NH}_4^+ \]The equilibrium constant \(K_c\) can be calculated as\[ K_c = \frac{K_a(\text{CH}_3\text{COOH}) \cdot K_b(\text{NH}_3)}{K_w} \]Substituting known values, \(K_c \approx 6.6 \times 10^{-11}\), which is quite small, indicating that this reaction does not go to completion as readily.

Key concepts

Equilibrium Constant

The equilibrium constant, often denoted as \( K \), is a number that indicates the extent to which a chemical reaction has proceeded to form products from reactants at equilibrium. In the context of acid-base reactions, this constant helps us understand whether a reaction will go to completion or reach a state where both reactants and products coexist.

• For reactions where \( K \) is much larger than 1, it suggests that the products are favored, indicating the reaction proceeds nearly to completion.
• Conversely, if \( K \) is much smaller than 1, the reaction does not favor products, suggesting that very little reaction has occurred.

Understanding the equilibrium constant is crucial for predicting the outcome of various acid-base interactions, which we'll explore in the subsequent sections.

Strong Acids and Strong Bases

When a strong acid reacts with a strong base, both substances completely ionize in solution. This means that they break down entirely into their constituent ions.

For example, in the reaction between hydrochloric acid (\( \mathrm{HCl} \)) and sodium hydroxide (\( \mathrm{NaOH} \)), you get water and salt as by-products:

• \[ \mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H}_2\mathrm{O} \]
• The equilibrium constant \( K \) for this reaction is exceedingly large, often exceeding \( 10^7 \).

This large value of \( K \) demonstrates that the reaction proceeds fully towards the formation of products, effectively going to completion.

Strong Acid with Weak Base

In reactions involving a strong acid and a weak base, like hydrochloric acid (\( \mathrm{HCl} \)) and ammonia (\( \mathrm{NH}_3 \)), the strong acid fully ionizes, while the weak base does not fully ionize.

The reaction can be represented as:

• \[ \mathrm{NH}_3 + \mathrm{H}_3\mathrm{O}^+ \rightarrow \mathrm{NH}_4^+ + \mathrm{H}_2\mathrm{O} \]
• To find the equilibrium constant \( K_c \), you use the formula \( K_c = \frac{K_w}{K_b(\mathrm{NH}_3)} \), where \( K_w \) is the ion product of water.
• Given \( K_w = 1 \times 10^{-14} \) and \( K_b \mathrm{(NH}_3\mathrm{)} \approx 1.8 \times 10^{-5} \), you find \( K_c \approx 5.6 \times 10^{8} \).

This large \( K_c \) value indicates that the products are heavily favored, showing that the reaction proceeds substantially towards completion.

Weak Acid with Strong Base

Reactions involving a weak acid and a strong base are also quite common. For instance, when acetic acid (\( \mathrm{CH}_3\mathrm{COOH} \)) reacts with sodium hydroxide (\( \mathrm{NaOH} \)), water and an acetate ion are formed.

The equilibrium for this reaction is described as:

• \[ \mathrm{CH}_3\mathrm{COOH} + \mathrm{OH}^- \rightarrow \mathrm{CH}_3\mathrm{COO}^- + \mathrm{H}_2\mathrm{O} \]
• To calculate \( K_c \), the equation \( K_c = \frac{K_w}{K_a(\mathrm{CH}_3\mathrm{COOH})} \) is used.
• Given \( K_a \approx 1.8 \times 10^{-5} \), you determine \( K_c \approx 5.6 \times 10^{9} \).

This very high value of the equilibrium constant indicates that the reaction proceeds almost entirely towards the formation of the products, approaching completion.

Weak Acid with Weak Base

When a weak acid reacts with a weak base, as in the interaction between acetic acid (\( \mathrm{CH}_3\mathrm{COOH} \)) and ammonia (\( \mathrm{NH}_3 \)), neither the acid nor the base fully ionizes.

The equilibrium can be expressed by the equation:

• \[ \mathrm{CH}_3\mathrm{COOH} + \mathrm{NH}_3 \rightarrow \mathrm{CH}_3\mathrm{COO}^- + \mathrm{NH}_4^+ \]
• To find the equilibrium constant \( K_c \), use \( K_c = \frac{K_a(\mathrm{CH}_3\mathrm{COOH}) \cdot K_b(\mathrm{NH}_3)}{K_w} \).
• With the known values, \( K_c \approx 6.6 \times 10^{-11} \).

This small \( K_c \) value signifies that the reaction only minimally favors product formation, meaning it does not go to completion. Instead, it reaches an equilibrium where both reactants and products are present in significant concentrations.