Question

Consider the equation: $$ \mathrm{HA}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \leftrightharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{A}^{-}(a q) $$ a. If water is a better base than \(\mathrm{A}^{-},\) which way will the equilibrium lie? b. If water is a better base than \(\mathrm{A}^{-}\) , is HA a strong or a weak acid? c. If water is a better base than \(\mathrm{A}^{-},\) is the value of \(K_{\mathrm{a}}\) greater or less than 1 ?

Short answer

a. The equilibrium will lie to the right since water is a better base and has a higher tendency to accept protons compared to A-. b. HA is a strong acid, as water's stronger basicity and the right-sided equilibrium favor its ionization. c. The value of Ka is greater than 1, as a higher Ka value correlates to stronger acid behavior and we have determined that HA is a strong acid.

Step-by-step solution

Determine the better base

In this case, we are given that water is a better base than A-. What this means is that water has a higher tendency to accept protons compared to A-. Therefore, in order to reach equilibrium, the reaction will favor the formation of H3O+ (aq) and A- (aq) since water successfully outcompetes A- for protons. Hence, the equilibrium lies to the right. **b. Nature of the acid HA**

Strong or Weak Acid

Since the equilibrium favors the right side of the reaction, indicating that HA is donating protons to water, we can conclude that HA is indeed an acid. However, we still need to determine whether it is a strong or weak acid. Due to water's stronger basicity compared to A- and the fact the equilibrium lies to the right, HA must be a strong acid. Strong acids tend to ionize readily in water, and in the given case, the nature of water allows it to do so. **c. Ka value of the reaction**

Comparing Ka value to 1

Ka stands for the acid dissociation constant, which measures the extent of dissociation of an acid. A larger Ka value indicates stronger acid behavior, while a smaller Ka value indicates weaker acid behavior. In our case, since we determined that HA is a strong acid, we can infer that its Ka value must be greater than 1. This is because strong acids have a greater tendency to ionize in water, in comparison to weak acids which have a Ka value lesser than 1.

Key concepts

Strong Acid

A strong acid is one that completely or nearly completely ionizes in water, releasing hydrogen ions (H⁺). This means when a strong acid like hydrochloric acid (HCl) is dissolved in water, virtually all its molecules dissociate into H⁺ ions and their corresponding anions (Cl⁻ in the case of HCl).
The characteristic of strong acids:

• They have a high tendency to donate protons (H⁺) to water or any base they interact with.
• They have little to no undissociated acid molecules in solution.
• The equilibrium of their dissociation reaction lies far to the right, indicating near-complete ionization.

In the context of an acid-base reaction, if water competes with another base for protons and still allows complete dissociation of the acid, it indicates the acid's strong nature. Strong acids also have large dissociation constants, suggesting their readiness to donate protons and form products.

Weak Acid

Weak acids, unlike strong acids, only partially ionize in water. This means that only a portion of their molecules dissociate to release H⁺ ions, while the rest remain intact in the solution. An example of a weak acid is acetic acid ( CH₃COOH ), which only partially dissociates in water.
gCharacteristics of weak acids include:

• A low tendency to donate protons (H⁺).
• The presence of a significant amount of undissociated molecules in the solution.
• The equilibrium of the dissociation reaction lies more towards the left, indicating limited ionization.

In the discussed exercise, if HA had been a weak acid, water would not be effective enough in pulling protons away, resulting in limited ionization and a minor shift of equilibrium toward products. As a result, weak acids have smaller dissociation constants compared to strong acids, reflective of their limited ionization.

Acid Dissociation Constant (Ka)

The acid dissociation constant, represented as \( K_a \), is a numerical value that expresses the extent to which an acid can dissociate in a solution. It is determined by the ratio of the concentration of products (ions) to the concentration of the undissociated acid. The equation for a generic acid \( HA \) ionizing in water is:\[K_a = \frac{[H_3O^+][A^-]}{[HA]}\]Where:

• \( [H_3O^+] \) is the concentration of the hydronium ion.
• \( [A^-] \) is the concentration of the conjugate base.
• \( [HA] \) is the concentration of the undissociated acid.

gA higher \( K_a \) value indicates a more complete ionization and a stronger acid. Conversely, a smaller \( K_a \) signifies a weaker acid and reduced ionization. So, when determining whether an acid is strong or weak, the \( K_a \) value is key: for strong acids, \( K_a > 1 \), showing a greater capability to donate protons and achieve equilibrium far to the right.