Question

In water, the hydrogen phosphate ion, \(\mathrm{HPO}_{4}^{2-}\), can act both as a weak base and as a weak acid. (a) Write an equilibrium equation that shows hydrogen phosphate acting as a weak acid in water. (b) Write an equilibrium equation that shows bisulfate acting as a weak base in water. (c) What information would you need to help you determine whether a solution of hydrogen phosphate is going to be slightly acidic or slightly basic? How would you use that information to find out?

Short answer

(a) The equilibrium equation for hydrogen phosphate ion $\mathrm{HPO_{4}^{2-}}$ acting as a weak acid in water is: \[\mathrm{HPO_{4}^{2-}(aq) + H_{2}O(l) \rightleftharpoons H_{2}PO_{4}^{-}(aq) + OH^{-}(aq)}\] (b) The equilibrium equation for hydrogen phosphate ion $\mathrm{HPO_{4}^{2-}}$ acting as a weak base in water is: \[\mathrm{HPO_{4}^{2-}(aq) + H_{2}O(l) \rightleftharpoons H_{2}PO_{4}^{-}(aq) + OH^{-}(aq)}\] (c) To determine whether a solution containing hydrogen phosphate will be slightly acidic or slightly basic, we need the values of Ka and Kb for the respective reactions. If Ka > Kb, the solution will be slightly acidic, and if Ka < Kb, the solution will be slightly basic. Initial concentrations and other components affecting pH may also be considered for a more refined understanding.

Step-by-step solution

(a) Hydrogen phosphate as a weak acid in water

In order to write the equilibrium equation that shows hydrogen phosphate ion acting as a weak acid in water, we need to represent the dissociation of this species in an aqueous solution. The equation will show hydrogen phosphate, water, the conjugate base, and a hydronium ion. The equilibrium equation for hydrogen phosphate ion acting as a weak acid in water is: \[\mathrm{HPO_{4}^{2-}(aq) + H_{2}O(l) \rightleftharpoons H_{2}PO_{4}^{-}(aq) + OH^{-}(aq)}\]

(b) Hydrogen phosphate as a weak base in water

Now we will write the equilibrium equation that shows hydrogen phosphate ion acting as a weak base in water. To do this, we will represent the dissociation of this species in aqueous solution, during which it interacts with water molecules, resulting in the formation of its conjugate acid and hydroxide ions. The equilibrium equation for hydrogen phosphate ion acting as a weak base in water is: \[\mathrm{HPO_{4}^{2-}(aq) + H_{2}O(l) \rightleftharpoons H_{2}PO_{4}^{-}(aq) + OH^{-}(aq)}\]

(c) Information required and its usage

To determine whether a solution containing hydrogen phosphate will be slightly acidic or slightly basic, we need to know the equilibrium constants for the reactions representing hydrogen phosphate acting as a weak acid and a weak base in water. These constants are the acid dissociation constant (Ka) and the base dissociation constant (Kb). The information we would need is: 1. The value of Ka for the reaction as a weak acid: \(\mathrm{HPO_{4}^{2-} + H_{2}O \rightleftharpoons H_{2}PO_{4}^{-} + OH^{-}}\) 2. The value of Kb for the reaction as a weak base: \(\mathrm{HPO_{4}^{2-} + H_{2}O \rightleftharpoons H_{2}PO_{4}^{-} + OH^{-}}\) Once we have these values, we can compare them to determine which reaction has a greater tendency to occur. - If Ka > Kb, the hydrogen phosphate ion has a higher tendency to act as a weak acid, and the solution will be slightly acidic. - If Ka < Kb, the hydrogen phosphate ion has a higher tendency to act as a weak base, and the solution will be slightly basic. In addition to the Ka and Kb values, knowing the initial concentration of hydrogen phosphate in the solution and any other components affecting the pH of the solution would be helpful to further refine our understanding of whether the solution will be acidic or basic.

Key concepts

Hydrogen Phosphate Ion

The hydrogen phosphate ion, denoted as \( \mathrm{HPO}_{4}^{2-} \), is a versatile component in chemical systems, specifically in aqueous solutions. It has the unique ability to act both as a weak acid and a weak base in water. This dual capability classifies it as an amphoteric species, which is crucial in understanding its behavior in various chemical contexts.

When hydrogen phosphate acts as a weak acid, it donates a proton (\( \mathrm{H^{+}} \)) to water, resulting in the formation of dihydrogen phosphate (\( \mathrm{H_{2}PO_4^{-}} \)) and hydroxide ions (\( \mathrm{OH^{-}} \)). This behavior is demonstrated in the equilibrium reaction:

\[ \mathrm{HPO_{4}^{2-}(aq) + H_{2}O(l) \rightleftharpoons H_{2}PO_{4}^{-}(aq) + OH^{-}(aq)} \]
Conversely, as a weak base, the hydrogen phosphate ion can accept a proton from water, forming the same products. This dual nature is not only interesting but also significant in buffer systems, where it helps maintain stability in pH by neutralizing small amounts of added acids or bases.

Equilibrium Constant

The equilibrium constant is a key concept in understanding the direction and extent of chemical reactions. When discussing the hydrogen phosphate ion, the relevant equilibrium constants are the acid dissociation constant (\( K_a \)) and the base dissociation constant (\( K_b \)). These constants provide valuable insight into whether the hydrogen phosphate ion will more likely act as an acid or a base.

• \( K_a \) represents the equilibrium constant for the reaction where hydrogen phosphate acts as an acid: \[ \mathrm{HPO_{4}^{2-} + H_{2}O \rightleftharpoons H_{2}PO_{4}^{-} + OH^{-}} \]
• \( K_b \) represents the base-like behavior of the ion in the same type of dissociation reaction.

To predict whether a solution of hydrogen phosphate will be acidic or basic, one must compare these two values. If \( K_a > K_b \), the solution will lean towards being acidic; if \( K_b > K_a \), it will be more basic. This comparison guides chemists in predicting and controlling the pH of solutions effectively.

Weak Acid and Base

Weak acids and bases are substances that do not completely dissociate in water. This means they only partially donate or accept protons, making their reactions reversible. The hydrogen phosphate ion is a textbook example of a species that acts as both a weak acid and a weak base, which makes it an important tool in creating buffer solutions.

As a weak acid, hydrogen phosphate partially donates a proton to water, showing its reversible nature by forming its conjugate base (\( \mathrm{H_{2}PO_{4}^{-}} \)). Similarly, as a weak base, it accepts a proton from water, forming the same products and emphasizing the reversible and partial nature of the reaction.

The ability of a substance to act as both a weak acid and base allows it to resist changes in pH when small amounts of strong acids or bases are added, thereby maintaining equilibrium within a solution. This quality is particularly useful in biological and chemical systems that require a stable pH environment, such as human blood or natural waterways.