Question

Write the chemical equations and \(K_{\mathrm{a}}\) expressions for the stepwise dissociation of \(\mathrm{H}_{3} \mathrm{PO}_{4}\).

Short answer

H₃PO₄ dissociates in three steps with dissociation constants Kₐ₁, Kₐ₂, and Kₐ₃ for each step.

Step-by-step solution

Write the first dissociation equation

Phosphoric acid ( H_3PO_4 ) dissociates stepwise. In the first step, it loses one hydrogen ion to form the dihydrogen phosphate ion. The chemical equation for this is: H₃PO₄ (aq) ⇌ H₂PO₄⁻ (aq) + H⁺ (aq)

Write the first dissociation constant expression

The expression for the acid dissociation constant (K_a1) for the first dissociation is written using the concentrations of the products over the reactants. It is given by:\[ K_{a1} = \frac{[H^+][H_2PO_4^-]}{[H_3PO_4]} \]

Write the second dissociation equation

The dihydrogen phosphate ion ( H_2PO_4^- ) can further dissociate to lose another hydrogen ion, forming the hydrogen phosphate ion. The chemical equation for this step is: H₂PO₄⁻ (aq) ⇌ HPO₄²⁻ (aq) + H⁺ (aq)

Write the second dissociation constant expression

The acid dissociation constant for the second step (K_a2) is expressed similarly, using the concentrations of the new products over the reactants:\[ K_{a2} = \frac{[H^+][HPO_4^{2-}]}{[H_2PO_4^-]} \]

Write the third dissociation equation

The hydrogen phosphate ion ( HPO_4^{2-} ) can undergo a final dissociation to produce the phosphate ion. The equation for this dissociation is: HPO₄²⁻ (aq) ⇌ PO₄³⁻ (aq) + H⁺ (aq)

Write the third dissociation constant expression

The acid dissociation constant for the last dissociation step (K_a3) is given by:\[ K_{a3} = \frac{[H^+][PO_4^{3-}]}{[HPO_4^{2-}]} \]

Key concepts

Chemical Equations

Chemical equations are essential tools that help us depict chemical reactions using symbols and formulas. They provide a clear picture of how substances interact and transform during reactions. In the context of phosphoric acid dissociation, chemical equations allow us to track its stepwise dissociation into ions. Each step of dissociation can be represented using a chemical equation, which shows the reactants and products involved. For example, the dissociation of phosphoric acid (\(\text{H}_3\text{PO}_4\)) starts with forming the dihydrogen phosphate ion (\(\text{H}_2\text{PO}_4^-\)) and a hydrogen ion (\(\text{H}^+\)). This is written as: \[ \text{H}_3\text{PO}_4 (\text{aq}) \rightleftharpoons \text{H}_2\text{PO}_4^- (\text{aq}) + \text{H}^+ (\text{aq}) \] Continuing this stepwise dissociation, further equations represent the loss of additional hydrogen ions, producing different ions at each step.

Dissociation Constant

The dissociation constant, often represented as \(K_a\), is a measure of the extent of dissociation of an acid in water. It indicates how readily an acid releases its hydrogen ions in solution. Each step of an acid's dissociation has its own dissociation constant, labeled as \(K_{a1}, K_{a2},\) and so on. These constants are derived from the concentrations of the species involved in equilibrium reactions. For instance, the dissociation constant expression for the first dissociation of phosphoric acid is given by: \[ K_{a1} = \frac{[H^+][H_2PO_4^-]}{[H_3PO_4]} \] This expression implies that the acid dissociation constant is calculated by taking the product of the concentrations of the products, divided by the concentration of the reactant. Larger \(K_a\) values indicate stronger acids, which dissociate more completely, while smaller values point to weaker acids.

Phosphoric Acid

Phosphoric acid, chemically known as \(\text{H}_3\text{PO}_4\), is a polyprotic acid, meaning it can donate more than one proton or hydrogen ion. It is commonly found in cola drinks, fertilizers, and detergents. This acid dissociates in a stepwise manner, gradually losing one hydrogen ion at a time. As it loses these hydrogen ions, phosphoric acid transitions through various ionic forms, such as \(\text{H}_2\text{PO}_4^-\) and \(\text{HPO}_4^{2-}\) until it finally forms \(\text{PO}_4^{3-}\). Phosphoric acid's behavior as it dissociates in steps is key to its role in buffering applications, helping maintain stable pH levels in different systems.

Stepwise Dissociation

Stepwise dissociation refers to a multi-stage process where a compound, such as a polyprotic acid, loses its ions one at a time. This incremental release is crucial since each step is accompanied by its distinct equilibrium state and dissociation constant. In the case of phosphoric acid, stepwise dissociation involves three main stages:

• First, \(\text{H}_3\text{PO}_4\) dissociates to form \(\text{H}_2\text{PO}_4^-\).
• Second, \(\text{H}_2\text{PO}_4^-\) further dissociates to \(\text{HPO}_4^{2-}\).
• Lastly, \(\text{HPO}_4^{2-}\) transforms into \(\text{PO}_4^{3-}\).

Each stage of dissociation has its respective \(K_a\) value, which reflects the acid's strength at that particular stage. Understanding each step is crucial for predicting the behavior of acids in different chemical environments. Knowing the values for each step helps chemists determine how an acid will behave when added to solutions or react with other substances.