The acid dissociation constant (K_a) for the ammonium ion (NH₄⁺) is 5 × 10⁻¹⁰. This value is derived from the base dissociation constant of its conjugate base, ammonia (NH₃).
Understanding Ammonium Dissociation
Ammonium (NH₄⁺) is the conjugate acid of ammonia (NH₃). When we refer to the "dissociation constant" of ammonium, we are specifically interested in its acid dissociation constant (K_a). This constant quantifies the extent to which ammonium ions donate a proton (H⁺) when dissolved in water.
- Ammonia (NH₃): A weak base that accepts a proton from water, forming ammonium and hydroxide ions.
NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq) - Ammonium (NH₄⁺): A weak acid that donates a proton to water, forming ammonia and hydronium ions.
NH₄⁺(aq) + H₂O(l) ⇌ NH₃(aq) + H₃O⁺(aq)
The Relationship Between Ammonia and Ammonium
The acid dissociation constant (K_a) of an acid and the base dissociation constant (K_b) of its conjugate base are intrinsically linked through the ion product of water (K_w). At 25°C, the value of K_w is 1.0 × 10⁻¹⁴.
The relationship is expressed as:
K_a × K_b = K_w
Calculating Ammonium's Acid Dissociation Constant (K_a)
To determine the K_a of ammonium, we utilize the known base dissociation constant (K_b) of ammonia. The base dissociation constant (K_b) of ammonia is 2 × 10⁻⁵.
Here's how the calculation is performed:
-
Identify the K_b of ammonia:
K_b (for NH₃) = 2 × 10⁻⁵ -
Recall the ion product of water (K_w):
K_w = 1.0 × 10⁻¹⁴ (at 25°C)
(For more information on the autoionization of water, you can refer to sources like Wikipedia.) -
Apply the relationship to find K_a:
K_a = K_w / K_b -
Perform the calculation:
K_a = (1.0 × 10⁻¹⁴) / (2 × 10⁻⁵)
K_a = 0.5 × 10⁻⁹
K_a = 5 × 10⁻¹⁰
Summary of Constants
The following table summarizes the key equilibrium constants involved:
| Constant | Value | Description |
|---|---|---|
| K_b (Ammonia) | 2 × 10⁻⁵ | Base dissociation constant of NH₃ |
| K_w | 1.0 × 10⁻¹⁴ | Ion product of water (at 25°C) |
| K_a (Ammonium) | 5 × 10⁻¹⁰ | Acid dissociation constant of NH₄⁺ |
Significance of the K_a Value
A K_a value of 5 × 10⁻¹⁰ is quite small. This indicates that ammonium is a weak acid, meaning it does not readily dissociate into hydrogen ions and ammonia in water. The equilibrium heavily favors the intact ammonium ion rather than its dissociated products. Understanding these constants is fundamental in studying acid-base equilibria in chemistry.
(For a deeper dive into acid-base equilibrium, resources like Khan Academy can be helpful.)
