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In this article, we will be learning about the different types of **dissociation constant**: what they are, what they mean, and how to calculate them

- This article covers the
**dissociation constant.** - First, we will define what the dissociation constant is and what it measures.
- Then, we will look at the
**dissociation constant (K**_{d}). - Next, we will cover the
**Acid Dissociation Constant (K**and the_{a})**base dissociation constant**(K_{b}). and see how they measure the strength of their respective species. - Lastly, we will learn about the
**water dissociation constant (K**_{w}).

## Define Dissociation Constant

A **dissociation constant **is a type of **equilibrium constant** that measure the tendency of a species to dissociate (separate) into smaller components.

**Dissociation constant**are

**Equilibrium Constants**, so they tell us which "side" of the equilibrium is favored. If the dissociation constant is large (>1), it means that products are favored (i.e. the dissociation is favored). However, if the dissociation constant is small (<1), it means that the reactant is favored (i.e. the species tends not to dissociate)There are several types of dissociation constants that we will be discussing today. These are: 1) The general dissociation constant: K

_{d.}2) The Acid Dissociation Constant: K

_{a.}3) The base dissociation constant: K

_{b.}4) The water dissociation constant: K

_{w.}

## Dissociation Constant Kd

The **dissociation constant (K _{d}) **measures the

**tendency**of a species to break up into its components.

For a general dissociation:

$$A_aB_b \rightleftharpoons aA + bB$$

The formula for the dissociation constant is:

$$K_d=\frac{[A]^a[B]^b}{[A_aB_a]}$$

Where [A] is the Concentration of species A, [B] is the concentration of species B, [A_{a}B_{b}] is the Concentration of species A_{a}B_{a}, and K_{d} is the dissociation constant

The dissociation constant can be used for things like the dissociation of a **coordination complex **(compound with a metal center bonded to several other species called **ligands**) or the dissociation of a salt.

For example, here is the dissociation of [Ag(NH_{3})_{2}]^{+} (a coordination complex):

$$ Ag(NH_3)_2^+ \rightleftharpoons Ag^+ + 2NH_3$$

$$K_d=\frac{[Ag^+][NH_3]^2}{[Ag(NH_3)_2^+]}$$

And here is the dissociation of NaCl (a salt):

$$NaCl \rightleftharpoons Na^+ + Cl^-$$

$$K_d=\frac{[Na^+][Cl^-]}{[NaCl]}$$

## Acid Dissociation Constant

The **acid dissociation constant (K _{a})** measures the strength of an acid.

The **conjugate base **is the species that **results **from the **losing its proton** (and can now act as a base).

**two ways**.

**1) Water is included**For a general dissociation:$$HA_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + A^-_{(aq)}$$Where HA is our acid and A

^{-}is our conjugate baseThe equation for K

_{a}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 and [HA] is the concentration of the acid

Liquids (and solids) are not included in Equilibrium Constants, so water is left out

**2) Water is excluded**For a general dissociation:$$HA_{(aq)} \rightleftharpoons H^+_{(aq)} + A^-_{(aq)} The equation for K

_{a}is:$$K_a=\frac{[H^+][A^-]}{[HA]}$$K

_{a}measures the strength of an acid. The larger the K

_{a}, the stronger the acid, since there is a higher concentration of H

^{+}/H

_{3}O

^{+}ions.

Here, concentration (our y-axis) is measured in molarity (moles/liter).

Weak acids tend to only partially dissociation, meaning there is a smaller concentration of these ions compared to stronger acids.

pH is equal to -log[H^{+}] or -log[H_{3}O^{+}], meaning that a greater concentration of these ions indicates a strong acid (low pH number=very acidic)

Below is a table showing some acids and their dissociation constant values from strongest to weakest:

Name of Acid | K_{a} value |

Hydroiodic acid (HI) | 2x10^{9} |

Sulfuric acid (H_{2}SO_{4}) | 1x10^{2} |

Nitric acid (HNO_{3}) | 2.3x10^{1} |

Hydrofluoric acid (HF) | 6.3x10^{-4} |

Nitrous acid (HNO_{2}) | 5.6x10^{-4} |

Formic acid (HCO_{2}H) | 1.78x10^{-4} |

Generally, strong acids are those that have a K_{a}>1, since they dissociate completely.

## Base Dissociation Constant

The **base dissociation constant (K _{b}) **measures the strength of a base

The **conjugate acid **is the species that results from the base gaining a proton (and can now act as an acid)

Like with the acid dissociation constant, there are two ways to write it:

1) Water is included

For a general dissociation:

$$B_{(aq)} + H_2O_{(l)} \rightleftharpoons BH^+_{(aq)} + OH^-_{(aq)}$$

Where B is our base and BH^{+} is our conjugate acid

The equation for K_{b} is:

$$K_b=\frac{[BH^+][OH^-]}{[B]}$$

Where [BH^+] is the concentration of the conjugate acid, [OH^{-}] is the concentration of the hydroxide ion, and [B] is the concentration of the base

2) Water is excluded

For a general dissociation:

$$BOH_{(aq)} \rightleftharpoons B^+_{(aq)} + OH^-_{(aq)}$$

Where BOH is our base and B^+ is the conjugate acid

The equation for K_{b }is:

$$K_b=\frac{[B^+][OH^-]}{[BOH]}$$

Like with K_{a}, the magnitude of K_{b} determines a base's strength. However, instead of the strength coming from the concentration of H^{+}/H_{3}O^{+}, it instead comes from the concentration of OH^{-}.

Here is a table with some common bases and their K_{b} values:

Name of Base | K_{b} value |

Lithium hydroxide (LiOH) | 2.29x10^{0} |

Potassium hydroxide (KOH) | 3.16x10^{-1} |

Sodium hydroxide (NaOH) | 6.31x10^{-1} |

Ammonia (NH_{3}) | 1.77x10^{-5} |

Ammonium hydroxide (NH_{4}OH) | 1.79x10^{-5} |

Pyridine (C_{5}H_{5}N) | 1.78x10^{-9} |

## Water Dissociation Constant

The **water dissociation constant (K _{w}) **describes how water dissociates into its ions

_{w}is:$$K_w=[OH^-][H^+]$$Where [OH

^{-}] is the concentration of the hydroxide ion and [H

^{+}] is the concentration of the hydrogen ionThe value of K

_{w}is dependent on temperature. The standard value (at room temperature, which is ~25°C) is 1.00·10

^{-14}.Below is a table of K

_{w }values based on temperature:

Temperature (°C) | K_{w} |

10 | 0.29x10^{-14} |

15 | 0.45x10^{-14} |

20 | 0.69x10^{-14} |

25 | 1.01x10^{-14} |

30 | 1.47x10^{-14} |

Based on this, we can see that an increase in temperature causes an increase in dissociation

K_{w} and acid/base strength

For any acid/base pair:

$$K_a*K_b=K_w$$

Because of this, this can tell us two things:

- We can calculate K
_{a}when given K_{b}and vice versa - The strength of the acid and conjugate base are
*inversely related*

If an acid is very strong, this means that its conjugate base will be weak and vice versa. For example, take hydroiodic acid (K_{a}=2x10^{9}):

$$K_w=K_a*K_b$$

$$K_b=\frac{K_w}{K_a}$$

$$K_b=\frac{1x10^{-14}}{2x10^9}$$

$$K_b=5x10^{-24}$$

Therefore, the conjugate base, iodide (I^{-}) is a *very *weak base

## Dissociation Constant - Key takeaways

- A
**dissociation constant**is a type of equilibrium constant that measure the tendency of a species to dissociate (separate) into smaller components - The dissociation constant (K
_{d}) measures the tendency of a species to break up into its components.- For a general dissociation:
$$A_aB_b \rightleftharpoons aA + bB$$

The formula for the dissociation constant is:

$$K_d=\frac{[A]^a[B]^b}{[A_aB_a]}$$

- For a general dissociation:
The acid dissociation constant (K

_{a}) measures the strength of an acidFor a general dissociation:$$HA_{(aq)} \rightleftharpoons H^+_{(aq)} + A^-_{(aq)}The equation for K

_{a}is:$$K_a=\frac{[H^+][A^-]}{[HA]}$$

The

**base dissociation constant (K**measures the strength of a base_{b})- For a general dissociation:
$$BOH_{(aq)} \rightleftharpoons B^+_{(aq)} + OH^-_{(aq)}$$

The equation for K

_{b }is:$$K_b=\frac{[B^+][OH^-]}{[BOH]}$$

- For a general dissociation:
The

**water dissociation constant (K**describes how water dissociates into its ions_{w})The dissociation reaction is:$$H_2O \rightleftharpoons OH^- + H^+$$So the formula for K

_{w}is:$$K_w=[OH^-][H^+]$$

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##### Frequently Asked Questions about Dissociation Constant

What is the equation for the acid dissociation constant?

For a general dissociation:

HA <--> A^{-} + H^{+}

The equation is:

K_{a}=[A^{-}][H^{+}]/[HA]

What does dissociation constant mean?

A **dissociation constant **is a type of equilibrium constant that measure the tendency of a species to dissociate (separate) into smaller components

What is the dissociation constant of water?

The **water dissociation constant (K _{w}) **describes how water dissociates into its ions

At room temperature, K_{w}=1x10^{-14}

How to find the dissociation constant?

The dissociation constant is equal to the concentration of the products (raised to their coefficients) divided by the concentration of the reactant

How to calculate kd dissociation constant?

For a general dissociation:

A_{x}B_{y} <--> xA + yB

The dissociation constant (K_{d}) is:

K_{d}=[A]^{x}[B]^{y}/[A_{x}B_{y}]

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