# Dissociation Constant

Imagine you are boiling some water for pasta. When you pour in salt and stir, the salt begins to disappear. Well, it isn't actually disappearing, instead, it is dissociating (meaning it is breaking down into its ions). However, if you were to accidentally completely boil off the water (for example, you were too busy studying and forgot about it), the salt would reappear.

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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

• First, we will define what the dissociation constant is and what it measures.
• Then, we will look at the dissociation constant (Kd).
• Next, we will cover the Acid Dissociation Constant (Ka) and the base dissociation constant (Kb). and see how they measure the strength of their respective species.
• Lastly, we will learn about the water dissociation constant (Kw).

## 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.

These dissociation reactions are reversible, meaning the original species can be restored. For example, see the dissociation below of Gomberg's dimer:

Fig.1-Gomberg's dimer dissociates into two halves

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: Kd. 2) The Acid Dissociation Constant: Ka.3) The base dissociation constant: Kb.4) The water dissociation constant: Kw.

## Dissociation Constant Kd

The dissociation constant (Kd) 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, [AaBb] is the Concentration of species AaBa, and Kd 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(NH3)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 (Ka) 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).

The acid dissociation can be written one of two ways. 1) Water is includedFor 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 Ka 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 excludedFor a general dissociation:$$HA_{(aq)} \rightleftharpoons H^+_{(aq)} + A^-_{(aq)} The equation for Ka is:$$K_a=\frac{[H^+][A^-]}{[HA]}$$Ka measures the strength of an acid. The larger the Ka, the stronger the acid, since there is a higher concentration of H+/H3O+ ions. Fig.2-Comparison of strong vs. weak acid dissociation Here, concentration (our y-axis) is measured in molarity (moles/liter). Weak acids tend to only partially dissociation, meaning there is a smaller concentration of these ions compared to stronger acids. pH is equal to -log[H+] or -log[H3O+], meaning that a greater concentration of these ions indicates a strong acid (low pH number=very acidic) Below is a table showing some acids and their dissociation constant values from strongest to weakest:  Name of Acid Ka value Hydroiodic acid (HI) 2x109 Sulfuric acid (H2SO4) 1x102 Nitric acid (HNO3) 2.3x101 Hydrofluoric acid (HF) 6.3x10-4 Nitrous acid (HNO2) 5.6x10-4 Formic acid (HCO2H) 1.78x10-4 Generally, strong acids are those that have a Ka>1, since they dissociate completely. ## Base Dissociation Constant The base dissociation constant (Kb) measures the strength of a base The conjugate acid is the species that results from the base gaining a proton (and can now act as an acid) Like with the acid dissociation constant, there are two ways to write it: 1) Water is included For a general dissociation:$$B_{(aq)} + H_2O_{(l)} \rightleftharpoons BH^+_{(aq)} + OH^-_{(aq)}$$Where B is our base and BH+ is our conjugate acid The equation for Kb is:$$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)}$$Where BOH is our base and B^+ is the conjugate acid The equation for Kb is:$$K_b=\frac{[B^+][OH^-]}{[BOH]}$$Like with Ka, the magnitude of Kb determines a base's strength. However, instead of the strength coming from the concentration of H+/H3O+, it instead comes from the concentration of OH-. Here is a table with some common bases and their Kb values:  Name of Base Kb value Lithium hydroxide (LiOH) 2.29x100 Potassium hydroxide (KOH) 3.16x10-1 Sodium hydroxide (NaOH) 6.31x10-1 Ammonia (NH3) 1.77x10-5 Ammonium hydroxide (NH4OH) 1.79x10-5 Pyridine (C5H5N) 1.78x10-9 ## Water Dissociation Constant The water dissociation constant (Kw) describes how water dissociates into its ions The dissociation reaction is:$$H_2O \rightleftharpoons OH^- + H^+$$So the formula for Kw is:$$K_w=[OH^-][H^+]$$Where [OH-] is the concentration of the hydroxide ion and [H+] is the concentration of the hydrogen ionThe value of Kw is dependent on temperature. The standard value (at room temperature, which is ~25°C) is 1.00·10-14.Below is a table of Kw values based on temperature:  Temperature (°C) Kw 10 0.29x10-14 15 0.45x10-14 20 0.69x10-14 25 1.01x10-14 30 1.47x10-14 Based on this, we can see that an increase in temperature causes an increase in dissociation Kw and acid/base strength For any acid/base pair:$$K_a*K_b=K_w$$Because of this, this can tell us two things: 1. We can calculate Ka when given Kb and vice versa 2. The strength of the acid and conjugate base are inversely related If an acid is very strong, this means that its conjugate base will be weak and vice versa. For example, take hydroiodic acid (Ka=2x109):$$K_w=K_a*K_bK_b=\frac{K_w}{K_a}K_b=\frac{1x10^{-14}}{2x10^9}K_b=5x10^{-24}$$Therefore, the conjugate base, iodide (I-) is a very weak base ## Dissociation Constant - Key takeaways • A dissociation constant is a type of equilibrium constant that measure the tendency of a species to dissociate (separate) into smaller components • The dissociation constant (Kd) measures the tendency of a species to break up into its components. • For a general dissociation:$$A_aB_b \rightleftharpoons aA + bB$$The formula for the dissociation constant is:$$K_d=\frac{[A]^a[B]^b}{[A_aB_a]}$$• The acid dissociation constant (Ka) measures the strength of an acid • For a general dissociation:$$HA_{(aq)} \rightleftharpoons H^+_{(aq)} + A^-_{(aq)}The equation for Ka is:$$K_a=\frac{[H^+][A^-]}{[HA]}$$

• The base dissociation constant (Kb) measures the strength of a base

• For a general dissociation:

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

The equation for Kb is:

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

• The water dissociation constant (Kw) describes how water dissociates into its ions

• The dissociation reaction is:$$H_2O \rightleftharpoons OH^- + H^+$$So the formula for Kw is:$$K_w=[OH^-][H^+]$$

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What is the equation for the acid dissociation constant?

For a general dissociation:

HA <--> A- + H+

The equation is:

Ka=[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 (Kwdescribes how water dissociates into its ions

At room temperature, Kw=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:

AxBy <--> xA + yB

The dissociation constant (Kd) is:

Kd=[A]x[B]y/[AxBy]

## Test your knowledge with multiple choice flashcards

True or False: Dissociation is irreversible

For the dissociation below, write the expression for Kd:$$A_aB_b \rightleftharpoons aA + bB$$

Which of the following is a valid expression for Ka?

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