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Dissociation Constant

Q: What is the equation for the acid dissociation constant?

For a general dissociation: HA <--> A - + H + The equation is: K a =[A - ][H + ]/[HA]

Q: 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

Q: 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

Q: 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 ]

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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True or False: Dissociation is irreversible

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For the dissociation below, write the expression for Kd: $A_{a} B_{b} ⇌ a A + b B$

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Is acetic acid a strong acid?Ka=1.8x10-5

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Which of the following is a valid expression for Ka?

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Which of the following are valid Kb expressions?

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What is the standard value for Kw?

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True or False: Kb and Ka for an acid/base pair are directly related (when one increases, so does the other)

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What is the expression for Kw?

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Which of the following are valid Kb expressions?

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What is the standard value for Kw?

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True or False: Kb and Ka for an acid/base pair are directly related (when one increases, so does the other)

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What is the expression for Kw?

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True or False: Dissociation is irreversible

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For the dissociation below, write the expression for Kd: $A_{a} B_{b} ⇌ a A + b B$

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Is acetic acid a strong acid?Ka=1.8x10-5

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Which of the following is a valid expression for Ka?

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Last Updated: 01.12.2023
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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_a) and the 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).

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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:

Dissociation Constant Example of dissociation StudySmarter

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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: 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:

$A_{a} B_{b} ⇌ a A + b B$

The formula for the dissociation constant is:

$K_{d} = \frac{[A]^{a} [B]^{b}}{[A_{a} B_{a}]}$

Where [A] is the Concentration of species A, [B] is the concentration of species B, [A_aB_b] is the Concentration of species A_aB_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(NH₃)₂]⁺ (a coordination complex):

$A g (N H_{3})_{2}^{+} ⇌ A g^{+} + 2 N H_{3}$

$K_{d} = \frac{[A g^{+}] [N H_{3}]^{2}}{[A g (N H_{3})_{2}^{+}]}$

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

$N a C l ⇌ N a^{+} + C l^{-}$

$K_{d} = \frac{[N a^{+}] [C l^{-}]}{[N a C l]}$

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).

The acid dissociation can be written one of two ways. 1) Water is includedFor a general dissociation:

H A_{(a q)} + H_{2} O_{(l)} ⇌ H_{3} O_{(a q)}^{+} + A_{(a q)}^{-}

Where HA is our acid and A^- is our conjugate baseThe equation for K_a is:

K_{a} = \frac{[H_{3} O^{+}] [A^{-}]}{[H A]}

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 K_a is:

K_{a} = \frac{[H^{+}] [A^{-}]}{[H A]}

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⁺/H₃O⁺ ions.

Dissociation Constant Dissociation of stong vs weak acid StudySmarter

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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	K_a 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 K_a>1, since they dissociate completely.

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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:

$B_{(a q)} + H_{2} O_{(l)} ⇌ B H_{(a q)}^{+} + O H_{(a q)}^{-}$

Where B is our base and BH⁺ is our conjugate acid

The equation for K_b is:

$K_{b} = \frac{[B H^{+}] [O H^{-}]}{[B]}$

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:

$B O H_{(a q)} ⇌ B_{(a q)}^{+} + O H_{(a q)}^{-}$

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

The equation for K_bis:

$K_{b} = \frac{[B^{+}] [O H^{-}]}{[B O H]}$

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⁺/H₃O⁺, 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)	2.29x10⁰
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 (K_w) describes how water dissociates into its ions

The dissociation reaction is:

H_{2} O ⇌ O H^{-} + H^{+}

So the formula for K_w is:

K_{w} = [O H^{-}] [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_wvalues 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=2x10⁹):

$K_{w} = K_{a} * K_{b}$

$K_{b} = \frac{K_{w}}{K_{a}}$

$K_{b} = \frac{1 x 10^{- 14}}{2 x 10^{9}}$

$K_{b} = 5 x 10^{- 24}$

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:
  $A_{a} B_{b} ⇌ a A + b B$
  The formula for the dissociation constant is:
  $K_{d} = \frac{[A]^{a} [B]^{b}}{[A_{a} B_{a}]}$
The acid dissociation constant (K_a) measures the strength of an acid
- For a general dissociation:$$HA_{(aq)} \rightleftharpoons H^+_{(aq)} + A^-_{(aq)}The equation for K_a is: $K_{a} = \frac{[H^{+}] [A^{-}]}{[H A]}$
The base dissociation constant (K_b) measures the strength of a base
- For a general dissociation:
  $B O H_{(a q)} ⇌ B_{(a q)}^{+} + O H_{(a q)}^{-}$
  The equation for K_bis:
  $K_{b} = \frac{[B^{+}] [O H^{-}]}{[B O H]}$
The water dissociation constant (K_w) describes how water dissociates into its ions
- The dissociation reaction is: $H_{2} O ⇌ O H^{-} + H^{+}$ So the formula for K_w is: $K_{w} = [O H^{-}] [H^{+}]$

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True or False: Dissociation is irreversible

False

For the dissociation below, write the expression for K_d:

$A_{a} B_{b} ⇌ a A + b B$

$K_{d} = \frac{[A]^{a} [B]^{b}}{[A_{a} B_{b}]}$

Is acetic acid a strong acid?

K_a=1.8x10^-5

Which of the following is a valid expression for K_a?

$K_{a} = \frac{[H_{3} O^{+}] [A^{-}]}{[H A]}$

Which of the following are valid K_b expressions?

$K_{b} = \frac{[B H^{+}] [O H^{-}]}{[B]}$

What is the standard value for K_w?

1x10^-14

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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_xB_y <--> xA + yB

The dissociation constant (K_d) is:

K_d=[A]^x[B]^y/[A_xB_y]

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