Acid dissociation constant
Intros
Lessons
Examples
Lessons
 Use the relationship between the K_{a} and K_{w} expressions to find an unknown K_{b} value.
 Ethanoic acid, or acetic acid CH_{3}COOH is a weak acid with K_{a} = 1.4*10^{5.1}
 Write the formula of its conjugate base.
 Find the K_{b} for its conjugate base using the relationship between K_{a}/K_{b} and K_{w}.
 Explain using the K_{a}/K_{b} expression why K_{a} and K_{b} values are not normally used when studying strong acids and bases.
^{1} Source for K_{a} acid dissociation constants: ATKINS, P. W., & DE PAULA, J. (2006). Atkins' Physical chemistry. Oxford, Oxford University Press.
 Ethanoic acid, or acetic acid CH_{3}COOH is a weak acid with K_{a} = 1.4*10^{5.1}
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Topic Notes
Introduction to Acid Dissociation Constant
The acid dissociation constant (Ka) and base dissociation constant (Kb) are fundamental concepts in chemistry, crucial for understanding the behavior of acids and bases in solution. Our introductory video provides a comprehensive overview of these constants, serving as an essential foundation for further study. This lesson aims to equip you with the knowledge to recall equilibrium ionization expressions for weak acids and bases, a skill vital for analyzing chemical reactions. You'll learn to relate Ka and Kb for conjugate acidbase pairs, understanding their inverse relationship. Additionally, we'll explore methods for calculating concentrations of aqueous ions in weak acids and bases solutions, a practical application of these concepts. By mastering these objectives, you'll gain a deeper understanding of acidbase chemistry and its realworld implications, setting the stage for more advanced topics in chemical equilibria.
Understanding Weak Acids and Bases
When it comes to understanding acids and bases, one crucial distinction lies in their strength, which is determined by their ability to dissociate in solution. Strong acids and bases undergo complete dissociation, while weak acids and bases exhibit partial dissociation. This fundamental difference has significant implications for their behavior and the mathematical expressions used to describe their properties.
Weak acids and weak bases are characterized by their partial dissociation in aqueous solutions. Unlike their strong counterparts, which completely break apart into ions, weak acids and bases only partially separate into their constituent ions. This partial dissociation is a key concept in understanding the behavior of these substances in solution.
For weak acids, the partial dissociation process can be represented by the following equilibrium:
HA H+ + A
Where HA represents the weak acid, H+ is the hydrogen ion (proton), and A is the conjugate base. Similarly, for weak bases, the partial dissociation can be expressed as:
B + H2O BH+ + OH
Where B is the weak base, BH+ is the conjugate acid, and OH is the hydroxide ion.
The concept of partial dissociation is crucial because it means that in a solution of a weak acid or base, there is a mixture of both the undissociated molecules and the dissociated ions. This equilibrium state is dynamic, with constant forward and reverse reactions occurring.
One important consequence of partial dissociation is that the Kw expression, which represents the ion product of water (Kw = [H+][OH]), cannot be directly applied to weak acids and bases. The Kw expression is based on the assumption of complete dissociation, which is not the case for weak acids and bases.
To accurately describe the behavior of weak acids and bases, we need to use different expressions: Ka for weak acids and Kb for weak bases. These expressions take into account the partial dissociation and the equilibrium that exists in the solution.
The acid dissociation constant, Ka, is defined as:
Ka = [H+][A] / [HA]
Similarly, the base dissociation constant, Kb, is expressed as:
Kb = [BH+][OH] / [B]
These expressions allow us to quantify the extent of dissociation and provide a measure of the strength of weak acids and bases. The smaller the Ka or Kb value, the weaker the acid or base, respectively.
In contrast, strong acids and bases undergo complete dissociation in aqueous solutions. For example, hydrochloric acid (HCl) completely dissociates into H+ and Cl ions in water. This complete dissociation means that the concentration of H+ ions in solution is equal to the initial concentration of the acid. Similarly, strong bases like sodium hydroxide (NaOH) completely dissociate into Na+ and OH ions.
The difference in dissociation behavior between strong and weak acids/bases has important practical implications. Strong acids and bases react more vigorously and can cause more severe chemical burns. They also have a more pronounced effect on pH, quickly changing the acidity or alkalinity of a solution. Weak acids and bases, on the other hand, have a more moderate effect on pH and are often used in buffer solutions to maintain stable pH levels.
Understanding the concept of partial dissociation and the need for Ka and Kb expressions is crucial for accurately predicting and describing the behavior of weak acids and bases in various chemical and biological systems. This knowledge is essential in fields such as environmental science, biochemistry, and pharmaceutical research, where the properties of weak acids and bases play a significant role in many processes and reactions.
Ka and Kb Expressions
Ka and Kb expressions are fundamental concepts in acidbase chemistry, providing quantitative measures of the strength of acids and bases, respectively. These expressions are closely related to the equilibrium constant (Keq) and play a crucial role in understanding the dissociation process of acids and bases in aqueous solutions.
The Ka expression, or acid dissociation constant, represents the extent to which an acid dissociates in water. For a generic acid HX, the Ka expression is:
Ka = [H+][X] / [HX]
Where [H+] is the concentration of hydronium ions, [X] is the concentration of the conjugate base, and [HX] is the concentration of the undissociated acid. The Ka value indicates the strength of an acid; a higher Ka corresponds to a stronger acid that dissociates more readily in solution.
Similarly, the Kb expression, or base dissociation constant, quantifies the strength of bases. For a generic base B, the Kb expression is:
Kb = [BH+][OH] / [B]
Here, [BH+] represents the concentration of the conjugate acid, [OH] is the hydroxide ion concentration, and [B] is the concentration of the undissociated base. A higher Kb value indicates a stronger base that accepts protons more readily.
Both Ka and Kb expressions are derived from the equilibrium constant (Keq) for the respective dissociation reactions. For acids, the dissociation process can be represented as:
HX + H2O H3O+ + X
The Ka expression is essentially the Keq for this reaction, with the concentration of water omitted as it remains constant in dilute solutions. Similarly, for bases, the reaction is:
B + H2O BH+ + OH
The Kb expression corresponds to the Keq for this reaction, again omitting the water concentration.
The significance of these expressions lies in their ability to quantify and compare the strength of acids and bases. For example, hydrochloric acid (HCl) has a Ka of approximately 10^7, indicating it is a strong acid that dissociates almost completely in water. In contrast, acetic acid (CH3COOH) has a Ka of about 1.8 × 10^5, showing it is a weak acid that dissociates only partially.
For bases, sodium hydroxide (NaOH) has a very high Kb, indicating it is a strong base that dissociates completely. Ammonia (NH3), with a Kb of about 1.8 × 10^5, is a weak base that only partially accepts protons in solution.
It's important to note that Ka and Kb are inversely related for conjugate acidbase pairs. The product of Ka and Kb for a conjugate pair is always equal to the ion product of water (Kw), which is 1.0 × 10^14 at 25°C. This relationship is expressed as:
Ka × Kb = Kw
This inverse relationship means that a strong acid will have a weak conjugate base, and vice versa. For instance, HCl (strong acid) has Cl as its conjugate base, which is an extremely weak base.
Understanding Ka and Kb expressions is crucial in various applications, including buffer solutions, pH calculations, and predicting the direction of acidbase reactions. These constants allow chemists to quantitatively assess and compare the strength of bases, providing a foundation for more complex chemical analyses and applications in fields ranging from environmental science to pharmaceutical development.
In summary, Ka and Kb expressions are powerful tools in acidbase chemistry, offering a quantitative measure of acid and base strength. They are directly related to the equilibrium constant and the dissociation process, providing valuable insights into the behavior of acids and bases in solution. By understanding these expressions, chemists can predict and control chemical reactions, design effective
Relationship Between Ka, Kb, and Kw
Understanding the relationship between Ka, Kb, and Kw is crucial in acidbase chemistry. These constants are interconnected and play a vital role in determining the strength of acids and bases. Let's explore their relationship and derive the important equation Ka * Kb = Kw.
Ka represents the acid dissociation constant, which measures the strength of an acid in solution. Kb is the base dissociation constant, indicating the strength of a base. Kw is the ion product constant of water, which remains constant at 1.0 x 10^14 at 25°C.
To derive the equation Ka * Kb = Kw, we need to consider conjugate acidbase pairs. A conjugate acidbase pair consists of two species that differ by a single proton. For example, consider the acid HA and its conjugate base A:
HA + H2O H3O+ + A
The Ka expression for this reaction is:
Ka = [H3O+][A] / [HA]
Now, let's consider the reaction of the conjugate base A with water:
A + H2O HA + OH
The Kb expression for this reaction is:
Kb = [HA][OH] / [A]
Multiplying Ka and Kb, we get:
Ka * Kb = ([H3O+][A] / [HA]) * ([HA][OH] / [A])
The [HA] and [A] terms cancel out, leaving us with:
Ka * Kb = [H3O+][OH]
We know that [H3O+][OH] = Kw, so we can conclude:
Ka * Kb = Kw
This equation demonstrates the inverse relationship between acid strength and its conjugate base strength. As Ka increases (stronger acid), Kb decreases (weaker conjugate base), and vice versa. This relationship is fundamental in understanding acidbase equilibria.
The inverse relationship between acid strength and conjugate base strength can be explained by considering the stability of the species involved. A strong acid readily donates protons, resulting in a stable conjugate base that has little tendency to accept protons. Conversely, a weak acid holds onto its protons more tightly, leading to a conjugate base that is more willing to accept protons.
This relationship allows us to calculate one value (Ka or Kb) if we know the other, using the Kw relationship. For example, if we know the Ka of an acid, we can calculate the Kb of its conjugate base:
Kb = Kw / Ka
Let's consider some examples to illustrate this concept:
1. Acetic acid (CH3COOH) has a Ka of 1.8 x 10^5. To find the Kb of its conjugate base, acetate ion (CH3COO), we can use:
Kb(CH3COO) = Kw / Ka(CH3COOH) = (1.0 x 10^14) / (1.8 x 10^5) = 5.6 x 10^10
2. The hydroxide ion (OH) has a Kb of 1.0 x 10^14. To find the Ka of its conjugate acid, water (H2O), we use:
Ka(H2O) = Kw / Kb(OH) = (1.0 x 10^14) / (1.0) = 1.0 x 10^14
These examples demonstrate how the Ka *
pKa and pKb Values
In chemistry, pKa and pKb are essential concepts used to quantify the strength of acids and bases. These logarithmic forms are particularly useful when dealing with strong acids and bases, as they provide a more manageable scale for comparison. The 'p' in pKa and pKb stands for the negative logarithm, similar to pH.
Mathematically, pKa is defined as the negative logarithm of the acid dissociation constant (Ka): pKa = log(Ka). Similarly, pKb is the negative logarithm of the base dissociation constant (Kb): pKb = log(Kb). These logarithmic forms compress the wide range of Ka and Kb values into a more practical scale, typically ranging from about 2 to 14 for pKa.
The relationship between pKa and Ka (or pKb and Kb) is inverse. A lower pKa value indicates a stronger acid, as it corresponds to a higher Ka value. Conversely, a higher pKa value suggests a weaker acid. For bases, a lower pKb value indicates a stronger base, while a higher pKb value suggests a weaker base.
Interpreting pKa and pKb values is crucial in understanding acidbase behavior. Acids with pKa values less than 0 are considered strong acids, as they dissociate completely in water. Those with pKa values between 0 and 4 are moderately strong, while acids with pKa values greater than 4 are considered weak. For bases, pKb values follow a similar pattern, with strong bases having pKb values less than 0.
Examples of common acids and their approximate pKa values include: hydrochloric acid (HCl, pKa 7), acetic acid (CHCOOH, pKa 4.76), and carbonic acid (HCO, pKa 6.4). For bases, examples include sodium hydroxide (NaOH, pKb 0.8), ammonia (NH, pKb 4.75), and methylamine (CHNH, pKb 3.36).
Understanding pKa and pKb is crucial in various fields, including biochemistry, environmental science, and pharmaceutical research. These values help predict the behavior of acids and bases in different pH environments, which is essential for understanding chemical reactions, buffer systems, and the properties of various compounds. By using the logarithmic scale, scientists can more easily compare and analyze the relative strengths of acids and bases across a wide spectrum of chemical species.
Calculating Concentrations in Weak AcidBase Solutions
Calculating concentrations of aqueous ions in weak acidbase solutions is a fundamental skill in chemistry. This process involves using Ka (acid dissociation constant) and Kb (base dissociation constant) values to solve equilibrium problems. Let's break down the steps and explore some examples to master this essential technique.
StepbyStep Guide for Weak Acid Solutions:
 Write the dissociation equation for the weak acid.
 Set up the ICE table (Initial, Change, Equilibrium).
 Express Ka in terms of equilibrium concentrations.
 Solve for the equilibrium concentration of H+ ions.
 Calculate other ion concentrations using the equilibrium expression.
Example Problem: Weak Acid
Calculate the pH and concentration of all species in a 0.1 M solution of acetic acid (CH3COOH). Ka = 1.8 × 10^5
Solution:
 CH3COOH H+ + CH3COO
 ICE table:
Initial: [CH3COOH] = 0.1 M, [H+] = [CH3COO] = 0
Change: x, +x, +x
Equilibrium: (0.1  x), x, x  Ka = [H+][CH3COO] / [CH3COOH] = x² / (0.1  x) = 1.8 × 10^5
 Assuming x « 0.1 (will verify later):
x² / 0.1 = 1.8 × 10^5
x = (1.8 × 10^6) = 1.34 × 10^3 M  [H+] = [CH3COO] = 1.34 × 10^3 M
[CH3COOH] = 0.1  1.34 × 10^3 0.0987 M
pH = log[H+] = 2.87
StepbyStep Guide for Weak Base Solutions:
 Write the dissociation equation for the weak base.
 Set up the ICE table.
 Express Kb in terms of equilibrium concentrations.
 Solve for the equilibrium concentration of OH ions.
 Calculate other ion concentrations and pH.
Example Problem: Weak Base
Calculate the pH and concentration of all species in a 0.05 M solution of ammonia (NH3). Kb = 1.8 × 10^5
Solution:
 NH3 + H2O NH4+ + OH
 ICE table:
Initial: [NH3] = 0.05 M, [NH4+] = [OH] = 0
Change: x, +x, +x
Equilibrium: (0.05  x), x, x  Kb = [NH4+][OH] / [NH3] = x² / (0.05  x) = 1.8 × 10^5
 Assuming x « 0.05:
x² / 0Conclusion
In this article, we've explored the crucial concepts of Ka and Kb in understanding weak acidbase behavior. These constants play a pivotal role in determining the strength and dissociation of acids and bases, providing essential insights into their chemical properties. The introductory video served as a valuable visual and auditory foundation, helping to solidify these abstract concepts. We've discussed how Ka and Kb relate to equilibrium constants, pH calculations, and buffer solutions. Understanding these principles is fundamental for students and professionals alike in the field of chemistry. We encourage readers to apply these concepts in problemsolving scenarios, such as predicting acidbase reactions or calculating pH values. Further exploration of acidbase chemistry will undoubtedly enhance your comprehension of chemical processes in various scientific and industrial applications. Remember, mastering Ka and Kb is key to unlocking a deeper understanding of acidbase equilibria and their wideranging implications in chemistry.
Understanding Acid and Base Dissociation Constants
What is the acid/base dissociation constant? From K_{w} to K_{a} and K_{b}.
Step 1: Introduction to Acid and Base Dissociation Constants
The acid dissociation constant (K_{a}) and the base dissociation constant (K_{b}) are fundamental concepts in chemistry that describe the extent to which acids and bases dissociate in water. These constants are crucial for understanding the behavior of weak acids and bases in aqueous solutions.
K_{a} represents the equilibrium constant for the dissociation of a weak acid into its conjugate base and a proton (H^{+}). Similarly, K_{b} represents the equilibrium constant for the dissociation of a weak base into its conjugate acid and a hydroxide ion (OH^{}).
Step 2: Recap of the Ionic Product of Water (K_{w})
Before diving into K_{a} and K_{b}, it's essential to recall the concept of the ionic product of water, denoted as K_{w}. The autoionization of water can be represented by the equilibrium:
H_{2}O H^{+} + OH^{}
The equilibrium constant for this reaction is K_{w}, which is equal to 1.0 x 10^{14} at 25°C. This means that the product of the concentrations of hydrogen ions and hydroxide ions in pure water is always 1.0 x 10^{14} at this temperature.
Step 3: Relationship Between K_{a} and K_{b}
For a conjugate acidbase pair, there is a direct relationship between K_{a} and K_{b}. This relationship can be derived from the fact that the product of the concentrations of H^{+} and OH^{} is always equal to K_{w}.
For a weak acid (HA) dissociating in water:
HA H^{+} + A^{}
The equilibrium constant for this reaction is K_{a}.
For the conjugate base (A^{}) reacting with water:
A^{} + H_{2}O OH^{} + HA
The equilibrium constant for this reaction is K_{b}.
The relationship between K_{a} and K_{b} can be expressed as:
K_{a} x K_{b} = K_{w}
This equation shows that the product of the acid dissociation constant and the base dissociation constant for a conjugate acidbase pair is equal to the ionic product of water.
Step 4: Calculating Concentrations in Weak AcidBase Solutions
To calculate the concentrations of ions in weak acid or base solutions, we use the expressions for K_{a} and K_{b}. For a weak acid (HA), the expression for K_{a} is:
K_{a} = [H^{+}][A^{}] / [HA]
For a weak base (B), the expression for K_{b} is:
K_{b} = [OH^{}][BH^{+}] / [B]
These expressions allow us to calculate the concentrations of the ions in solution, given the initial concentration of the weak acid or base and the value of K_{a} or K_{b}.
Step 5: Practical Applications and Examples
Understanding K_{a} and K_{b} is essential for various practical applications, such as calculating the pH of solutions, predicting the direction of acidbase reactions, and designing buffer solutions. For example, if we know the K_{a} of acetic acid, we can calculate the pH of a solution of acetic acid by determining the concentration of H^{+} ions.
Similarly, knowing the K_{b} of ammonia allows us to calculate the pH of an ammonia solution by determining the concentration of OH^{} ions.
Conclusion
In summary, the acid dissociation constant (K_{a}) and the base dissociation constant (K_{b}) are crucial for understanding the behavior of weak acids and bases in aqueous solutions. These constants are related to the ionic product of water (K_{w}) and are essential for calculating the concentrations of ions in solution. By mastering these concepts, we can better understand and predict the behavior of acids and bases in various chemical contexts.
FAQs

What is the base dissociation constant KB?
The base dissociation constant (Kb) is a measure of how completely a base dissociates in an aqueous solution. It quantifies the strength of a base by indicating its ability to produce hydroxide ions (OH) when dissolved in water. A larger Kb value indicates a stronger base.

What is the formula for the dissociation constant of a base?
For a base B that dissociates in water according to the equation B + H2O BH+ + OH, the formula for Kb is:
Kb = [BH+][OH] / [B]
Where [BH+], [OH], and [B] represent the equilibrium concentrations of the conjugate acid, hydroxide ion, and undissociated base, respectively.

Does a higher KB mean stronger base?
Yes, a higher Kb value indicates a stronger base. Bases with larger Kb values dissociate more completely in water, producing more hydroxide ions. For example, a base with Kb = 1 × 10^3 is stronger than a base with Kb = 1 × 10^5.

What is the base dissociation equation?
The general base dissociation equation is:
B + H2O BH+ + OH
Where B is the base, BH+ is the conjugate acid, and OH is the hydroxide ion. This equation represents the equilibrium established when a base dissolves in water.

How are Ka and Kb related for conjugate acidbase pairs?
For a conjugate acidbase pair, Ka and Kb are inversely related. Their product is equal to the ion product of water (Kw):
Ka × Kb = Kw = 1.0 × 10^14 (at 25°C)
This relationship means that if an acid is strong (high Ka), its conjugate base will be weak (low Kb), and vice versa.
Prerequisite Topics
Understanding the acid dissociation constant (Ka) is crucial in chemistry, but to fully grasp this concept, it's essential to have a solid foundation in certain prerequisite topics. Two key areas that significantly contribute to comprehending acid dissociation constants are strong and weak acids and bases and the relationship between two variables.
Firstly, a thorough understanding of weak acids and bases is fundamental to grasping the concept of acid dissociation constants. The Ka value is directly related to the strength of an acid, indicating how readily it dissociates in water. Strong acids have large Ka values, while weak acids have smaller ones. By familiarizing yourself with the characteristics and behaviors of strong and weak acids, you'll be better equipped to interpret and apply Ka values in various chemical scenarios.
Moreover, the acid dissociation constant is intrinsically linked to equilibrium concepts in chemistry. Understanding how weak acids partially dissociate in solution and reach a state of dynamic equilibrium is crucial for comprehending Ka. This knowledge allows you to predict the extent of dissociation and calculate important parameters such as pH and concentration of species in solution.
Secondly, the relationship between two variables plays a significant role in understanding acid dissociation constants. In chemistry, this concept is particularly important when considering the relationship between Ka, Kb, and Kw. These constants are interconnected, and understanding how they relate to each other is crucial for solving problems involving acidbase equilibria.
For instance, the product of Ka and Kb for a conjugate acidbase pair is always equal to Kw, the ion product constant of water. This relationship allows chemists to calculate one constant if the other is known. Additionally, understanding how these variables relate to each other helps in predicting the behavior of acids and bases in different solutions and at varying concentrations.
By mastering these prerequisite topics, you'll develop a strong foundation for understanding acid dissociation constants. This knowledge will enable you to solve complex problems involving acidbase equilibria, predict chemical behaviors, and apply these concepts in realworld scenarios. Whether you're studying buffer solutions, titrations, or more advanced topics in chemistry, a solid grasp of these fundamental concepts will prove invaluable.
In conclusion, taking the time to thoroughly understand strong and weak acids and bases and the relationship between variables will significantly enhance your ability to work with acid dissociation constants. These prerequisite topics provide the necessary context and mathematical framework to fully appreciate the role of Ka in chemistry and its applications in various chemical processes.
In this lesson, we will learn:
 To recall the equilibrium ionization expressions for weak acids and bases.
 How to relate K_{a} and K_{b} for conjugate acid/base pairs.
 How to calculate concentration of aqueous ions in weak acid/base solutions.
Notes:
 In Autoionization of water, we looked at the equilibrium:
2 H_{2}O_{(l)} $\, \rightleftharpoons \,$ H_{3}O^{+} _{(aq)} + OH^{} _{(aq)}
The equilibrium constant was expressed as:K_{w} = [H_{3}O^{+}] [OH^{}] = 1 * 10 ^{14} at 25^{o}C
We saw the effect of adding strong acids/bases to equilibrium concentrations of water and dissolved ions. That was straightforward because strong acids and bases experience 100% dissociation in water.
We also saw in  In strong and weak acids and bases that weak acids and bases do not experience 100% dissociation. This makes expressions for their dissociation in water more complicated.
 Every weak acid has an acid dissociation constant, K_{a} and a weak base a base dissociation constant, K_{b}. These are equilibrium constants showing how much the acid/base dissociates when dissolved in water (aqueous solution).
For a weak acid HX dissolved in water:K_{a} = $\frac{[H_3O^{+}] [X^{}]}{[HX]}$
For a weak base B dissolved in water:K_{b} = $\frac{[HB^{+}] [OH^{}]}{[B]}$
 Just like in the ionization of water and other equilibria; this is an equilibrium constant expression. This means that the higher the K_{a}/K_{b} value, the greater the degree of dissociation (because the concentrations of the dissociated ions, in the numerator, are larger values) and therefore the stronger the acid or base.
 Remember that for strong acids and bases K_{a}/K_{b} values are not normally used. This is because in the K_{a} expression, their [HX] or [B] is equal to or almost zero due to complete dissociation, so the values are incredibly large.
 For strong acids, pK_{a} is used instead of K_{a}. pK_{a} is the negative logarithm of the K_{a} value and is more appropriate to use for strong acids, instead of the extremely large K_{a} values they have.
 In Conjugate acids and bases, we learned in a conjugate pair that a stronger conjugate acid will have a weaker the conjugate base. This relationship affects the concentration of aqueous ions and therefore affects the K_{a} and K_{b} values for a conjugate acid/base pair!
Consider the equations for the conjugate pair acidbase pair HX and X^{}:Conjugate acid: $\qquad$ HX + H_{2}O $\, \rightleftharpoons \,$ X^{} + H_{3}O^{+} $\qquad$ K_{a} = $\frac{[H_3O^{+}] [X^{}]}{[HX]}$ Conjugate base: $\qquad$ X^{} + H_{2}O $\, \rightleftharpoons \,$ HX + OH^{} $\qquad$ K_{b} = $\frac{[HX] [OH^{}]}{[X^{}]}$
 Both equations depend on [X^{}] and [HX] so K_{a} and K_{b} themselves can be related, and terms cancelled out:
As you can see, the result is the product of [H_{3}O^{+}] and [OH^{}] which is the expression for K_{w}. Therefore for a conjugate pair:K_{a} * K_{b} = K_{w}
 Both equations depend on [X^{}] and [HX] so K_{a} and K_{b} themselves can be related, and terms cancelled out:
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