Relationship between Ka and Kb | Chemistry | Khan Academy

Khan Academy Organic Chemistry
10 Aug 201411:20
EducationalLearning
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TLDRThe video script discusses the concept of conjugate acid-base pairs, focusing on NH4+ and NH3 as an example. It explains how these molecules react with water, forming H3O+ and OH-, and how their Ka and Kb values relate to the auto-ionization constant of water (Kw). The script further illustrates the inverse relationship between the strength of an acid and the weakness of its conjugate base, using HCl and Cl- as an example. It also demonstrates how to calculate Ka and pKa values from given Kb, and vice versa, for a weak base like methylamine.

Takeaways
  • 📚 NH4+ and NH3 are a conjugate acid-base pair, with NH4+ acting as an acid and NH3 as a weak base.
  • 💧 The Ka for the reaction of NH4+ donating a proton to water is 5.6 x 10^-10.
  • 🔄 NH3 takes a proton from water to form NH4+ and OH-, with a Kb of 1.8 x 10^-5.
  • ➡️ When combining the reactions of NH4+ and NH3, the net reaction is the auto-ionization of water, producing H3O+ and OH- with an equilibrium constant Kw of 1.0 x 10^-14.
  • 🔢 The product of Ka and Kb for a conjugate acid-base pair equals Kw, which is a fundamental relationship in acid-base chemistry.
  • 📈 The stronger the acid (higher Ka), the weaker the conjugate base (lower Kb), and vice versa.
  • 🧪 For strong acids like HCl, Ka is extremely high, and the conjugate base (Cl-) has a very low Kb, making it a weak base.
  • 📝 The pKa is calculated as the negative logarithm of Ka, and similarly, pKb is the negative logarithm of Kb.
  • ∑ The sum of pKa and pKb for a conjugate acid-base pair equals 14, derived from the negative logarithm of Kw.
  • 🔍 Given the Kb of methylamine as 3.7 x 10^-4, the calculated Ka for the methylammonium ion is 2.7 x 10^-11.
  • 📊 The pKa of the methylammonium ion is found to be 10.57 by taking the negative log of the calculated Ka value.
Q & A

  • What is the conjugate acid-base pair mentioned in the script?

    -The conjugate acid-base pair mentioned in the script is NH4+ (ammonium ion) and NH3 (ammonia).

  • How does NH4+ function in an aqueous solution?

    -NH4+ functions as an acid in an aqueous solution by donating a proton to water, forming H3O+ (hydronium ion).

  • What is the role of NH3 in water?

    -NH3 acts as a weak base in water by accepting a proton from water, resulting in the formation of NH4+ and OH- (hydroxide ion).

  • What is the Ka value for the reaction involving NH4+ and water?

    -The Ka value for the reaction involving NH4+ and water is 5.6 times 10 to the negative 10.

  • What is the Kb value for the reaction involving NH3 and water?

    -The Kb value for the reaction involving NH3 and water is 1.8 times 10 to the negative 5.

  • What is the net reaction when combining the reactions of NH4+ and NH3 with water?

    -The net reaction is the auto-ionization of water, where one water molecule acts as an acid and the other as a base, resulting in the formation of H3O+ and OH-.

  • What is the equilibrium constant (Kw) for the auto-ionization of water?

    -The equilibrium constant (Kw) for the auto-ionization of water is 1.0 times 10 to the negative 14.

  • How is the value of Kw related to Ka and Kb for a conjugate acid-base pair?

    -The value of Kw is related to Ka and Kb for a conjugate acid-base pair by the equation: Ka times Kb equals Kw.

  • What does the Ka value for HCl indicate about its strength as an acid?

    -A very high Ka value for HCl indicates that it is a strong acid.

  • How can you calculate the Ka value for the methylammonium ion if given the Kb value for methylamine?

    -You can calculate the Ka value for the methylammonium ion using the equation Ka times Kb equals Kw. By plugging in the given Kb value for methylamine (3.7 times 10 to the negative 4), you can solve for Ka.

  • What is the relationship between pKa and pKb?

    -The relationship between pKa and pKb is given by the equation pKa plus pKb equals 14, which is derived from the negative logarithm of Kw.

  • How can you find the pKb for methylamine if given its pKa?

    -You can find the pKb for methylamine by using the relationship pKa plus pKb equals 14. If the pKa is known, you simply subtract it from 14 to find the pKb.

Outlines
00:00
🌟 Auto-Ionization of Water and the Relationship between Ka, Kb, and Kw

This paragraph discusses the auto-ionization of water and the interplay between Ka (acid dissociation constant) and Kb (base dissociation constant) for a conjugate acid-base pair. It explains how the ammonium ion (NH4+) acts as an acid, donating a proton to water to form hydronium ion (H3O+), leaving behind ammonia (NH3). Conversely, NH3 acts as a base, accepting a proton from water to form NH4+ and hydroxide ion (OH-). The Ka and Kb values for these reactions are given, and it is shown that their product equals the ion-product constant of water (Kw), which is 1.0 x 10^-14 at 25°C. The summary emphasizes the relationship that when two reactions are combined, the equilibrium constants are multiplied to give the net equilibrium constant, in this case, Kw. The concept of Ka and Kb being reciprocally related to each other's magnitude is also highlighted, with stronger acids having weaker conjugate bases and vice versa.

05:02
📚 Calculating Ka and pKa from Kb and pKb for a Conjugate Acid-Base Pair

The second paragraph focuses on calculating the Ka (acid dissociation constant) and pKa (negative logarithm of Ka) for a conjugate acid from the given Kb (base dissociation constant) and pKb (negative logarithm of Kb). Using methylamine as an example, the paragraph explains how to calculate the Ka value for the methylammonium ion (CH3NH3+), given the Kb value for methylamine. It demonstrates the use of the relationship Ka * Kb = Kw to solve for Ka and then calculates the pKa by taking the negative logarithm of Ka. The summary also introduces the concept of pKa and pKb being related through the equation pKa + pKb = 14 at 25°C, which is derived from the constant value of Kw. The process of finding pKb from a given pKa, and vice versa, is also discussed.

10:02
🔢 Determining pKb from pKa and the Relationship between Ka, Kb, pKa, and pKb

In the final paragraph, the focus is on determining the pKb (negative logarithm of base dissociation constant) from a given pKa and the relationship between Ka, Kb, pKa, and pKb. The paragraph illustrates how to find the pKb value for methylamine using the pKa value of its conjugate acid, the methylammonium ion. By using the equation pKa + pKb = 14, the pKb is calculated, and the summary confirms the correctness of the result by showing that the negative logarithm of the calculated pKb value matches the given Kb value for methylamine. This paragraph emphasizes the practical application of the relationships between Ka, Kb, pKa, and pKb in acid-base chemistry, providing a clear and concise method for calculating one from the other.

Mindmap
Keywords
💡Conjugate acid-base pair
A conjugate acid-base pair consists of a weak acid and its corresponding weak base. In the context of the video, NH4+ and NH3 are an example of such a pair, where NH4+ is the acid and NH3 is the base. This concept is central to understanding the acid-base reactions and equilibria discussed in the video, as it shows how these molecules can donate and accept protons in water, leading to the auto-ionization of water.
💡Acid
An acid is a substance that can donate a proton (H+) in a chemical reaction. In the video, NH4+ is described as functioning as an acid because it donates a proton to water, forming H3O+. Acids are important in chemistry and biochemistry, as they play roles in many reactions and are involved in the regulation of pH in biological systems.
💡Base
A base is a substance that can accept a proton (H+) in a chemical reaction. In the video, NH3 is described as a weak base because it can accept a proton from water, forming NH4+. Bases are essential in many chemical processes, including neutralizing acids and maintaining the pH balance in solutions.
💡Ka
The Ka value, or acid dissociation constant, is a measure of the strength of an acid in a solution. It is the equilibrium constant for the reaction of an acid donating a proton to a water molecule. In the video, the Ka for the reaction of NH4+ with water is given as 5.6 times 10 to the negative 10, indicating a weak acid.
💡Kb
The Kb value, or base dissociation constant, is a measure of the strength of a base in a solution. It is the equilibrium constant for the reaction of a base accepting a proton from a water molecule. In the video, the Kb for the reaction of NH3 with water is given as 1.8 times 10 to the negative 5, indicating a weak base.
💡Auto-ionization of water
The auto-ionization of water refers to the spontaneous dissociation of water molecules into hydronium ions (H3O+) and hydroxide ions (OH-). This process is essential for establishing the pH scale and is the basis for the equilibrium constant Kw. In the video, the net reaction of NH4+ and NH3 reacting with water molecules is shown to be the auto-ionization of water, with the equilibrium constant Kw being 1.0 times 10 to the negative 14.
💡Kw
The Kw value, or the ion product of water, is the equilibrium constant for the auto-ionization of water. It is the product of the concentrations of hydronium ions (H3O+) and hydroxide ions (OH-) in a solution at equilibrium. In the video, the calculation of Kw from the Ka and Kb values of NH4+ and NH3 demonstrates the relationship between these constants and the auto-ionization process.
💡pKa and pKb
The pKa and pKb values are the negative logarithms of the Ka and Kb values, respectively. They are used to express the strength of an acid or a base in a more convenient form, where a lower pKa indicates a stronger acid and a lower pKb indicates a stronger base. In the video, the calculation of pKa and pKb for the methylammonium ion and methylamine illustrates the inverse relationship between the strength of an acid and its conjugate base.
💡Methylamine
Methylamine is an organic compound and a weak base with the chemical formula CH3NH2. In the video, the Kb value for methylamine is given, and the Ka value for its conjugate acid, the methylammonium ion, is calculated using the relationship between Ka, Kb, and Kw. Methylamine's role in the video is to demonstrate how to calculate the Ka of a conjugate acid using the known Kb of its conjugate base.
💡Methylammonium ion
The methylammonium ion, with the chemical formula CH3NH3+, is the conjugate acid of methylamine. It is formed when methylamine donates a proton. In the video, the Ka value for the methylammonium ion is calculated from the known Kb value of methylamine, illustrating the relationship between the Ka and Kb of a conjugate acid-base pair.
💡Auto-ionization constant
The auto-ionization constant, denoted as Kw, is the equilibrium constant for the auto-ionization of water. It represents the product of the concentrations of hydronium ions (H3O+) and hydroxide ions (OH-) in water at equilibrium. The value of Kw is a fundamental constant in acid-base chemistry and is used to relate the strengths of acids and bases in aqueous solutions.
💡Inverse relationship
An inverse relationship is a type of correlation between two variables where an increase in one variable leads to a decrease in the other, and vice versa. In the context of the video, the inverse relationship refers to the strength of an acid and its conjugate base, where a strong acid will have a weak conjugate base, and a weak acid will have a strong conjugate base.
Highlights

NH4+ and NH3 are a conjugate acid-base pair, with NH4+ acting as an acid and NH3 as a weak base.

The ammonium ion (NH4+) donates a proton to water, forming H3O+ and leaving behind NH3.

The Ka for the reaction of NH4+ with water is 5.6 x 10^-10.

NH3 takes a proton from water, forming NH4+ and leaving behind OH-.

The Kb for the reaction of NH3 with water is 1.8 x 10^-5.

Adding the two reactions of NH4+ and NH3 results in the auto-ionization of water, producing H3O+ and OH-.

The equilibrium constant for the auto-ionization of water (Kw) is 1.0 x 10^-14.

The product of Ka and Kb for a conjugate acid-base pair equals Kw.

Calculating the value of Kw confirms the relationship between Ka and Kb for the NH4+/NH3 pair.

For a strong acid like HCl, its conjugate base (Cl-) has a very small Kb value.

The stronger the acid, the weaker the conjugate base, as described by the Ka and Kb relationship.

Methylamine is a weak base with a Kb value of 3.7 x 10^-4.

Using the relationship Ka × Kb = Kw, the Ka value for the methylammonium ion can be calculated.

The calculated Ka value for the methylammonium ion is 2.7 x 10^-11.

The pKa is determined by taking the negative log of the Ka value.

The pKa for the methylammonium ion is found to be 10.57.

The pKb can be calculated by subtracting the pKa from 14, as pKa + pKb = 14.

The calculated pKb for methylamine is 3.43.

The relationship between Ka and Kb, and pKa and pKb, is fundamental in understanding acid-base chemistry.

Transcripts

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