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Relative strength of acids and bases

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Intros
Lessons
  1. Which is the stronger acid / base?
  2. Competing conjugate acids/bases.
  3. Using Ka/Kb expressions to find Keq.
  4. Using Ka/Kb expressions to find Keq (continued).
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Examples
Lessons
  1. Find the equilibrium constant for two competing weak acids and their conjugate pairs.
    Ethanoic acid, CH3COOH and carbonic acid, H2CO3 are both weak acids. Their Ka acidity constants1 are below:
    Ka (CH3COOH) = 1.4*10-5
    Ka (H2CO3) = 4.5*10-7
    1. Identify their conjugate bases and write the equilibrium equation for the reaction of the two conjugate pairs.
    2. Use the Ka values above to calculate which side of the equation is favoured. Which is the stronger acid?
  2. Use the Ka expression to compare the strengths of two weak acids.
    Formic acid, HCOOH, and butanoic acid, CH3CH2CH2COOH, are both weak acids. Their Ka acidity constants1 are below:
    Ka (HCOOH): 1.8*10-4
    Ka (CH3CH2CH2COOH): 1.5*10-5

    Write a Keq expression using the two weak acids and their conjugate bases to explain which is the stronger acid.



    1 Source for acidity constant (Ka) data: ATKINS, P. W., & DE PAULA, J. (2006). Atkins' Physical chemistry. Oxford, Oxford University Press.
    Topic Notes
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    Introduction to Relative Strength of Acids and Bases

    Understanding the relative strength of acids and bases is a fundamental concept in chemistry. This topic explores how different acids and bases compare in terms of their ability to donate or accept protons. The introduction video provides a crucial foundation for grasping these concepts, offering visual explanations and real-world examples. By watching this video, students can gain a clear understanding of how acid-base strength is measured and its significance in chemical reactions. The relative strength of acids and bases plays a vital role in various chemical reactions, from industrial applications to biological systems. It influences reaction rates, equilibrium constants, and pH levels. Mastering this topic is essential for predicting chemical behavior, understanding buffer solutions, and analyzing titration curves. As we delve deeper into acid-base chemistry, this introduction serves as a springboard for more advanced concepts, making it an indispensable starting point for chemistry students and enthusiasts alike.

    Understanding Ka and Kb Expressions

    In the realm of chemistry, understanding acid-base interactions is crucial. Two key concepts that help us quantify the strength of acids and bases are Ka (acid dissociation constant) and Kb (base dissociation constant). These expressions play a vital role in determining how readily acids and bases dissociate in aqueous solutions.

    Ka, or the acid dissociation constant, is a measure of the strength of an acid in solution. It represents the extent to which an acid dissociates into its constituent ions. The larger the Ka value, the stronger the acid. This means that acids with higher Ka values will dissociate more completely in water, producing a higher concentration of hydrogen ions (H+).

    On the other hand, Kb, or the base dissociation constant, quantifies the strength of a base. It indicates how readily a base accepts protons or releases hydroxide ions (OH-) in solution. Similar to Ka, a larger Kb value signifies a stronger base, meaning it dissociates more extensively in water.

    To illustrate the concept of Ka, let's compare two common acids: ethanoic acid (CH3COOH) and phosphoric acid (H3PO4). Ethanoic acid, also known as acetic acid, has a Ka value of approximately 1.8 × 10^-5. In contrast, phosphoric acid has a much larger Ka value of about 7.5 × 10^-3 for its first dissociation step.

    The significant difference in Ka values between these two acids tells us that phosphoric acid is a stronger acid than ethanoic acid. This means that in aqueous solutions, phosphoric acid will dissociate to a greater extent, producing more hydrogen ions and thus creating a more acidic environment compared to ethanoic acid under similar conditions.

    It's important to note that Ka and Kb values are typically expressed on a logarithmic scale, similar to pH. This logarithmic nature means that even small differences in Ka or Kb values can represent substantial differences in acid or base strength.

    In general, the relationship between Ka and acid strength is directly proportional: as Ka increases, so does the strength of the acid. Conversely, for bases, a larger Kb value indicates a stronger base. This principle allows chemists to predict and compare the behavior of different acids and bases in various chemical reactions and equilibria.

    Understanding Ka and Kb expressions is not only crucial for theoretical chemistry but also has practical applications in various fields. In environmental science, these concepts help in analyzing water quality and soil acidity. In biochemistry, they play a role in understanding enzyme kinetics and buffer systems in living organisms. Industrial processes, such as wastewater treatment and pharmaceutical development, also rely heavily on these principles to optimize chemical reactions and product formulations.

    By mastering the concepts of Ka and Kb, chemists and students can gain deeper insights into acid-base chemistry, predict reaction outcomes, and design more effective experiments and processes. Whether you're working in a laboratory, studying environmental systems, or developing new materials, a solid grasp of these fundamental expressions will prove invaluable in your scientific endeavors.

    Comparing Acid and Base Strength

    Understanding the relative strength of acids and bases is crucial in chemistry, particularly when dealing with conjugate pairs and equilibrium reactions. To determine which of two acids or bases is stronger, we rely on their Ka (acid dissociation constant) and Kb (base dissociation constant) values. These constants provide quantitative measures of an acid's or base's strength in aqueous solutions.

    For acids, a higher Ka value indicates a stronger acid. This means the acid dissociates more readily in water, releasing more hydrogen ions (H+). Conversely, for bases, a higher Kb value signifies a stronger base, which more easily accepts protons in solution. When comparing acids, the one with the larger Ka is stronger, while for bases, the one with the larger Kb is stronger.

    An essential concept in acid-base chemistry is the relationship between conjugate acid-base pairs. A conjugate pair consists of an acid and its corresponding base, which differ by a single proton. The key principle to remember is that stronger acids have weaker conjugate bases, and stronger bases have weaker conjugate acids. This inverse relationship is fundamental to understanding acid-base equilibria.

    For example, consider the conjugate pair of hydrochloric acid (HCl) and chloride ion (Cl-). HCl is a strong acid, which means it readily donates protons. As a result, its conjugate base, Cl-, is a very weak base and has little tendency to accept protons. Conversely, the weak acid acetic acid (CH3COOH) has a relatively strong conjugate base, the acetate ion (CH3COO-).

    When writing equilibrium equations for competing conjugate pairs, it's important to place the stronger acid in the reactants and the weaker acid in the products. This arrangement reflects the direction in which the reaction will predominantly proceed. Let's consider an example to illustrate this concept:

    Suppose we have acetic acid (CH3COOH) and the ammonium ion (NH4+). To determine which is the stronger acid, we compare their Ka values. Acetic acid has a Ka of approximately 1.8 × 10^-5, while the ammonium ion has a Ka of about 5.6 × 10^-10. Since acetic acid has the higher Ka, it is the stronger acid.

    Therefore, the equilibrium equation would be written as:

    CH3COOH + NH3 CH3COO- + NH4+

    In this equation, the stronger acid (CH3COOH) is on the left side as a reactant, while the weaker acid (NH4+) is on the right side as a product. This arrangement indicates that the reaction will favor the formation of the weaker acid and its conjugate base.

    Understanding these principles allows chemists to predict the direction of acid-base reactions and the relative positions of equilibria. It's important to note that while Ka and Kb values provide a quantitative measure of strength, the actual behavior of acids and bases can be influenced by factors such as concentration, temperature, and the presence of other species in solution.

    In summary, determining the stronger of two acids or bases involves comparing their Ka or Kb values, with higher values indicating greater strength. The concept of conjugate acid-base pairs is crucial, with stronger acids having weaker conjugate bases and vice versa. When writing equilibrium equations for competing conjugate pairs, always place the stronger acid in the reactants and the weaker acid in the products to accurately represent the favored direction of the reaction.

    Deriving Keq from Ka and Kb

    Understanding the relationship between the equilibrium constant expression (Keq) and the acid dissociation constant (Ka) or base dissociation constant (Kb) is crucial in chemistry. This mathematical derivation provides insight into how these constants are interconnected and how we can use them to predict the direction of acid-base reactions. Let's walk through the process of deriving the Keq expression using Ka and Kb values.

    To begin, let's consider a general acid-base reaction:

    HA + B A- + HB+

    Where HA is a weak acid, B is a weak base, A- is the conjugate base of HA, and HB+ is the conjugate acid of B. The equilibrium constant expression (Keq) for this reaction is expressed as:

    Keq = [A-][HB+] / [HA][B]

    Now, let's multiply both sides of this equation by [H+]/[H+], which equals 1 and doesn't change the equation:

    Keq = ([A-][HB+] / [HA][B]) × ([H+]/[H+])

    Rearranging the terms, we get:

    Keq = ([A-][H+] / [HA]) × ([HB+] / [B][H+])

    Here's where the connection to Ka and Kb becomes apparent. The term [A-][H+] / [HA] is the expression for Ka of the weak acid HA. Similarly, [HB+] / [B][H+] is the inverse of the Ka expression for the conjugate acid HB+.

    Let's define:

    Ka(HA) = [A-][H+] / [HA]

    Ka(HB+) = [H+][B] / [HB+]

    Substituting these into our Keq expression:

    Keq = Ka(HA) × (1 / Ka(HB+))

    This can be simplified to:

    Keq = Ka(HA) / Ka(HB+)

    This final expression shows that the equilibrium constant expression (Keq) for an acid-base reaction is the ratio of the Ka values of the stronger acid to the weaker acid. In this case, HA is the stronger acid, and HB+ is the weaker acid.

    It's important to note that we can also express this relationship using Kb values. Since Ka × Kb = Kw (the ion product of water), we can rewrite the Keq expression as:

    Keq = Kb(B) / Kb(A-)

    This derivation demonstrates the powerful connection between equilibrium constants and acid-base strength. By understanding this relationship, chemists can predict the direction and extent of acid-base reactions, calculate pH values, and design buffer solutions.

    In practice, this derivation allows

    Interpreting Keq Values

    Understanding the significance of Keq values is crucial in determining the direction of chemical equilibrium. The equilibrium constant, Keq, provides valuable insights into the relative concentrations of products and reactants at equilibrium. This knowledge is essential for predicting the outcome of chemical reactions and optimizing industrial processes.

    Keq values are always positive and represent the ratio of products to reactants at equilibrium. The magnitude of Keq indicates whether the equilibrium favors the formation of products or the persistence of reactants. When interpreting Keq values, there are two key scenarios to consider:

    1. Keq > 1: This indicates that the equilibrium favors the products. In such cases, the concentration of products at equilibrium is higher than that of reactants. The reaction tends to proceed forward, converting more reactants into products until equilibrium is reached.

    2. Keq < 1: This suggests that the equilibrium favors the reactants. Here, the concentration of reactants at equilibrium is higher than that of products. The reaction tends to proceed in reverse, with products converting back to reactants until equilibrium is achieved.

    To illustrate the interpretation of Keq values, let's consider an example calculation involving phosphoric acid (H3PO4) and ethanoic acid (CH3COOH). Suppose we have the following equilibrium reaction:

    H3PO4 + CH3COOH H2PO4- + CH3COOH2+

    After conducting experiments and measuring the concentrations at equilibrium, we calculate a Keq value of 0.08. How do we interpret this result?

    Since the Keq value is less than 1 (0.08 < 1), we can conclude that the equilibrium favors the reactants. This means that at equilibrium, there will be a higher concentration of phosphoric acid (H3PO4) and ethanoic acid (CH3COOH) compared to the concentration of dihydrogen phosphate ion (H2PO4-) and protonated ethanoic acid (CH3COOH2+).

    It's important to note that Keq values are temperature-dependent and can change with variations in temperature. Additionally, while Keq provides information about the relative concentrations at equilibrium, it does not indicate the rate at which equilibrium is reached.

    In summary, interpreting Keq values is essential for understanding the direction of equilibrium in chemical reactions. A Keq greater than 1 favors products, while a Keq less than 1 favors reactants. By analyzing these values, chemists can predict reaction outcomes, design more efficient processes, and gain valuable insights into the behavior of chemical systems at equilibrium.

    Practical Applications and Problem-Solving in Acid-Base Chemistry

    Understanding relative acid-base strength is crucial in chemistry and biochemistry, with numerous practical applications. This section will provide problem-solving strategies and real-world examples to help reinforce your understanding of acid-base chemistry.

    To determine relative acid-base strength, follow these steps:

    1. Identify the acid-base pairs in question.
    2. Compare the stability of the conjugate bases.
    3. Consider factors such as electronegativity, atom size, and resonance.
    4. Use pKa values when available for quantitative comparisons.

    Let's work through an example problem:

    Problem: Compare the relative strengths of acetic acid (CH3COOH) and hydrocyanic acid (HCN).

    Solution:

    1. Identify the conjugate bases: CH3COO- and CN-
    2. Compare the stability of these anions:
      • CH3COO- has resonance stabilization
      • CN- lacks resonance stabilization
    3. Conclusion: CH3COOH is a stronger acid than HCN because its conjugate base is more stable.

    For competing conjugate pairs, consider this problem-solving approach:

    1. Write out the acid-base reaction.
    2. Identify the acid-base pairs on each side.
    3. Compare the relative strengths of the acids and bases.
    4. Determine the direction of the equilibrium.

    Example: Will HCl react with CH3COO-?

    1. HCl + CH3COO- Cl- + CH3COOH
    2. Acid-base pairs: HCl/Cl- and CH3COOH/CH3COO-
    3. HCl is a stronger acid than CH3COOH
    4. The equilibrium favors the formation of CH3COOH and Cl-

    Real-world applications of understanding acid-base strength include:

    • Developing effective buffer solutions for biological systems
    • Optimizing industrial processes like wastewater treatment
    • Formulating pharmaceuticals with appropriate pH for absorption
    • Analyzing soil chemistry for agricultural purposes

    In biochemistry, acid-base chemistry plays a crucial role in:

    • Enzyme function and catalysis
    • Protein folding and stability
    • Maintaining cellular pH homeostasis
    • Drug design and delivery systems

    To reinforce your understanding, practice with various acid-base pairs:

    1. Compare the strengths of HF and HCl
    2. Determine if NH4+ will react with OH-
    3. Predict the direction of the reaction: H2CO3 + PO4^3- HCO3- + HPO4^2-
    4. Rank the following in order of increasing acid strength: H2O, HNO3, H2SO4, CH3COOH

    Remember, practice is key to mastering acid-base chemistry. As you work through problems, consider the following tips:

    • Always start by identifying the acid-base pairs involved
    • Use pKa values when

    Conclusion

    In this article, we've explored the crucial role of Ka and Kb in determining acid-base strength, providing a solid foundation for understanding chemical equilibria. We've walked through the process of deriving Keq and interpreting equilibrium constants, essential skills for any chemistry student. The introductory video served as a valuable visual and auditory aid, setting the stage for our in-depth discussion. Remember, mastering these concepts is key to solving complex acid-base problems. We encourage you to apply your newfound knowledge to practical scenarios and continue exploring this fascinating subject. For further resources, consider consulting advanced chemistry textbooks or online platforms specializing in acid-base chemistry. By building on these fundamental principles, you'll be well-equipped to tackle more advanced topics in chemical equilibria and acid-base reactions. Keep practicing and exploring to deepen your understanding of this essential area of chemistry.

    Relative Strength of Acids and Bases

    Which is the stronger acid / base? Competing conjugate acids/bases.

    Step 1: Understanding Acid and Base Strength

    To determine the relative strength of acids and bases, we first need to understand what makes an acid or base strong or weak. A strong acid is one that completely dissociates in water, releasing a high concentration of hydrogen ions (H3O+). Conversely, a weak acid only partially dissociates, resulting in a lower concentration of hydrogen ions. The same principle applies to bases, where a strong base fully dissociates to release hydroxide ions (OH-), while a weak base only partially dissociates.

    Step 2: Introduction to Ka and Kb

    The strength of an acid or base can be quantified using the acid dissociation constant (Ka) for acids and the base dissociation constant (Kb) for bases. These constants provide a measure of the extent to which an acid or base dissociates in water. A larger Ka value indicates a stronger acid, as it signifies a higher degree of dissociation. Similarly, a larger Kb value indicates a stronger base.

    Step 3: Writing Ka and Kb Expressions

    To compare the strengths of acids and bases, we write the Ka and Kb expressions. For an acid HA dissociating in water, the Ka expression is:
    Ka = [H3O+][A-] / [HA]
    For a base B dissociating in water, the Kb expression is:
    Kb = [BH+][OH-] / [B]
    These expressions help us understand the relationship between the concentrations of the dissociated ions and the undissociated acid or base.

    Step 4: Relating Ka and Kb to Keq

    When dealing with competing conjugate acid-base pairs, we need to consider the equilibrium constant (Keq) for the reaction. The relationship between Ka, Kb, and Keq is crucial in determining which acid or base is stronger. For a reaction involving two conjugate pairs, the equilibrium constant can be derived from the Ka and Kb values of the acids and bases involved.

    Step 5: Calculating Equilibrium Constants

    To find the equilibrium constant (Keq) for a reaction involving two competing conjugate pairs, we use the Ka and Kb values. The process involves mathematical calculations to derive Keq from the given Ka and Kb expressions. This step is essential for understanding the dynamic equilibrium established between the conjugate pairs in an aqueous solution.

    Step 6: Identifying the Stronger Acid or Base

    Once we have the Ka and Kb values, we can identify the stronger acid or base. The larger the Ka value, the stronger the acid, as it indicates a higher degree of dissociation. Similarly, the larger the Kb value, the stronger the base. By comparing these values, we can determine which of the competing conjugate pairs is the stronger acid or base.

    Step 7: Understanding Conjugate Pairs

    In any acid-base reaction, there are always conjugate pairs involved. A conjugate acid is the species formed when a base accepts a proton, and a conjugate base is the species formed when an acid donates a proton. The strength of a conjugate acid is inversely related to the strength of its conjugate base. Therefore, a strong acid will have a weak conjugate base, and a strong base will have a weak conjugate acid.

    Step 8: Establishing Equilibrium

    In an aqueous solution, the equilibrium between two conjugate pairs is dynamic, meaning the reaction can shift back and forth. The position of the equilibrium depends on the relative strengths of the acids and bases involved. By understanding the equilibrium expressions and the Ka and Kb values, we can predict the direction in which the equilibrium will shift and identify the stronger acid or base in the reaction.

    Step 9: Practical Application

    In practical terms, knowing the relative strength of acids and bases is essential for various chemical processes, including titrations, buffer solutions, and industrial applications. By mastering the concepts of Ka, Kb, and equilibrium constants, we can make informed decisions in both laboratory and real-world scenarios.

    FAQs

    1. What is the difference between Ka and Kb?

      Ka (acid dissociation constant) measures the strength of an acid, while Kb (base dissociation constant) measures the strength of a base. Ka represents how readily an acid donates protons in solution, and Kb represents how easily a base accepts protons. A higher Ka indicates a stronger acid, while a higher Kb indicates a stronger base.

    2. How do you determine which acid is stronger when comparing two acids?

      To determine which acid is stronger, compare their Ka values. The acid with the higher Ka value is the stronger acid. For example, if Acid A has a Ka of 1.0 × 10^-3 and Acid B has a Ka of 1.0 × 10^-5, Acid A is the stronger acid because it has a higher Ka value.

    3. What is the relationship between Keq and Ka/Kb?

      The equilibrium constant (Keq) for an acid-base reaction can be derived from the Ka and Kb values of the participating species. For a reaction between an acid HA and a base B, the relationship is expressed as Keq = Ka(HA) / Ka(HB+), where HB+ is the conjugate acid of B. This relationship allows us to predict the direction and extent of acid-base reactions.

    4. How do you interpret Keq values in acid-base reactions?

      Keq values indicate the direction of equilibrium in acid-base reactions. If Keq > 1, the equilibrium favors the products, meaning the reaction tends to proceed forward. If Keq < 1, the equilibrium favors the reactants, indicating the reaction tends to proceed in reverse. The magnitude of Keq provides information about the relative concentrations of products and reactants at equilibrium.

    5. What are some practical applications of understanding acid-base strength?

      Understanding acid-base strength has numerous practical applications, including: developing effective buffer solutions for biological systems, optimizing industrial processes like wastewater treatment, formulating pharmaceuticals with appropriate pH for absorption, analyzing soil chemistry for agricultural purposes, and understanding enzyme function and catalysis in biochemistry. This knowledge is crucial for predicting chemical behavior and designing efficient chemical processes across various fields.

    Prerequisite Topics

    Understanding the relative strength of acids and bases is a crucial concept in chemistry, but to fully grasp this topic, it's essential to have a solid foundation in several prerequisite areas. These fundamental concepts provide the necessary context and tools to analyze and compare the strength of different acids and bases effectively.

    One of the most important prerequisites is the acid dissociation constant. This concept is vital for quantifying the strength of acids and bases, as it directly relates to their ability to dissociate in solution. By understanding the acid dissociation constant, students can predict the behavior of acids and bases in various chemical reactions and compare their relative strengths.

    Closely related to this is the equilibrium constant, which plays a crucial role in determining the extent of acid-base reactions. The equilibrium constant expression helps in calculating the concentrations of species at equilibrium, which is essential for assessing the strength of acids and bases in solution.

    Another key prerequisite is solubility and ion concentration. This topic is particularly important when dealing with weak acids and bases, as their strength is often related to the concentration of hydrogen or hydroxide ions in solution. Understanding how to calculate and interpret ion concentrations is crucial for comparing the relative strengths of different acids and bases.

    The logarithmic scale, particularly the pH scale, is an indispensable tool in acid-base chemistry. This mathematical concept allows for the convenient expression of hydrogen ion concentrations over a wide range of values. Mastery of the logarithmic scale is essential for interpreting pH values and relating them to the strength of acids and bases.

    Lastly, while it may seem less directly related, knowledge of calculating cell potential in voltaic cells can provide valuable insights into the relative strength of acids and bases. This is because the strength of acids and bases can influence redox reactions, and understanding cell potentials can help in predicting the behavior of acids and bases in electrochemical contexts.

    By mastering these prerequisite topics, students will be well-equipped to tackle the complexities of comparing and analyzing the relative strength of acids and bases. Each concept builds upon the others, creating a comprehensive framework for understanding this fundamental aspect of chemistry. As students progress in their studies, they'll find that these prerequisite topics continually resurface, reinforcing their importance in the broader context of chemical principles and reactions.

    In this lesson, we will learn:

    • How to determine the stronger of two acids/bases in reactions between two competing conjugate pairs.
    • How to use ka/kb expressions to construct expressions for the equilibrium constant of two competing conjugate pairs.
    • How to calculate the equilibrium constant with two competing conjugate pairs.

    Notes:

    • In Acid dissociation constant we looked at the expression for ka (and kb), which tells us how dissociated a weak acid (or weak base) is in solution. The larger the Ka (or Kb) value, the stronger the acid (or base).
      That the Ka value is basically an “acid strength rating” is good to remember for solutions with multiple conjugate pairs. When two conjugate pairs are mixed together in equilibrium, there are two competing acids (and bases) both trying to be an acid – trying to donate H+ (and two competing bases both trying to accept H+). You can use the values for Ka and Kb to see which one is the stronger acid/base, and which side is the equilibrium favors.
      • For example, if solutions containing CH3COOH and H3PO4 were combined, there would be two acids both competing to donate protons to other species.
      • The stronger acid will do this to a greater extent. The Ka values1 will identify which it is: Ka (CH3COOH) = 1.4 * 10-5, while Ka (H3PO4) = 6.9 ∗* 10-3. This shows that H3PO4 donates protons with greater ability than CH3COOH.
        Therefore an equilibrium can be written:

        H3PO4 + CH3COO- ⇌\rightleftharpoons CH3COOH + H2PO4-

        The Ka values show, H3PO4 is the stronger acid which means the equilibrium should   favor the products. We can write an equilibrium constant expression for this:

        Keq = [CH3COOH][H2PO4−][H3PO4][CH3COO−]\frac{\left[CH_3COOH\right] \left[H_2PO_{4}^{-} \right] }{ \left[H_3PO_4\right] \left[CH_3COO^{-} \right] }

      • By multiplying through by [H+], the following expression is obtained:

        Keq = [CH3COOH][H2PO4−][H+][H3PO4][CH3COO−][H+]\frac{\left[CH_3COOH\right] \left[H_2PO_{4}^{-} \right] \left[H^{+} \right]}{ \left[H_3PO_4\right] \left[CH_3COO^{-} \right] \left[H^{+} \right]}

        While:

        Ka (H3PO4) = [H2PO4−][H+][H3PO4]\frac{ \left[H_2PO_{4}^{-} \right] \left[H^{+} \right]}{ \left[H_3PO_4\right] }

        And:

        Ka (CH3COOH) = [CH3COO−][H+][CH3COOH]\frac{ \left[CH_3COO^{-} \right] \left[H^{+} \right]}{ \left[CH_{3}COOH\right] }

      • Notice these are now expressions of dissociation? This can now be simplified using Ka expressions!

        Keq = Ka (H3PO4) ∗* 1Ka(CH3COOH)\frac{1}{K_a (CH_{3} COOH)}

      • Simplified further:

        Keq = Ka(H3PO4)Ka(CH3COOH)\frac{K_a(H_3PO_4)}{K_a (CH_{3} COOH)}

      • Both of these are known constants (we used them earlier!) so we can calculate an equilibrium constant to determine which side of the equilibrium is favored; it should back up our prediction that H3PO4 dissociates more:

        Keq = 6.9 ∗ 10−31.4 ∗ 10−5\large \frac{6.9 \, * \, 10^{-3}}{1.4 \, * \, 10^{-5}} = 492.86...

      • This value (a ratio of around 493:1) shows the equilibrium heavily favors the products as predicted by the acid dissociation constants. For any two conjugate pairs in competition, look up the Ka value for both conjugate acids then set up the equilibrium and Keq expression like this:

        Where:
        HX = conjugate acid (stronger acid; larger Ka),
        HY = conjugate acid (weaker acid; smaller Ka),
        X- = conjugate base of HX
        Y- = conjugate base of HY

        HX + Y- ⇌\rightleftharpoons HY + X-

        Keq = [Proucts][Reactamts]\large\frac{[Proucts]}{[Reactamts]} or:

        Keq = Ka(HX,  acid  in  reactants)Ka(HY,  acid  in  products)\large\frac{K_a (HX,\; acid\; in\; reactants)}{K_a (HY,\; acid\; in\; products)}

      • If done correctly, the Keq expression will yield a value greater than 1 (showing the equilibrium shifted right; that the stronger acid dissociates more). Another way to read this is that the equilibrium will favor the side with the weaker acid.