AL

Chemical Equilibrium and K Expressions

Introduction

  • Discussion of equilibrium constants with emphasis on the need to distinguish between 'big K' and 'little k'.

Key Concepts

Equilibrium Constant (K)

  • K (Big K): Refers to the equilibrium constant, denoted as $K_{eq}$.

  • k (Little k): Represents the rate constant.

  • It is crucial to mention that 'Big K' or $K_{eq}$ pertains to the equilibrium state of a reaction, while 'little k' focuses on reaction rates.

Setting Up the Equilibrium Expression

  • The general expression for the equilibrium constant for a reaction is given by the formula:

    K_{eq} = rac{[ ext{products}]}{[ ext{reactants}]}

  • Products and Reactants: In this expression, the concentrations of the products go in the numerator, while those of the reactants go in the denominator.

  • Coefficients as Exponents: The coefficients in the balanced chemical equation become the exponents in the equilibrium expression.

Interpretation of K Values

Large K Values

  • A large value of $K_{eq}$ indicates that the reaction favors the formation of products.

  • For example, if a reaction has a large $K_{eq}$, it suggests that the equilibrium concentration of products is significantly greater than that of the reactants.

  • Example: When considering a strong acid like hydrochloric acid (HCl), it dissociates completely, producing H$^{+}$ and Cl$^{-}$:
    ext{HCl}
    ightarrow ext{H}^{+} + ext{Cl}^{-}

  • The associated $K_{a}$ value for strong acids is typically much larger than 1, indicating favor towards products.

Small K Values

  • A small $K_{eq}$ value suggests that the reaction favors the reactants.

  • Example: Acetic acid, a weak acid found in vinegar, partially dissociates as follows:
    ext{CH}3 ext{COOH} ightleftharpoons ext{H}^{+} + ext{CH}3 ext{COO}^-

  • Its $K_{a}$ value is $1.8 imes 10^{-5}$, indicating a significant reverse reaction and favoring reactants.

Phases and Their Importance in Equilibrium Expressions

Exclusion of Solids and Liquids

  • When writing equilibrium expressions, solids and liquids do not appear because their activities are considered to be equal to 1.

Practice Problems

  • Creating equilibrium expressions requires understanding of phases present in a reaction.

Example Equilibrium Reaction

  1. Lead to considering the expression for a reaction such as: ext{A} ightleftharpoons ext{B} .

    • The correct equilibrium expression would factor the gaseous components and liquid/solid states appropriately.

    • Example forgetting about solids during expression derivation, pointing out errors in including them.

Manipulation of Equilibrium Constants

Reversing a Reaction

  • If the reaction is reversed, the new $K$ value becomes the reciprocal of the original:
    K{ ext{new}} = rac{1}{K{ ext{original}}}

Multiplying Reaction Coefficients

  • If a reaction is multiplied by a coefficient (n), the new $K$ value is raised to that power:
    K{ ext{new}} = K{ ext{original}}^n

Dividing Reaction Coefficients

  • If a reaction is divided by a coefficient, the new $K$ value takes the n-th root:
    K{ ext{new}} = K{ ext{original}}^{ rac{1}{n}}

Adding Reactions

  • When adding two reactions together, their equilibrium constants multiply:
    K{ ext{total}} = K1 imes K_2

Relationship between $Kc$ and $Kp$

Understanding the Context

  • $K_c$: Equilibrium constant expressed in terms of concentrations (molarity).

  • $K_p$: Equilibrium constant expressed in terms of partial pressures of gases.

  • Key formula for conversion:
    Kp = Kc imes (RT)^{ riangle n}

  • Where,

    • $R$ is the universal gas constant (0.0821 L·atm/(K·mol)),

    • $ riangle n$ is the difference in moles between gaseous products and gaseous reactants defined as:
      riangle n = ext{ (moles of gaseous products)} - ext{ (moles of gaseous reactants)}

Practical Context of the Conversion

  • For a reaction involving $N2O4$ reacting to form $2NO_2$, we have:

    • Products: 2 moles of NO$_2$

    • Reactants: 1 mole of N$2O4$.

    • Thus, $ riangle n = 2 - 1 = 1$.

ICE Table Methodology

  • The ICE table (Initial, Change, Equilibrium) approach is commonly used to find equilibrium concentrations.

Steps to Create an ICE Table

  1. Write the balanced chemical equation.

  2. Set up the ICE table:

    • I (Initial concentrations): Insert known concentrations.

    • C (Change): Define the changes in concentration as $x$ or $2x$ based on stoichiometry.

    • E (Equilibrium): Express equilibrium concentrations in terms of initial concentrations and $x$.

Key Considerations

  • Always ensure the equation is balanced before proceeding.

  • Understanding when to employ quadratic equations vs. approximations is critical for solving equilibrium problems efficiently.

  • Close attention must be given to coefficients and their influence on the $x$ values in your changes.

Conclusion

  • Ensure familiarity with concepts related to equilibrium constants in preparation for examinations and practical applications in chemical kinetics and reaction dynamics. Review handouts and homework resources to reinforce learning.