Deriving Kp and Kc: Understanding Equilibrium Constants
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Questions and Answers

What does the equilibrium constant, denoted as K, measure?

  • The volume of the system
  • The rate of the reaction
  • The dynamic balance between reactants and products (correct)
  • The energy change in the reaction
  • In the equilibrium constant expression, what does 'aA' represent?

  • Partial pressure of product D
  • Concentration of product C
  • Stoichiometric coefficient of reactant A (correct)
  • Number of moles of reactant B
  • For a gaseous system, what is substituted for concentrations in the equilibrium constant expression?

  • Ideal gas constant
  • Total pressure
  • Molar masses
  • Partial pressures (correct)
  • What law is used to derive Kp for gaseous systems?

    <p>Ideal Gas Law</p> Signup and view all the answers

    In the ideal gas law equation pV = nRT, what does 'n' represent?

    <p>Number of moles</p> Signup and view all the answers

    What does 'x' represent in the relationship between partial pressure and concentration for an ideal gas?

    <p>Mole fraction of the specific gas</p> Signup and view all the answers

    What is the final expression for the equilibrium constant Kp in terms of mole fractions?

    <p>(1 - x_C - x_D)^c * (1 - x_A)^d / (1 - x_A - x_C)^a</p> Signup and view all the answers

    What is the major difference between Kp and Kc equilibrium constants?

    <p>Kp uses partial pressures while Kc uses concentrations.</p> Signup and view all the answers

    Which constant is derived using partial pressures, according to the text?

    <p>Kp</p> Signup and view all the answers

    What does Le Chatelier's principle predict about systems at equilibrium?

    <p>They will shift to counteract changes and reach a new equilibrium.</p> Signup and view all the answers

    Which expression represents the equilibrium constant Kc formula directly from the text?

    Signup and view all the answers

    What does the equilibrium constant Kp predict about a system when pressure changes are introduced?

    <p>The system will shift to balance the pressure changes.</p> Signup and view all the answers

    Study Notes

    Deriving Kp and Kc: Understanding Equilibrium Constants

    Equilibrium is a central concept in chemistry, where a system maintains a dynamic balance between reactants and products. The equilibrium constant, denoted as K, is a quantitative measure that characterizes this balance. In this article, we'll delve into two specific equilibrium constants, Kp (the equilibrium constant for a gaseous system) and Kc (the equilibrium constant for a general system, often aqueous or solid), and their derivation from the equilibrium constant expression.

    The Equilibrium Constant Expression

    The equilibrium constant K is expressed as the ratio of the concentrations (or partial pressures for gases) of the products to the reactants, each raised to their stoichiometric coefficients. For a general reaction:

    [aA + bB \rightleftharpoons cC + dD]

    The equilibrium constant expression is:

    [K = \frac{[C]^c \times [D]^d}{[A]^a \times [B]^b}]

    For a gaseous system, we substitute partial pressures (p) for concentrations:

    [K_p = \frac{p_C^c \times p_D^d}{p_A^a \times p_B^b}]

    Deriving Kp

    To derive Kp, we'll use the ideal gas law:

    [pV = nRT]

    where (p) is the partial pressure, (V) is the volume, (n) is the number of moles, (R) is the ideal gas constant, and (T) is the temperature.

    The relationship between concentration and partial pressure for an ideal gas is:

    [p = x \times P_total]

    where (x) is the mole fraction of the specific gas and (P_total) is the total pressure of the mixture.

    So,

    [K_p = \frac{(x_C \times P_total)^c \times (x_D \times P_total)^d}{(x_A \times P_total)^a \times (x_B \times P_total)^b}]

    Since (P_total) cancels out, we are left with:

    [K_p = \frac{x_C^c \times x_D^d}{x_A^a \times x_B^b}]

    As the total mole fraction of all gases in a closed system is equal to 1:

    [x_A + x_B + x_C + x_D = 1]

    This means that:

    [x_A = 1 - x_C - x_D]

    [x_B = 1 - x_A - x_C]

    Substituting these expressions into the Kp formula, we get:

    [K_p = \frac{(1 - x_C - x_D)^c \times (1 - x_A - x_C)^d}{(1 - x_A - x_C)^a \times (x_A)^b}]

    Rearranging the terms, we obtain the final expression for Kp:

    [K_p = \frac{(1 - x_C - x_D)^c \times (1 - x_A)^d}{(1 - x_A - x_C)^a \times (x_A)^{b - d}}]

    Deriving Kc

    Kc is the equilibrium constant for a general system, so it's derived by using concentrations rather than partial pressures. We'll use the equilibrium constant expression:

    [K_c = \frac{[C]^c \times [D]^d}{[A]^a \times [B]^b}]

    This expression is straightforward and does not require any further manipulation.

    Le Chatelier's Principle and Equilibrium Constants

    The Kp and Kc values are used to determine how a system will respond to changes in conditions according to Le Chatelier's principle. If a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust itself to counteract the change and restore a new equilibrium. By calculating Kp and Kc values, one can predict how a system will respond to such conditions.

    Common Misconceptions

    It's important to avoid confusing Kp and Kc. Kp refers to the equilibrium constant for a gaseous system, and Kc refers to the equilibrium constant for a general system, often aqueous or solid. Both constants are derived from the equilibrium constant expression, but Kp uses partial pressures, while Kc uses concentrations. Additionally, Kp can be used to predict changes in a system due to changes in pressure, whereas Kc does not directly account for pressure changes.

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    Description

    Learn how to derive equilibrium constants Kp and Kc from the equilibrium constant expression using partial pressures for gaseous systems and concentrations for general systems. Explore the ideal gas law, Le Chatelier's principle, and common misconceptions related to these equilibrium constants.

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