Chemical Equilibrium

A. Law of Chemical Equilibrium

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

Properties & Key Points:

  • At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction, leading to constant concentrations of reactants and products.
  • \( K_c \): Equilibrium constant for concentrations.
  • \([A], [B], [C], [D]\): Molar concentrations of the species.
  • \( a, b, c, d \): Stoichiometric coefficients of the balanced equation.
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B. Equilibrium Constant in Terms of Partial Pressure (\( K_p \))

\[K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}\]

Properties & Key Points:

  • For gaseous reactions, the equilibrium constant can also be expressed in terms of partial pressures.
  • \( K_p \): Equilibrium constant for partial pressures.
  • \( P_A, P_B, P_C, P_D \): Partial pressures of the gases.
  • \( a, b, c, d \): Stoichiometric coefficients of the balanced equation.
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C. Relationship Between \( K_c \) and \( K_p \)

\[K_p = K_c (RT)^{\Delta n}\]

Properties & Key Points:

  • The equilibrium constants \( K_c \) and \( K_p \) are related based on the reaction's change in the number of moles of gases.
  • \( K_p \): Equilibrium constant for partial pressures.
  • \( K_c \): Equilibrium constant for concentrations.
  • \( R \): Universal gas constant.
  • \( T \): Temperature in Kelvin.
  • \( \Delta n \): Change in moles of gas \((\text{moles of products} - \text{moles of reactants})\).
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D. Reaction Quotient (Q)

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

Properties & Key Points:

  • The reaction quotient, \( Q \), indicates the direction a reaction will proceed to reach equilibrium. If \( Q = K \), the system is at equilibrium. If \( Q < K \), the forward reaction is favored, and if \( Q > K \), the reverse reaction is favored.
  • \( Q \): Reaction quotient.
  • \([A], [B], [C], [D]\): Molar concentrations of the species.
  • \( a, b, c, d \): Stoichiometric coefficients of the balanced equation.
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E. Le Chatelier’s Principle

Properties & Key Points:

  • This principle states that if a system at equilibrium is disturbed, the system will adjust to minimize the disturbance and re-establish equilibrium.
  • Change in concentration: Adding or removing reactants or products shifts equilibrium to counter the change.
  • Change in pressure: Increasing pressure favors the direction with fewer moles of gas; decreasing pressure favors more moles.
  • Change in temperature: For exothermic reactions, increasing temperature favors the reverse reaction; for endothermic reactions, it favors the forward reaction.
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F. Degree of Dissociation

\[\alpha = \frac{\text{moles dissociated}}{\text{initial moles}}\]

Properties & Key Points:

  • The fraction of a substance that dissociates at equilibrium is called the degree of dissociation.
  • \( \alpha \): Degree of dissociation.
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G. Relation Between \( \alpha \) and \( K_c \) for Weak Electrolytes

\[K_c = C \alpha^2\]

Properties & Key Points:

  • For weak electrolytes, the equilibrium constant \( K_c \) can be expressed in terms of the degree of dissociation.
  • \( K_c \): Equilibrium constant.
  • \( C \): Initial concentration of the weak electrolyte.
  • \( \alpha \): Degree of dissociation.
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H. Ionic Product of Water (\( K_w \))

\[K_w = [H^+][OH^-]\]

Properties & Key Points:

  • The product of the concentrations of hydrogen ions and hydroxide ions in water at a particular temperature is constant, called the ionic product of water.
  • \( K_w \): Ionic product of water.
  • \( [H^+] \): Concentration of hydrogen ions.
  • \( [OH^-] \): Concentration of hydroxide ions.
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I. pH and pOH

\[\text{pH} = -\log[H^+]\]
\[\text{pOH} = -\log[OH^-]\]

Properties & Key Points:

  • The pH of a solution is the negative logarithm of the hydrogen ion concentration, and pOH is the negative logarithm of the hydroxide ion concentration.
  • pH: Measure of acidity.
  • pOH: Measure of basicity.
  • \([H^+], [OH^-]\): Concentrations of hydrogen and hydroxide ions.
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J. Relation Between pH and pOH

\[\text{pH} + \text{pOH} = 14\]

Properties & Key Points:

  • The sum of pH and pOH at a given temperature (typically 25°C) is constant.
  • pH: Measure of acidity.
  • pOH: Measure of basicity.
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