2.4 - Keq_ The Equilibrium Constant (2.5)

2.4 - Keq: The Equilibrium Constant

Introducing the Reaction Quotient

• Rate Law:

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    Described by the equation:[ aA + bB \rightarrow cC + dD ]

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    The reaction rate is given by:[ \text{rate} = k[A]^a[B]^b ]

• Reversible Reactions:

  • Introduces the concept of equilibrium and two rate equations:

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    Forward reaction:[ \text{rate}{forward} = k{forward}[A]^a[B]^b ]

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    Reverse reaction:[ \text{rate}{reverse} = k{reverse}[C]^c[D]^d ]

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    Equilibrium condition:[ \text{rate}{forward} = \text{rate}{reverse} ]

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    Derivation leads to:[ k_{forward}[A]^a[B]^b = k_{reverse}[C]^c[D]^d ]

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    Rearranging gives:[ \frac{k_{forward}}{k_{reverse}} = \frac{[C]^c[D]^d}{[A]^a[B]^b} ]

• Reaction Quotient (Qr):

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    Defined as:[ Q_r = \frac{[C]^c[D]^d}{[A]^a[B]^b} ]

  • A dimensionless measure of concentrations at any moment.

Understanding Equilibrium and Keq

• Equilibrium vs. Non-Equilibrium:

  • The system can either be at equilibrium or not.

  • Reaction Quotient (Qr) can indicate the direction of the reaction:

    • If ( Q_r = K_{eq} ): The system is at equilibrium.

    • If ( Q_r > K_{eq} ): Too many products; shift left.

    • If ( Q_r < K_{eq} ): Too many reactants; shift right.

Calculating Trial Keq

• Trial Condition:

  • When calculating Qr for comparison, label it as "trial Keq".

  • Example:

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      For the reaction:[ 2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g) ]

  • Given concentrations and calculating trial Keq:

    • If ( trial K_{eq} < K_{eq} ), the shift is right.

Ignoring Solids and Liquids in Keq

• Keq Calculations and Pure Substances:

  • Do not include solid (s) or liquid (ℓ) species in the Keq expression.

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    Example Reaction:[ Br_2(ℓ) + H_2(g) \rightleftharpoons 2HBr(g) ]

  • Concentration is not applicable for pure liquids or solids.

Meaning of Keq's Numerical Value

• Relation of Keq to Concentrations:

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    Keq is proportional to product concentrations and inversely proportional to reactant concentrations:[ K_{eq} \propto [products] ][ K_{eq} \propto \frac{1}{[reactants]} ]

• Factors Affecting Keq:

  • Changes in temperature affect K_eq.

  • Changes in pressure or concentration do not affect K_eq but can shift the equilibrium position.

Shifting Equilibria

• Le Châtelier's Principle:

  • Introduction of stressors (like temperature or pressure change) results in equilibrium shifts.

  • Example Scenarios:

    • Case 1: Increasing temperature favors endothermic reactions.

    • Case 2: Doubling volume results in equilibrium shifting to increase pressure.

    • Changes in concentration that arise from these shifts will maintain K_eq given the relation defined by the constant.