Chapter 17. Chemical Equilibrium
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3. Challenging Problem Type: Gas + Chemical Equilibrium
1. Equilibrium State
⑴ Equilibrium State: A state where the rates of the forward reaction and the reverse reaction are equal, resulting in no further change in the concentration of chemical species.
① Homogeneous: When all reactants and products are in the same state.
② Heterogeneous: When more than one state coexist.
⑵ Equilibrium Constant: A constant that remains constant at equilibrium.
① Concentration Equilibrium Constant, Kc: Calculated using molar concentrations for solutions.
② Pressure Equilibrium Constant, Kp: Used for gas-phase reactions.
③ Thermodynamic Equilibrium Constant, K: Introduces the concept of activity.
○ Activity of Gases
aideal gas = P ÷ Pº, Pº = 1 atm
⇔ aideal gas = P (unitless)
○ Activity of Solutions
asolution = C ÷ Cº, Cº = 1 M
⇔ asolution = C (unitless)
○ Activity of Solids and Liquids
asolid = aliquid = 1
○ Thermodynamic Equilibrium Constant
○ Mean Activity Coefficient γ: Geometric mean of activity coefficients of each ion.
○ Example: Mean activity coefficient of CaCl2 = (γCa2+ × γCl-)1/3
⑶ Derivation of Equilibrium Constant 1: Thermodynamic Interpretation
The free energy of A, B, C, D is expressed as follows.
Additionally, the change in free energy of the reaction is expressed as follows.
Therefore, the following conclusion is obtained.
For equilibrium constant K, the following equation holds.
Since ΔGº is constant, K is also constant.
⑷ Derivation of Equilibrium Constant 2: Kinetic Interpretation
If the rate constant for the forward reaction is k1 and for the reverse reaction is k-1, then the rate equation is as follows.
In equilibrium, the rates of the forward and reverse reactions are equal, thus:
Supplement: At equilibrium, it is possible to treat it as a single-step reaction and derive rate equations.
⑸ Reaction Quotient Q: A constant indicating the extent of reaction at a given moment.
① Relationship between ΔGr (free energy change at a certain time) and standard free energy change ΔGrº
○ Standard Gibbs Free Energy Change ΔGrº: Change in free energy when 1 mole of product is formed under standard conditions.
○ ΔGrº ＜ 0: Spontaneous forward reaction at standard conditions, K＞1
○ ΔGrº ＞ 0: Spontaneous reverse reaction at standard conditions, K＜1
○ ΔGrº = 0: Equilibrium at standard conditions, K = 1
② Relationship between Reaction Quotient Q and Equilibrium Constant K
○ Q > K: Spontaneous reverse reaction
○ Q < K: Spontaneous forward reaction
○ Q = K: Equilibrium state
⑹ Manipulation of Reaction Equations
① Rule 1: If the equilibrium constant K0 is multiplied by a coefficient k, the new equilibrium constant is K = K0k.
② Rule 2: If equilibrium constants K1 and K2 correspond to two reactions, then their addition yields K = K1 × K2.
③ Rule 3: If the equilibrium constant K1 corresponds to a reaction from which another reaction with equilibrium constant K2 is subtracted, then their subtraction yields K = K1 ÷ K2.
⑺ Predicting the Extent of Reaction Based on Equilibrium Constant K
① K ＞ 103: Product-dominant reaction
② K = 10-3 ~ 103: No dominant direction
③ K ＜ 10-3: Reactant-dominant reaction
2. Le Chatelier’s Principle
⑴ Definition: Principle stating that a system at equilibrium will shift its position to minimize any change that is imposed upon it.
⑵ Shift due to Concentration Changes
① Adding a substance causes a shift in the direction that reduces the added substance.
② Adding an irrelevant substance does not cause a shift.
⑶ Shift due to Volume Changes
① Increasing the volume of a gas shifts the equilibrium in the direction of increased gas molecules.
○ (Note) Natural tendency is to resist change, but in this case, amplification of change is observed.
② Increasing the pressure of a gas shifts the equilibrium in the direction of decreased gas molecules.
③ Increasing the volume of a solution shifts the equilibrium in the direction of increased particles.
④ Effect of Inert Gas Addition
○ Constant volume condition: No shift in equilibrium
○ Constant pressure condition: Inert gas increases volume, causing a shift in the direction of increased gas molecules.
⑷ Shift due to Temperature Changes
① Higher temperature favors endothermic reactions.
② At higher temperature, equilibrium constant of exothermic reactions decreases, while that of endothermic reactions increases.
③ (Note) With increased temperature, the number of molecules surpassing activation energy increases, causing an increase in both forward and reverse reactions.
3. Challenging Problem Type: Gas + Chemical Equilibrium
⑴ Reasons for Difficulty
① Equilibrium constant is calculated using pressure, but the chemical reaction itself should be considered in terms of moles, leading to increased calculations.
② Tip: Solve problems using pressure only.
⑵ Initial State
① Calculate based on ⑶ to ⑸.
② When temperature changes: Since equilibrium constant changes, consider the given state as the initial state.
⑶ Fixed Volume Apparatus
① Define initial pressures of A, B, C as PA0, PB0, PC0.
② Since pressure ratio is the same as mole ratio, the final pressures can be represented as follows.
③ α can be determined based on the given equilibrium constant.
⑷ Total Pressure as Constant
① Define initial pressures of A, B, C as PA0, PB0, PC0.
② First, carry out the chemical reaction and adjust the ideal gas equation, yielding the same final state.
③ In considering the mole ratio of the chemical reaction, the later pressures of A, B, C can be represented as follows.
④ Considering the ideal gas equation, the final pressures of A, B, C can be represented as follows.
⑤ α can be determined based on the given equilibrium constant.
⑸ Constant Final Volume
① Mostly, questions ask whether Pf = β.
② First estimate the final pressure using the ideal gas equation.
○ Calculate nf
○ Calculate α
○ Calculate individual pressures
③ Confirm if the assumption Pf = β is valid by substituting into the given equilibrium constant.
Input: 2019.01.01 11:53