Lecture Notes: Relationship Between Free Energy and Reaction Quotient
Key Concepts
- Delta G (ΔG): Instantaneous change in free energy between reactants and products.
- Reaction Quotient (Q): Indicates the current state of a reaction; similar in form to the equilibrium constant (K).
- Delta G Zero (ΔG°): Standard change in free energy under standard conditions.
- R (Gas Constant): A constant value used in the calculation of free energy.
- Temperature (T): Measured in Kelvin.
Relationship Between ΔG and Reaction Characteristics
- ΔG < 0: Reaction is spontaneous in the forward direction.
- ΔG > 0: Reaction is non-spontaneous in the forward direction.
- ΔG = 0: Reaction is at equilibrium.
Example: Synthesis of Ammonia
- Given Conditions:
- Temperature: 25 degrees Celsius
- Standard ΔG°: -33.0 kilojoules
- Partial pressures: 1 atm for nitrogen, hydrogen, and ammonia.
Calculation
- Equation: ΔG = ΔG° + RT ln(Q)
- Determine Q:
- For gases, use partial pressures instead of concentrations.
- Q = (P_ammonia)^2 / (P_nitrogen)(P_hydrogen)^3
- With partial pressures at 1 atm, Q = 1.
- ΔG Calculation:
- ln(1) = 0, so ΔG = ΔG° = -33.0 kilojoules
- Reaction is spontaneous as ΔG is negative.
Adjusting Partial Pressures
- New Conditions: Partial pressures at 4.0 atm.
- Re-calculation:
- Q = (4.0^2) / (4.0^1 * 4.0^3) = 0.0625
- Calculate ΔG with new Q value
- Result: ΔG = -39.9 kilojoules/mole
- Still spontaneous, as ΔG is negative.
Reaction Progress and Equilibrium
- Q < K: Reaction proceeds forward, making more products.
- Increase in Q: As products form, Q increases.
- Effect on ΔG: As Q increases, ΔG moves towards zero.
Equilibrium State
- Q = K: Equilibrium achieved, ΔG = 0.
- No Driving Force: At equilibrium, reactants and products have equal free energy.
Summary
- ΔG provides insight into the spontaneity and direction of a reaction.
- The relationship between Q and K (equilibrium constant) determines the progress of a reaction.
- At equilibrium, ΔG is zero, indicating no net change in the system.
These concepts are crucial for understanding chemical thermodynamics and predicting reaction behavior under various conditions.