Thermodynamics 2: Le Chatelier's Principle and Additivity of Free Energy

Overview of Objectives

• Predict how changes in concentration influence the direction and magnitude of reactions (Le Chatelier’s Principle).

• Balance equations for two sequential biochemical reactions.

• Calculate the overall $riangle G^o$ for two sequential biochemical reactions.

• Calculate the overall $riangle G$ for two sequential biochemical reactions.

Le Chatelier's Principle

• Definition:

  • "When equilibrium is disturbed the reaction will respond to nullify the disturbance."

• Scope:

  • Applies to reversible reactions.

• Disturbances that can affect equilibrium include:

  • Change in temperature.

  • Change in pH.

  • Change in concentrations of [reactants] or [products].

Temperature Effects on Exothermic Reactions

• Exothermic Reactions:

  • Heat is released as a product.

  • Example Reaction:

  • $NO<em>2 (g) \rightleftharpoons N</em>2O_4 (g) + \text{heat}$

  • Color Change: Brown to Colorless

  • Enthalpy Change: $riangle H = -13.6 \text{kcal/mole}$

• Effect of Temperature:

  • Adding heat can reverse the direction of the reaction.

  • Removing heat will favor the forward reaction.

pH Changes and Buffer Responses

• Buffers:

  • Substances that minimize changes in pH.

• Situations:

  • If pH increases:

  • Conjugate acid (HA) releases [H+].

  • Consequence: [HA] decreases; [A-] increases.

  • If pH decreases:

  • Conjugate base (A-) picks up [H+].

  • Consequence: [HA] increases; [A-] decreases.

Response to Changes in Concentration

• Example of Sugar Interconversion:

  • In glycolysis, the interconversion of glucose-6-phosphate (G6P) and fructose-6-phosphate (F6P) is a vital reaction.

  • If initially $[G6P] = [F6P]$, reaction direction based on concentration changes:

  • If $[F6P]$ increases: Reaction proceeds to the right (toward G6P).

  • If $[G6P]$ decreases: Reaction proceeds to the left (toward F6P).

  • Equilibrium Constant: $K_{eq} = 1.97$.

Practical Limitations of Reversible Reactions

• Some reactions may be theoretically reversible, but practically irreversible under biological conditions.

• Example:

  • Glucose Oxidation:

  • $C<em>6H</em>{12}O<em>6 + 6O</em>2 \rightarrow 6CO<em>2 + 6H</em>2O$

  • Gibbs Free Energy Change: $riangle G^o = -686 \text{kcal/mole}$.

Additivity of Free Energy

• In cellular processes, the oxidation of glucose to CO2 and H2O is executed in multiple smaller reactions.

  • Total free energy from these steps accounts for the overall free energy of glucose oxidation.

  • Total Reaction Gibbs Free Energy Change: $riangle G^o = -686 \text{kcal/mol}$ for the entire process from Glucose to CO2 and H2O.

Multiplying/Dividing $K_{eq}$ and Adding/Subtracting Free Energy

• When modifying equilibrium constants or free energy:

  • Multiplying $K_{eq}$:

  • $-RT \ln (Keq<em>1 \cdot Keq</em>2) = \triangle G^o<em>1 + \triangle G^o</em>2$

  • Dividing $K_{eq}$:

  • $-RT \ln \left( \frac{Keq<em>1}{Keq</em>2} \right) = \triangle G^o<em>1 - \triangle G^o</em>2$

• Properties of logarithms used here:

  • Adding Exponents = Adding Logs:

  • $\log<em>{10}(10^2 \cdot 10^2) = \log</em>{10}(10^2) + \log_{10}(10^2)$

  • Subtracting Exponents = Subtracting Logs:

  • $\log<em>{10}(10^5/10^2) = \log</em>{10}(10^5) - \log_{10}(10^2)$.

Relationship Between Equilibrium Constants and Free Energy Changes

• A 10-fold change in $K<em>{eq}$ or $Q</em>c$ corresponds to a change in free energy $\triangle G^o$ or $\triangle G$ of:

  • $1.36 \text{kcal/mol}$.

• Additional Information:

  • Conversion factor: $1 \text{kcal} = 4.184 \text{kJ}$.

Sequential Biochemical Reactions and Additivity of Free Energy

• Overcoming Unfavorable Reactions:

  • Phosphorylation of glucose, a part of glycolysis, is endergonic:

  • Balanced Overall Equation:

  • $\text{Glucose} + \text{Pi} \rightarrow \text{glucose-6-phosphate}$

  • $\triangle G^o = +3.3 \text{kcal/mole}$

  • Coupling Reaction:

  • $\text{ATP} \rightarrow \text{ADP} + \text{Pi}$

  • $\triangle G^o = -7.3 \text{kcal/mole}$

• Importance of Coupling:

  • This coupling is essential in driving endergonic reactions forward by harnessing energy from exergonic reactions such as ATP hydrolysis.

Conclusion

• Acknowledgments:

  • Thank you for your attention!

  • Focus on the principles of Le Chatelier's Principle and additivity of free energy to master the dynamics of biochemical reactions.