Summary Physical Organic Chemistry
4.1 Thermodynamic Analyses of Binding
Solute-solute interactions: one is the host and the other the guest
- The host (H) is the larger molecule, and it encompasses the smaller guest (G) molecule
Knowledge of thermodynamics of binding is essential for designing of synthetic systems that perform
functions and tasks
- Often the goal: to bind a desired molecule from solution and interact with it in some manner
(performing a reaction, giving of a signal)
[HG]
- Ka : association constant = [H][G]
[H][G]
- Kd : dissociation constant =
[HG]
- Ka and Kd are reciprocals
- ΔG° = -RT ln(Ka)
ΔG reflects the change in Gibbs free energy for the conversion of
one mole of H and G to one mole of HG if H and G started in their
standard states and HG ended in its standard state
Low and high concentrations that make H and G or HG dominant
- When the initial concentrations of H and G are the same
and are both below kd, free H and G will dominate the equilibrium
- When the initial concentrations of H and G are above kd, then HG will dominate
- When the concentrations of free H and G equal kd, [HG] = kd
- The entropy of a solution of H, G and HG will increase more rapidly upon dilution when
creating free H and G, because there are two species that are leading to an entropic
stabilization relative to the one HG
- Upon dilution, an HG complex will continually dissociate to H and G due to the favourable
entropy of the entire solution
Standard state:
- When the entropy of a solution of reactants becomes more favourable faster than the
entropy of a solution of products upon dilution it means that the Gibbs free energy of the
solution is changing upon dilution
- To compare different systems: the entropy resulting from dissolution in a solvent is the same
for any solute, regardless of its identity (not when comparing reactions)
- The potential for a spontaneous change in composition to occur is the difference in the Gibbs
free energies of H, G and HG in their standard states plus a term that reflects the mismatch
between the experimental ratios of H, G and HG and their intrinsic rations at standard state
- μH = μoH + RT ln(aH)
- When a ΔG* diagram would show HG higher in energy than H and G, it means that given this
reference state, free H and G are preferred
The influence of change in heat capacity:
- ΔHo and ΔSo won’t change with temperature
- This is often not true for many types of binding interaction a clear indication that the heat
capacities of the reactants and products are different
- Heat capacity: amount of energy that a substance absorbs as a function of temperature
- HA° = HA°’ + (T – 298) CP(A)°
T
- SA°(Tf) = SA°(Ti) + CP(A)° lnTf
i
4.1 Thermodynamic Analyses of Binding
Solute-solute interactions: one is the host and the other the guest
- The host (H) is the larger molecule, and it encompasses the smaller guest (G) molecule
Knowledge of thermodynamics of binding is essential for designing of synthetic systems that perform
functions and tasks
- Often the goal: to bind a desired molecule from solution and interact with it in some manner
(performing a reaction, giving of a signal)
[HG]
- Ka : association constant = [H][G]
[H][G]
- Kd : dissociation constant =
[HG]
- Ka and Kd are reciprocals
- ΔG° = -RT ln(Ka)
ΔG reflects the change in Gibbs free energy for the conversion of
one mole of H and G to one mole of HG if H and G started in their
standard states and HG ended in its standard state
Low and high concentrations that make H and G or HG dominant
- When the initial concentrations of H and G are the same
and are both below kd, free H and G will dominate the equilibrium
- When the initial concentrations of H and G are above kd, then HG will dominate
- When the concentrations of free H and G equal kd, [HG] = kd
- The entropy of a solution of H, G and HG will increase more rapidly upon dilution when
creating free H and G, because there are two species that are leading to an entropic
stabilization relative to the one HG
- Upon dilution, an HG complex will continually dissociate to H and G due to the favourable
entropy of the entire solution
Standard state:
- When the entropy of a solution of reactants becomes more favourable faster than the
entropy of a solution of products upon dilution it means that the Gibbs free energy of the
solution is changing upon dilution
- To compare different systems: the entropy resulting from dissolution in a solvent is the same
for any solute, regardless of its identity (not when comparing reactions)
- The potential for a spontaneous change in composition to occur is the difference in the Gibbs
free energies of H, G and HG in their standard states plus a term that reflects the mismatch
between the experimental ratios of H, G and HG and their intrinsic rations at standard state
- μH = μoH + RT ln(aH)
- When a ΔG* diagram would show HG higher in energy than H and G, it means that given this
reference state, free H and G are preferred
The influence of change in heat capacity:
- ΔHo and ΔSo won’t change with temperature
- This is often not true for many types of binding interaction a clear indication that the heat
capacities of the reactants and products are different
- Heat capacity: amount of energy that a substance absorbs as a function of temperature
- HA° = HA°’ + (T – 298) CP(A)°
T
- SA°(Tf) = SA°(Ti) + CP(A)° lnTf
i
