Course Code: CHM-DSC-251
Subject: Physical Chemistry - II
In a mixture of multiple components, the contribution of each component to the total thermodynamic property of the system is described by Partial Molar Quantities.
Chemical potential is the partial molar Gibbs free energy. It represents the change in the total Gibbs energy of a system when one mole of a specific component is added at constant temperature and pressure.
μi = (dG / dni)T, P, nj
Physical Significance: Chemical potential acts as the "driving force" for the transfer of matter. Matter spontaneously moves from a region of higher chemical potential to a region of lower chemical potential until the chemical potentials are equalized.
This equation shows that the chemical potentials of components in a system are not independent of each other. At constant temperature and pressure, for a multi-component system:
Σ ni dμi = 0
This implies that if the chemical potential of one component increases, the chemical potential of at least one other component must decrease to maintain the balance.
A system is in a state of thermodynamic equilibrium when there are no driving forces for further change.
The Law of Mass Action states that the rate of a chemical reaction is proportional to the product of the active masses (or concentrations) of the reactants.
Thermodynamic derivations allow us to relate these constants based on partial pressures (Kp), molar concentrations (Kc), and mole fractions (Kx).
| Constant | Definition Basis | Relationship Equation |
|---|---|---|
| Kp | Partial Pressures of gases | Kp = Kc (RT)^Δn |
| Kc | Molar concentrations | Kc = Kp (RT)^-Δn |
| Kx | Mole fractions | Kp = Kx (P)^Δn |
Where Δn is the change in the number of moles of gaseous products minus gaseous reactants.
If a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the equilibrium will shift in a direction that tends to counteract the change.
The Van't Hoff Reaction Isotherm relates the Gibbs free energy change (ΔG) to the reaction quotient (Q) and the equilibrium constant (K).
ΔG = ΔG° + RT ln Q
At equilibrium, ΔG = 0, leading to: ΔG° = -RT ln K.
Biological systems often use reaction coupling, where a non-spontaneous (endoergic, ΔG > 0) reaction is driven by a spontaneous (exoergic, ΔG < 0) reaction, such as the hydrolysis of ATP, so that the overall ΔG is negative.
Q: What is the physical significance of ΔG = 0?
A: It signifies that the system is at chemical equilibrium; the rate of the forward reaction equals the rate of the reverse reaction.
Q: How does a catalyst affect the equilibrium constant?
A: A catalyst does not change the equilibrium constant or the position of equilibrium; it only speeds up the time it takes to reach equilibrium.
Q: Define Chemical Potential.
A: It is the partial molar Gibbs energy, representing the change in free energy per mole of substance added at constant T and P.