- Physical Chemistry I
Spring 2015, Unique 51170
Lecture Summary, 10 March 2015
Now that we know a variety of ways to determine free energy:
dG = dH - TdS
dG = VdP - SdT,
etc., we can determine the direction of spontaneous change for any thermodynamic transformation. If the change in free energy of the system is < 0, the reaction will proceed spontaneously. If deltaG > 0, then the process will not go forward spontaneously, and we need to change the system in some way to make that happen, for example by changing temperature or pressure. If deltaG = 0, the system is in equilibrium, meaning that free energy considerations in both the forward and backwards direction are balanced, and the system will not change any further. The magnitude of deltaG does not yet matter to us - a larger negative number does not make that process "more" spontaneous than another. The only questions we care about now are if deltaG > 0, < 0, or = 0.
Chemical Potential: So far we have only discussed how the energy (usually freeenergy) of a system changes as a function of pressure, temperature, and volume. Thus far we have kept the final variable in the ideal gaslaw, n, constant. However, in a chemical reaction taking place in a closed orisolated system, although no matter is exchanged between the system and the surroundings, the energy of the system will most definitely changeas reactants are converted to products. We therefore need a way of understanding how free energy changes as a function of the amountand chemical identity of the subtances that fill the system.
To begin this, we introduced the concept of chemical potential (mu), which is the change in free energy of a system caused by the change inthe moles of the reactants and products in that system. It is the potential energy held by a system as a function of the chemical bondscontained by and intermolecular interactions between molecules in that system. A chemical reaction will reach equilibrium when the sumof all chemical potentials in the system equals 0. If the chemical potentials of the reactants are greater than the chemicalpotentials of the products, the reaction will proceed spontaneously in the forward direction until the system reaches equilibrium. Wedefined a reaction coordinate, z, to tell us at what composition of reactants and products this willoccur. Looking ahead, we will define an equilibrium constant, K(p), which is the product of the partial pressures of every component in thesystem raised to their signed stoichiometric coefficient, nu.