## Thermodynamics (again)

### First Law

Energy is conserved. Under normal circumstances, the total amount of energy is constant. Because there are so many different forms of energy, it is difficult to measure total energy within a system but we can measure energy changes.

E = Efinal - Einitial

Note that the energy change is positive when the final state has more energy than the initial state. The energy can be increased by adding heat energy (q) or doing work (w) on the system.

E = q + w

When heat is added to the system, it has a positive sign, and we call the change endothermic. When it is released by the system, it has a negative sign, and we call it exothermic. (The same sign convention goes for work.)

Because of the First Law of Thermodynamics:

1. We can calculate the enthalpy of a reaction when we know the enthalpy of formation of each reactant and product.

2. We can estimate the enthalpy of reaction by considering the energy of bonds made and bonds broken.

Example: The combustion of cyclobutane releases 2597 kJ/mol. What is the standard enthalpy of formation of this compound?

C4H8 + 6 O2 4 CO2 + 4 H2O

-2597 = (4)(-394) + (4)(-242) - Hf(cyclobutane)

Hf(cyclobutane) = 53 kJ/mol

### Second Law and Entropy

The Second Law of Thermodynamics concerns entropy, or disorder. It states that the entropy of an isolated system increases over time.

We can define entropy as disorder or, more specifically, as unusable energy. You can't make a system more ordered without adding energy to the system. Entropy (S) is related to heat energy (Q) and temperature in Kelvin (T):

S = Q/T

When we discuss energy changes in chemical reactions, we use the concept of the Gibb's free energy, G, that is the amount of energy available in a chemical reaction for work. The Gibb's free energy includes a term for the heat of the reaction and a term for the heat value of the entropy change. A reaction will proceed (negative G) when heat is given off in a reaction or when the increase in entropy times temperature (in K) is greater than the energy absorbed.

G = H - TS

Because the entropy change can't be used for work, the maximum efficiency for energy conversion in a chemical reaction is the ratio of the change in the Gibb's free energy and the change in enthalpy, G/H. The greater the entropy change and the higher the temperature, the lower is the chemical efficiency.

G/H = 1 - (TS)/H

We can relate the Gibb's free energy at standard conditions to the equilibrium constant, K, and to an electrochemical cell potential, E, so both of these also have an entropy contribution. In the equations below the gas constant R = 8.314472 J/(K)(mol), n is the number of moles of electrons transferred, and Faraday's constant F = 96,500 coulombs/mol.

G0 = -RT ln(K)

G = -nFE

How does the potential of an electrochemical cell relate to energy? The SI unit of power is a watt (1 joule/sec). This is equal to the potential in volts times the current in amps (WAV).

watts = (amps)(volts)

Professor Patricia Shapley, University of Illinois, 2012