# Chapter 20 - Thermodynamics: Entropy, Free Energy, and Reaction Direction

• A spontaneous change in a system happens when certain criteria are met and there is no continual input of energy from outside the system. Water, for example, freezes spontaneously at 1 atm and 5°C.

• A natural activity, such as burning or falling, may require a little "push" to get started—for example, a spark to ignite gasoline vapors.

• A thrust in your car's engine to knock a book off your desk—but, after the procedure is complete when it starts, it provides the energy required for it to continue. A nonspontaneous event, on the other hand, Change happens only if the environment provides the system with input on a continual basis.

• In terms of energy If a change occurs spontaneously in one direction under certain conditions, it is not spontaneous.

• The first law accounts for a process's energy but not its direction. When gasoline burns in a car engine, the potential energy difference between the bonds in the fuel mixture and those in the exhaust gases is transformed to the kinetic energy of the moving automobile and its parts plus the heat emitted into the environment, according to the first law.

• But why doesn't the engine's heat transform exhaust gases back into gasoline and oxygen? According to the first law, as an ice cube melts in your palm, the energy in your hand is transferred to kinetic energy as the solid transforms into a liquid.

• But why doesn't the pool of water in your cupped palm return the heat to your hand and cause it to refreeze?

• Neither of these events contradicts the first rule; if you measure the work and heat in each case, you will discover that energy is conserved; yet, these reverse changes never occur. That is, the first law does not anticipate the second law, the path of a spontaneous transformation.

• Perhaps the sign of the enthalpy change (H), the heat acquired or lost at constant pressure (qP), is the criteria for spontaneity; indeed, leading scientists believed so for most of the nineteenth century.

• If this were true, we would expect exothermic (H 0) processes to be spontaneous and endothermic (H > 0) processes to be nonspontaneous. Let's look at several instances to determine whether this is correct.

• Processes that occur on their own with H 0. At certain temperatures and pressures, all freezing and condensing reactions are exothermic and spontaneous:

• H2O(l) ⟶ H2O(s) ΔH°rxn = −ΔH°fus = −6.02 kJ (1 atm; T = 0°C)

• The burning of methane and all other combustion reactions are spontaneous and exothermic:

• CH4(g) + 2O2(g) ⟶ CO2(g) + 2H2O(g) ΔH°rxn = −802 kJ

• When we examine the preceding instances of spontaneous endothermic reactions, we see that they all have one thing in common: the chemical entities—atoms, molecules, or ions—have more freedom of movement after the transition. To put it another way, following the modification, the particles have a greater range of energy of motion, (kinetic energy); we say their energy has become more scattered, diffused, or disseminated.

• The phase transitions transform a solid, in which motion is constrained, into a liquid, in which particles have more freedom to move around each other, and finally into a gas, in which particles have considerably greater freedom of motion. As a result, the energy from the movement is more scattered.

• When a salt is dissolved, it converts a crystalline solid and a pure liquid into distinctions. Because solvent molecules are moving and interacting, their freedom of motion is increased and their motion energy is more distributed.

• In chemical processes, fewer moles of crystalline solids create more moles of gases and/or solvated ions, increasing particle freedom of motion and dispersing the energy of motion: A change in the freedom of mobility of particles in a system, that is, the dispersal of their energy of motion is a critical element in determining the direction of a spontaneous event in thermodynamic terms.

• Energy quantification Consider a system containing 1 mol of N2 gas and focusing on one molecule. It is traveling across space (translating) at some speed, spinning at some frequency, and its atoms are vibrating at some frequency at any given time.

• The molecule then collides with another or with the container, and these values of motional (kinetic) energy states vary.

• The whole quantum at any one time, the molecule's state comprises of its electrical states as well as its translational, rotational, and vibrational states.

• The total number of microstates. The energy of all molecules in a system is quantized in the same way.

• Each quantized state of the system is referred to as a microstate, and the entire energy of the system is distributed over one microstate at any one time.

• It is distributed throughout a different microstate the following moment. The total number of microstates conceivable for a system of 1 mol of molecules is mind-boggling, on the magnitude of a total of 101023.

• Dispersion of energy Each microstate has the same sum under a particular set of conditions as much energy as any other. As a result, for the system, any microstate is equally feasible and the rules of probability dictate that all microstates are equally likely over time.

• The number of microstates for a system is the number of ways it may divide (distribute or spread) its kinetic energy across all of its particles' different movements.

• In previous chapters, we introduced entropy (S) as a thermodynamic quantity that is directly connected to the number of ways a system's energy may be spread.

• The movements of its particles, and we discovered that entropy plays an important role in the creation.

• Some potential solutions Ludwig Boltzmann, an Austrian mathematician and physicist, was born in 1877.

• The number of microstates (W) was connected to a system's entropy:

• S = k ln W

• where k, the Boltzmann constant, is the universal gas constant (R, 8.314 J/molK) divided by Avogadro's number (NA), i.e. R/NA = 1.381023 J/K Because the word W refers to the number of microstates, it has no units; hence, S has units of J/K is an abbreviation for joules/kelvin. Thus, Entropy is lower in a system with fewer microstates (smaller W) (lower S).

• The entropy of a system with more microstates (bigger W) is greater (higher S).