Notes On Entropy and Gibbs Energy

Berthelot (1860's)--rxns with negative DH were spontaneous

J Willard Gibbs (late 1800's)--negative DH not only criteria, but entropy also important

A Brief Review of Enthalpy:

  • Spontaneous- a process that takes place w/o imput of energy from external source.

  • Natural tendency --------> decrease in energy

  • Examples

    water flows downhill, a spring unwinds  
    CH4(g) + 2O2(g) ------> C02(g) + 2H2O(g) DHrxn = - 802 kJ
    4Fe(s) + 3O2(g) -----> 2Fe2O3(s) DHrxn = -1648kJ
    Zn(s) + 2HCl(aq) -----> H2(g) + ZnC12(aq) DHrxn = -150kJ

    These rxns do not occur spontaneously in the reverse direction.

    • Some endothermic rxns do occur spontaneously, however.

    At any temperature greater than 0, ice will melt  
    H2O(s) -----> H2O(l) DHfus = +6.0 kJ
    NaCl(s) -----> Na+(aq) + Cl-(aq) DHsol'n = + 64 kJ
    Ba(OH)2(s) + 2NH4NO3(s) -----> Ba(NO3)2(s) + 2H2O(l) + 2NH3(g)  

    Clearly then, having DH greater than zero is not a general criterion of spontaneity.

    2nd Law of Thermodynamics: Entropy

    (Remember, the lst Law is Conservation of Energy: Etot = Ek + Ep = constant)

    Spontaneous, unidirectional processes often are referred to as irreversible processes.

    ex. scrambled eggs--don't unscramble

    • System--that part of the universe where the change of interest occurs

    • Surroundings--the rest of the universe

    When any kind of process has occurred--the system and its surroundings cannot be changed to be exactly like they were before.

    Carnot (1824) studied operation of heat engines (steam & internal combustion)

    Heat engines are designed to convert heat into work

    Carnot showed:

    1. why the engines must be operated at a higher temp than surroundings
    2. why all the energy cannot be converted into work
    3. how ratio of work output to heat input ratio depends on temperature difference between system and surroundings

    Entropy has the symbol S

    DS = qsystem / Tsystem

    2nd Law can also be written as q = TDS

    q -- energy transfered to or from a system

    T -- Kelvin Temperature

    if Tsys = Tsurroundings, and no heat is lost due to friction, then DS = q system / T system

    if irreversible, then the inequality sign appears

    DS greater than 0 when q for the system is positive (heat in)

    DS less than 0 when q for the system is negative (heat out)

    Unit for S is J/K

    The total entropy change (DS) for a spontaneous process must be positive. This includes surroundings, as well as system.
    Entropy, unlike energy, need not be conserved--entropy increases when a natural process occurs.

    Carnot Cycle

    In a Carnot cycle, the system traverses two isothermal and two adiabatic paths to return to the original state. Each of the paths is carried out reversibly.

  • Isothermal process--carried out at a constant temperature

  • Adiabatic process--one for which there is no transfer of heat into or out of the system (q = 0)

    Net work in one passage around the Carnot cycle is

      Wnet = -nRT(Th-Tl)ln(VB/VA)

    Entropy--measure of disorder or randomness of a system

    There are two types of disorder in a substance:

    • positional disorder--refers to the distribution of the particles in space

    • thermal disorder--refers to the distribution of the available energy among the particles

    Any process that produces a more random distribution of the particles in space gives rise to an increase in the total entropy of the substance. So does any constant pressure process that increases the temperature of the particles.

    • 3rd Law of Thermodynamics--the entropy of a perfect crystalline substance is zero at absolute zero

    There is an increase in entropy on melting & vaporization

    Phase transition, e.g. melting at constant P

    At normal freezing temp, Tf, an infinitesimally small change in external conditions (e.g.-lowering of the temp) serves to reverse the process.

    q = DH fusion

    DS fusion = qrev/Tm = DH fus/Tm---called molar entropy of fusion

    Entropy increases when a solid melts and decreases when it freezes

    DSvap = DHvap / Tb

    Molar entropies of gases & solutions depends on concentrations--due to change in positional disorder.
    This differs from enthalpy which is relatively free from effects of pressure or concentrations.

    Generally, the more atoms of a given type there are in a molecule, the greater the capacity of the molecule to take up energy and thus the greater the entropy. For molecules with approx. the same molecular masses, the more compact the molecule, the smaller the entropy.

    Standard Entropy Change is given by:  DSrxn = SDS(prod) - SDS(reactants)

    In general, the greater the difference between the total number of moles of gaseous products and the total number of moles of gaseous reactants, the greater the value of DSrxn.

    Tendency in nature -----> higher entropy

    Process that are both energy favored and entropy favored will be spontaneous.
    DH less than 0 and DS greater than 0

    Many reactions have values of DH and DS that are opposite to each other

    1. DH greater than 0 and DS greater than 0---rxn is endo- and has (+) DS

    2. DH less than 0 and DS less than 0---rxn is exo- and has (-) DS

      1) entropy favored
      2) energy favored

    these reactions may or may not be spontaneous: depends on temperature and relative sizes of DH & DS

    Gibbs energy

    Gibbs energy relates the energy that can be obtained as work from a process to the change in enthalpy, change in entropy and absolute temperature.

    Gibbs-Helmholtz Equation:  DGrxn = DHrxn - TDSrxn

    Criteria for spontaniety:

    1. if DGrxn is less than 0, then rxn is spontaneous

    2. if DGrxn greater than 0, then rxn is not spontaneous

    3. if DGrxn = 0, then rxn is at equilibrium, no net change occurs.

    Send questions, comments or suggestions to
    Gwen Sibert, at the
    Roanoke Valley Governor's School
    gsibert@rvgs.k12.va.us
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