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:
Most, but NOT all spontaneous rxns evolve energy
- For a rxn to be exothermic: DHrxn = SDHf(prod) - SDHf(reactants) must be less than 0
- DHrxn is called Standard Enthalpy Change
- Thermodynamic standard states = 1 atm, 1 M for sol'ns, 25 oC (298 K)
- DHrxn = SDHf(prod) - SDHf(reactants) and is approximately equal to DUrxn
- Standard enthalpy change is approximately equal to the Standard energy change
- Enthalpy is relatively independent of pressure and temperature.
Spontaneous- a process that takes place w/o imput of energy from external source.
Natural tendency --------> decrease in energy
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.
(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
- why the engines must be operated at a higher temp than surroundings
- why all the energy cannot be converted into work
- 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.
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.
A to B: isothermal expansion, (temp, Th)
wAB = -qAB = -nRThln(VB / VA)
B to C: adiabatic expansion,
qBC = 0
wBC = nCv ( Tl - Th) = -nCv ( Tl - Th)
C to D: isothermal compresssion, (temp, Tl)
wCD = -qCD =-nRTlln(VD / VC)
= nRTlln(VC / VD)
D back to A: adiabatic compression
qDA = 0
wDA = nCv ( Th - Tl) = - nCv ( Tl - Th)
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:
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.
- positional disorder--refers to the distribution of the particles in space
- thermal disorder--refers to the distribution of the available energy among the particles
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
these reactions may or may not be spontaneous: depends on temperature and relative sizes of DH & DS
- DH greater than 0 and DS greater than 0---rxn is endo- and has (+) DS
- DH less than 0 and DS less than 0---rxn is exo- and has (-) DS
1) entropy favored
2) energy favored
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:
- if DGrxn is less than 0, then rxn is spontaneous
- if DGrxn greater than 0, then rxn is not spontaneous
- 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
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