Thermodynamics vs. Kinetics Kinetics is concerned with reaction rates which depend on the activation energy.
Thermodynamics is concerned with the difference in energy between reactants and products Thermodynamics is concerned with the position of equilibrium, related to Keq
Laws of Thermodynamics First Law: the law of conservation of energy
Spontaneous Processes and Entropy
In chemistry we are interested in whether a particular reaction will “go” usually means a favorable equilibrium constant and a conveniently rapid rate Or will “not go” either an unfavorable equilibrium constant or a rate too slow to be useful
Spontaneous Processes We describe a process as “spontaneous” or “nonspontaneous.” spontaneous means you get more products than reactants at equilibrium. Keq > 1 Whether a reaction is spontaneous or not has nothing to do with its rate. A spontaneous reaction can be very fast or can be so slow that it appears not to take place at all
Examples of spontaneous processes Waterfalls run downhill spontaneously, but not uphill. A gas expands into a vacuum spontaneously, but does not flow out of its container to form a vacuum spontaneously. Water freezes below 0ºC spontaneously; ice melts above 0 ºC spontaneously.
2Na(s) + 2H2O (l)
H2 (g) + 2NaOH (aq)
spontaneous
H2 (g) + 2NaOH (aq)
2Na(s) + 2H2O (l)
nonspontaneous
We have emphasized enthalpy in our earlier discussions of thermodynamics Our expectation is that a reaction that leads to a decrease in the total energy of the system should be spontaneous (ΔH is negative; reaction is exothermic). But observation tells us that enthalpy alone is an insufficient indicator of spontaneity. some endothermic reactions are spontaneous spontaneity depends on temperature; some reactions are spontaneous at one temperature, but nonspontaneous at another
Two examples of spontaneous endothermic processes ice melts spontaneously at temperatures above 0 ºC but not below 0 ºC. H2O(s) H2O(l) ΔH º = + 6.01 kJ ammonium nitrate dissolves in water NH4NO3(s)
NH4+(aq) + NO3–(aq) ΔH º = + 25 kJ
Four possibilities ; examples of all four are known exothermic – spontaneous exothermic – nonspontaneous endothermic –spontaneous endothermic –nonspontaneous
Entropy A process is spontaneous if it leads to an increase in the entropy of the universe. Entropy is a measure of the randomness or disorder of a system. Entropy is related to probability.
Probability a probable event is one that can happen in many ways an improbable event is one that can happen in only one way
Entropy and Probability Expansion of ideal gas into a vacuum is spontaneous, but migration of gas molecules into one region of a container is nonspontaneous.
expansion of ideal gas into a vacuum is spontaneous
expansion of ideal gas into a vacuum is spontaneous
but migration of gas molecules into one region of a container is nonspontaneous
Why is the spontaneous process the one that gives equal numbers of gas molecules in both flasks? It is the most probable state -- the one that has the most ways of being achieved.
How many ways may 1 gas molecule be arranged in a two-bulb container? Left Right 1 0 0 1 probability that the gas 1 molecule will be in 2n left bulb = .5 where n = number of molecules
What is the probability that two gas molecules will be in the same bulb of a two-bulb container?
Left both green blue 0
Right 0 blue green both
probability that both gas molecules will be in left bulb = 0.25 1 1 = n 2 22 where n = number of molecules
What is the probability that 3 gas molecules will be in the same bulb of a two-bulb container?
Left Right 3 2 1 0
0 1 2 3
3 ways 3 ways
probability that all gas molecules will be in left bulb = .125 1 1 = n 2 23 where n = number of molecules
What is the probability that one mole of gas molecules will be in the same bulb of a two-bulb container?
where n = Avogadro’s number of molecules
probability that all gas molecules will be in left bulb is very small 1 1 = n 2 2N
What is the probability that 4 gas molecules will be equally distributed in a two-bulb container? Left Right 4 0 1 3 16 possibilities 2 2 3 1 0 4 6 Equal distribution is the most 16 probable out come
No. of ways 1 ways 4ways 6 ways 4ways 1 ways
An ordered state has a low probability of occurring and a small entropy, while a disordered state has a high probability of occurring and a high entropy
How are the entropy of different phases related? gas solid liquid Sgas Ssolid < Sliquid 0 A process is at equilibrium if: ΔSuniv = ΔSsystem + ΔSsurr = 0 Therefore we need to consider how the entropy of the system and the surroundings change during a process
Entropy changes in the System
Entropy changes in the System ΔSsystem is ΔSsystemis
+ if disorder increases
- if products are more ordered
than reactants Can be calculated from tables of thermodynamic values
ΔS°rxn = ΣnS° (products) – Σm S° (reactants)
We can often make good guesses as to the sign of ΔSsystem
Entropy changes in the System Calculate the standard entropy change for: 2CO(g ) + O2(g )
2CO2(g )
qualitative prediction: 2 moles of gas on the right, 3 on the left ; the products are more ordered than reactants; the sign of ΔS° is -
Entropy changes in the System If a reaction produces excess gas ΔSsystem is
+
If a reaction produces no net change in gas molecules ΔSsystem may be ( +) or ( - ) but the change will have a small value General Rule: a reaction that increases the total number of molecules or ions will increase ΔSsystem
Entropy changes in the surroundings How are surroundings affected by heating and cooling? exothermic reactions increases entropy of surroundings endothermic reactions decrease entropy of surroundings q −ΔHsystem ΔSsurr= ΔSsurr= T T
Surroundings
System
Heat
Surroundings
System
System
Heat
Surroundings Entropy
Surroundings
System
Heat
System
Heat
Entropy
System
Heat
Surroundings Entropy
Surroundings
What are the possibilities? ΔSsys+ ΔSsurr = ΔSuniv spontaneous? +
+
– +
– –
–
+
+ – ? ?
yes no
Spontaneity and temperature a reaction may be spontaneous at one temperature and nonspontaneous at a different temperature
ΔSuniv = ΔSsystem + ΔSsurr –ΔHsystem T
Gibbs Free Energy ΔSuniverse = ΔSsurroundings+ ΔSsystem we study the system; therefore reference “surroundings” in terms the system
Gibbs Free Energy Free Energy (ΔG) is a measure energy available to do work. a release of free energy during a chemical reaction is spontaneous. takes into account both enthalpy (heat released or absorbed) and entropy (disorder).
Criterion for spontaneity is the Gibbs free energy change The meaning of its +/- signs are opposite DSuniverse. At constant temperature and pressure, if ΔGsystem is negative,the reaction is spontaneous positive, the reaction is not spontaneous zero, the system is at equilibrium
Standard Free-Energy Changes
Standard Free Energies of Formation the change in free energy that accompanies the formation of 1 mole of a substance from its constituent elements at standard conditions ΔGf = kJ ΔGºf = kJ/mol
From Standard Free Energies of Formation ΔGºrxn = ΣnΔGºf (products)
–
Σm ΔGºf (reactants)
the standard free energies of formation of any element in its stable form equals zero
Example: Calculate the standard free-energy changes for the following reaction at 25ºC : 2C2H6(g ) + 7O2(g ) 4CO2(g )
Endothermic dissolution: at 25 º C ( 298 K) NH4Cl(s )
NH4+ (aq ) + Cl- (aq )
ΔHºf
-315.4 kJ/mol
-132.8 kJ/mol -167.2 kJ/mol
Sº
94.6 J/mol K
112.8 J/mol K 56.5 J/mol K
ΔGºf -203.9 kJ/mol
-79.5 kJ/mol -131. 2 kJ/mol
ΔGºrxn = -6.8 kJ/mol
Free Energy and Equilibrium
kinetic definition of equilibrium position: the point at which rates of forward and reverse reactions are equal thermodynamic definition : the point of minimum free energy; ΔG = 0
The relationship between ΔG and ΔG° ΔGº = ΔHº – TΔSº reactants in their standard state completely changing into products in their standard state as soon as the reaction starts the standard state condition no longer exists
ΔG = ΔH – TΔS the absolute change in free energy change
The relationship between ΔG and ΔG° ΔG = ΔGº + RT ln(Q ) ΔG = 0 at equilibrium
ΔG = ΔGº + RT ln
[products] [reactants]
The relationship between ΔG and ΔG° ΔG = ΔG° + RT ln(Q) ΔG = 0 at equilibrium a large negative value ΔG°
a large relative value for products needed to make (RTlnQ) equivalent to ΔG°
0 = ΔG° + RT ln
[products] [reactants]
The relationship between ΔG and ΔG° ΔG = ΔG° + RT ln(Q ) ΔG = 0 at equilibrium a large positive value ΔG°
a small relative value for products needed to make (RTlnQ) equivalent to ΔG°
0 = ΔG° + RT ln
[products] [reactants]
The relationship between ΔG and ΔG° ΔG = ΔG° + RT ln(Q ) at equilibrium: ΔG = 0 and Q = K 0 = ΔG° + RT ln K ΔG° = − RT ln K
Example ΔG°= -33.2 kJ for the reaction at 25ºC: N2(g )
+ 3H2(g )
2NH3(g )
Is the reaction going forward in the direction written under these conditions? P(NH3) = 12.9 atm, P(N2) = 0.87 atm, and P(H2) = 0.25 atm ?
