Spontaneous Processes and EntropySpontaneous Processes and Entropy

• First Law• “Energy can neither be created nor

destroyed“.• The energy of the universe is constant.

• Spontaneous Processes• Processes that occur without outside

intervention.• Spontaneous processes may be fast or

slow.–Many forms of combustion are fast–Conversion of diamond to graphite is

slow

Entropy (S)Entropy (S)• A measure of the randomness or A measure of the randomness or disorderdisorder. . • The driving force for a spontaneous The driving force for a spontaneous

process is an process is an increaseincrease in the in the entropyentropy of the of the universe.universe.

• Entropy is a thermodynamic function Entropy is a thermodynamic function describing the describing the numbernumber of of arrangements arrangements that are available to a system.that are available to a system.

• Nature proceeds toward the Nature proceeds toward the statesstates that that have the have the highesthighest probabilities of existing. probabilities of existing.

• The most likely is the most random.The most likely is the most random.

Positional EntropyPositional Entropy• The The probabilityprobability of occurrence of a of occurrence of a

particular state depends on the particular state depends on the numbernumber of of waysways (microstates) in which that (microstates) in which that arrangement can be achieved.arrangement can be achieved.

• Positional entropy increases from solid Positional entropy increases from solid to liquid to gas.to liquid to gas.

SSsolidsolid < S < Sliquidliquid << S << Sgasgas

• Solid state: molecules are Solid state: molecules are closeclose together together with relatively few positions available.with relatively few positions available.

• Gaseous state: molecules are Gaseous state: molecules are farfar apart, apart, with more positions available.with more positions available.

• Liquid state is Liquid state is closercloser to the to the solidsolid state state than gaseous state.than gaseous state.

SSsolidsolid < S < Sliquidliquid << S << Sgasgas

Second Law of ThermodynamicsSecond Law of Thermodynamics "In any spontaneous process there is

always an increase in the entropy of the universe"

"The entropy of the universe is increasing"

For a given change to be spontaneous, Suniverse must be positive

Suniv = Ssys + Ssurr

Temperature and Spontaneity• Entropy changes in the surroundings are primarily determined

by heat flow.• Exothermic reactions in a system at constant temperature

increase the entropy of surroundings.• ∆Ssurr = positive• Endothermic reactions in a system at constant temperature

decrease the entropy of surroundings.• ∆Ssurr = negative• The impact of the transfer of a given quantity of energy as heat

to or from the surroundings will be greater at lower temperatures.

•∆Ssurr for a reaction under conditions of constant temperature (K) and pressure:

∆Ssurr = -∆H / T

•Gaseous reactions:•Calculate change in the number of moles of gas, ∆ngas on going from reactants to products.•∆ngas is positive = entropy is positive

•2NaHCO3 (s) → Na2 CO3 (s) + CO2 (g) + H2O(g)•Gaseous products > Gaseous reactants•Change in Entropy = ∆S = positive

•Another factor that affects the sign of ∆S is degree of complexity of molecules.

H2 (g) → 2H(g)

•Decrease in complexity and increase in number of particles = increase in entropy

•“At absolute zero the entropy of a perfectly ordered pure crystalline substance is zero.”

•Since pure crystal is zero all other must be > 0.•Standard Entropy of 1 mol of substance, So is measured at 298 K (25o C) and 1 atm.•Units are J/K mol.•Values published in Appendix 4 of textbook.

Calculating Entropy Change in a Calculating Entropy Change in a ReactionReaction

Entropy is an extensive property (a function of the number of moles)

Generally, the more complex the molecule, the higher the standard entropy value

0 0 oreaction products reactantsp rS n S n S