Entropy

Entropy Entropy is defined as a state of disorder or randomness.

In general the universe tends to move toward release of energy and greater entropy.

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Entropy The statistical

interpretation of thermodynamics was pioneered by James Clerk Maxwell (1831–1879) and brought to fruition by the Austrian physicist Ludwig Boltzmann (1844–1906).

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EntropySpontaneous chemical processes often result in a final state is more Disordered or Random than the original.The Spontaneity of a chemical process is related to a change in randomness.Entropy is a thermodynamic property related to the degree of randomness or disorder in a system.

Reaction of potassium metal with water. The products are more randomly distributed than the reactants 4

Entropy and Thermodynamics

According to the second law or thermodynamics the entropy of the universe is always increasing.This is true because there are many more possibilities for disorder than for order.

Entropy

Royal Flush

Nothing hand

Entropy is Disorder Disorder in a system can take many forms.

Each of the following represent an increase in disorder and therefore in entropy:

1. Mixing different types of particles. i.e. dissolving salt in water.

2. A change is state where the distance between particles increases. Evaporation of water.

3. Increased movement of particles. Increase in temperature.

4. Increasing numbers of particles. Ex. 2 KClO3 2 KCl + 3O2

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Entropy StatesThe greatest increase in entropy is usually found when there is an increase of particles in the gaseous state.The symbol for the change in disorder or entropy is given by the symbol, DS.The more disordered a system becomes the more positive the value for DS will be.Systems that become more ordered have negative DS values.

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The entropy of a substance depends on its state: S (gases) > S (liquids) > S (solids)

Entropy, S

So (J/K-1mol-1)

H2O (liquid) 69.95

H2O (gas) 188.8 9

Entropy and States of Matter

S˚(Br2 liquid) < S˚(Br2 gas) S˚(H2O solid) < S˚(H2O liquid)

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Entropy, Phase & Temperature

S increases slightly with T

S increases a large amount with phase changes

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The Entropy of a substance increases with temperature.

Molecular motions of heptane, C7H16

Molecular motions of heptane at different temps.

Entropy and Temperature

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Entropy - BoltzmanLudwig Boltzman

S = k Ln W Entropy is proportional to the number of degrees of freedom or possible configurations in a system.

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Standard Entropy ValuesThe standard entropy, DSo, of a substance is the entropy change per mole that occurs when heating a substance from 0 K to the standard temperature of 298 K.Unlike enthalpy, absolute entropy changes can be measured.Like enthalpy, entropy is a state function. The change in entropy is the difference between the products and the reactants

DSo = S So (products) - S So (reactants)

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Standard Entropy Values

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The amount of entropy in a pure substance depends on the temperature, pressure, and the number of molecules in the substance. Values for the entropy of many substances at have been measured and tabulated. The standard entropy is also measured at 298 K.

Some standard enthalpy values

Gibbs Free Energy

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SpontaneityA chemical reaction is spontaneous if it results in the system moving form a less stable to a more stable state.Decreases in enthalpy and increases in entropy move a system to greater stability.The combination of the enthalpy factor and the entropy factor can be expressed as the Gibbs Free Energy.

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Gibbs Free EnergyThe standard free energy change is defined by this equation

DGo = DHo – T DSo

Where

DHo = the enthalpy changeDSo = the entropy change T = Kelvin temperature

A chemical reaction is spontaneous if it results in a negative free energy change.

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Gibbs Free EnergyPossible Combinations for free energy change:

DGo = DHo – T DSo

DG DH DS DH-TDSAlways Spontaneous

< 0 (-) < 0 (-) > 0 (+) Always (-)

Never Spontaneous

> 0 (+)

> 0 (+) < 0 (-) Always (+)

Spontaneous at High Temperature

< 0 (-) > 0 (+)

> 0 (+) > 0 (+)

(-) if T large(+) if T small

Spontaneous at Low Temperature

> 0 (+)< 0 (-)

< 0 (-) < 0 (-)(+) if T large(-) if T small

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Free Energy Problem 1A certain chemical reaction is exothermic with a standard enthalpy of - 400 kJ mol-1. The entropy change for this reaction is +44 J mol-1 K-1. Calculate the free energy change for this reaction at 25 oC. Is the reaction spontaneous?

SolutionConvert the entropy value to kJ. 44 J mol-1 K-1 = 0.044

kJ mol-1 K-1

 DG = - 400 kJ mol-1 – (298 K)(0.044 kJ mol-1 K-1)  DG = - 400 kJ mol-1 – 13.1 kJ mol-1 DG = - 413.1 kJ mol-1 . Since DG is negative the reaction is spontaneous. Note. Because DH <0 and DS >0, this reaction is spontaneous

at all temperatures.

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Free Energy Problem 2A certain chemical reaction is endothermic with a standard enthalpy of +300 kJ mol-1. The entropy change for this reaction is +25 J mol-1 K-1. Calculate the free energy change for this reaction at 25 oC. Is the reaction spontaneous?

SolutionConvert the entropy value to kJ. 25 J mol-1 K-1 = 0.025

kJ mol-1 K-1

 DG = + 300 kJ mol-1 – (298 K)(0.025 kJ mol-1 K-1)  DG = + 300 kJ mol-1 – 7.45 kJ mol-1 DG = + 292.55 kJ mol-1 . Since DG is positive the reaction is non-spontaneous. Note. Because DH >0 and DS >0, this reaction is non-

spontaneous at low temperatures. It the temperature were substantially increased it would become spontaneous.

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