Thermodynamics pt 1:Introduction to Spontaneity, Entropy, and Gibbs Free Energy

Intro to Thermodynamics

• Some things happen without influence, some things don’t.

• For example, decay just happens, without input. But creation requires work. Water flows downhill, but you need a pump to force water uphill.

• Iron exposed to air will rust (Fe2O3). But rusted iron will not re-convert to Fe(s) and O2. These are examples of irreversible processes.

X

Spontaneity

• What determines the direction of a process?

• The first law of thermodynamics tells us that

• This means that if a reaction occurs, the total energy of the universe is unchanged.

• In this lecture, we address the word “if”.

• Why do some reactions occur, whereas others don’t?

• Let’s first begin by determining the criteria for a spontaneous process

∆U=q+w

Spontaneity

• A spontaneous process is any process that occurs sustainably without external influence (i.e. work). ANY PROCESS THAT IS SPONTANEOUS IN ONE DIRECTION MUST BE NON-SPONTANEOUS IN THE OPPOSITE DIRECTION (thermodynamically irreversible).

• Why? Work must be done by the surroundings to return the system to the original state, but this causes permanent changes to the surroundings.

Hot Cold

• Thermodynamics allows us to determine if a process will occur, and in which direction. Kinetics tells us how fast the reaction will go.

Spontaneity

• Spontaneous changes need not be fast.

• Ex. Diamonds spontaneously convert to graphite, but this process takes centuries.

• What dictates the tendency of a process to spontaneously occur?

• When this question was first addressed in the 1860’s, it was thought that the only criteria for spontaneity was that a reaction be exothermic.

Spontaneity

• Since exothermic processes are “energetically downhill” processes, it was a logical assertion.

• However, this was quickly proved to be incorrect.

• The dissolution of NaCl(s) in water is spontaneous, but endothermic

𝑁𝑎𝐶𝑙 (𝑠 )→𝑁 𝑎+¿ (𝑎𝑞) +𝐶 𝑙− (𝑎𝑞 )∆𝐻𝑜=+3.9 𝑘𝐽

𝑚𝑜𝑙 ¿

• Some spontaneous processes are temperature dependent. For example, ice spontaneously melts at any temperature greater than 0oC.

𝐻2𝑂 (𝑠 )→𝐻2𝑂 (𝐿 )∆𝐻 𝑓𝑢𝑠=+6.01 𝑘𝐽𝑚𝑜𝑙

Entropy

• What is the common pattern with all spontaneous change?

• Spontaneous changes lead to increases in disorder. • Expansion of gases creates a randomized, less ordered system

• Liquid water is much less ordered than ice. Ice atoms are held in place, liquid atoms tumble around.

• Dissolving a salt in water yields ions that are free to move about randomly

• The cooling of a hot block in air results in energy transfer to surrounding air molecules, which increases their kinetic energy and leads to more random motion and collisions

• This disorder is called ENTROPY (S)

• The more disordered a system, the larger its entropy. Entropy can be better thought of as a measure of how distributed the energy of a system is.

• Ex. A hot metal block added to cold water; the thermal energy disperses so that it is no longer confined to the metal, but rather imparted on all of the molecules (metal and water).

• Entropy, denoted S, is a state function

• An increase in disorder represents a positive change in entropy (ΔS > 0), while increases in order are negative (ΔS < 0)

• To relate ΔS to heat, we consider a reversible path between the states.

Entropy

Reversible Processes

• Imagine we have a reversible process. In a reversible process, the direction of a process can be reversed by an infinitesimally small change in one variable (Attaining a reversible condition is theoretical)• Ex. Pure water at exactly 0oC and 1 atm. The tiniest change in

pressure at constant temperature (isothermal) will cause the water to move either toward the solid or liquid phase. w ≈ 0

• For an “reversible” isothermal process, like a phase change:

• The heat term in the numerator accounts for the proportionality between thermal transfer and disorder, the temperature term in the denominator accounts for the disorder that already exists in the system.

∆ 𝑆𝑠𝑦𝑠=𝑞𝑟𝑒𝑣

𝑇

THE ENTROPY OF THE UNIVERSE IS CONTINUALLY INCREASING!(not conserved!!!)

Second Law of Thermodynamics

∆𝑆𝑢𝑛𝑖𝑣=∆𝑆𝑠𝑦𝑠+∆𝑆𝑠𝑢𝑟𝑟

𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒𝑝𝑟𝑜𝑐𝑒𝑠𝑠 :∆𝑆𝑢𝑛𝑖𝑣=∆𝑆𝑠𝑦𝑠+∆ 𝑆𝑠𝑢𝑟𝑟=0

𝒊𝒓𝒓𝒆𝒗𝒆𝒓𝒔𝒊𝒃𝒍𝒆 𝒑𝒓𝒐𝒄𝒆𝒔𝒔 :∆𝑺𝒖𝒏𝒊𝒗=∆𝑺𝒔𝒚𝒔+∆𝑺𝒔𝒖𝒓𝒓>𝟎

• For any irreversible process in which the system becomes more ordered, the increase in disorder of the surroundings must be greater in magnitude, and visa versa. The universe can NEVER become more ordered.

• Considering the example of rust:

• ΔSsys is NEGATIVE. Why?• Most combination reactions have negative entropy because you are reducing

the number of free species. Here, we have taken 7 total moles of reactant and formed 2 moles of product

• Gases have much higher entropies than solids. Here, we have consumed a gas to form a solid.

• ΔSsurr is POSITIVE because the reaction is highly exothermic. The thermal energy gained by the surrounding atmosphere causes a high degree of disorder in the atmosphere.

• The disorder to the surroundings caused by this process MUST be greater than the order obtained by the system.

∆𝑆𝑠𝑦𝑠+∆𝑆𝑠𝑢𝑟𝑟>0

Molecular Interpretation of Entropy

• When we change phase from gas to liquid/solid or liquid to solid, we limit the motion of the molecules (i.e. the number of ways they can release energy)

• There are three types of motion: translational, vibrational, rotational. The number of ways molecules can move are its degrees of freedom

Degrees of Freedom

Vibrational motion only

Vibrational motion, restricted rotational & translational motion

All motion

• Gases, being the least ordered, have the most ways of dissipating thermal energy. Hence, they have the highest entropy.

Determine the sign of ΔSsys

• A(g) + 2B(g) ---> AB2(s)

• H2O(s) ---> H2O (L)

• NaCl(s) ---> Na+(aq) + Cl-(aq)

• FeCl2(s) + H2(g) ---> Fe(s) + 2HCl(g)

• A(g) + 2B(g) ---> C(g)

H2O (L)

negative

positive

positive

positive

negative

Third Law of Thermodynamics

• All molecular motion stops at 0oK (absolute zero). Therefore, S=0, and the molecules arrange themselves in perfect order.

• The plot below shows a heating curve of entropy. The sharp increases at phase boundaries is due to the added degrees of freedom

Calculations of Entropy Changes of Reactions

• Standard molar entropies, So (J/mol K) are shown to the right .

1. Unlike enthalpies of formation, entropies are NOT zero for elemental forms of substances

2. Gases > Liquids > Solids3. For the same phase, entropy increases

with molar mass4. For the same phase and same molar mass,

entropy increases with the number of atoms in the molecule.

∆𝑆𝑟𝑥𝑛𝑜 =∑𝑛𝑆𝑜 (𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 )−∑ 𝑛𝑆𝑜 (𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠)

Examples

• Which would you expect to have the higher molar entropy?

• H2O(L) or H2O(g)

• CO2(g) or H2O(g)

• Zn(s) or Li(s)

• NaClO4(s) or He(g)

So What is the Criteria for Spontaneity?

• We have seen that spontaneous processes increase the entropy of the universe

• ΔHsys does not have to be negative, and ΔSsys does not have to be positive.

• This brings us back to the initial question: What is the criteria of a spontaneous process?

• Let’s use ΔH and ΔS concurrently to derive an expression

Math Time: Derivation of Gibbs Free Energy

∆𝑺𝒖𝒏𝒊𝒗=∆𝑺𝒔𝒚𝒔+∆𝑺𝒔𝒖𝒓𝒓

• If the surroundings include “everything else”, then we can assert that for any process occurring in the system, the surroundings are large enough that their temperature and pressure are constant.

∆𝑆𝑢𝑛𝑖𝑣=∆𝑆𝑠𝑦𝑠−𝑞𝑠𝑦𝑠

𝑇

∆𝐺=∆𝐻−𝑇 ∆𝑆

−𝑇 ∆𝑆𝑢𝑛𝑖𝑣=∆𝐻 𝑠𝑦𝑠−𝑇 ∆𝑆𝑠𝑦𝑠

Gibbs Free Energy∆𝑆𝑢𝑛𝑖𝑣=∆𝑆𝑠𝑦𝑠−

∆𝐻 𝑠𝑦𝑠

𝑇

Sign of Gibbs Free Energy Dictates Direction of Reaction

• If ΔG is negative, the reaction is spontaneous in the forward direction

• If ΔG is zero, the reaction is at equilibrium

• If ΔG is positive, the reaction is spontaneous in the reverse direction

What is Gibbs Free Energy?

• As you would imagine, it is very difficult to directly calculate ΔSuniv.

• However, the Gibbs Free Energy (-TΔSuniv) allows us to relate it to ΔH and ΔS of the system. Hence, by following the 2nd law of thermodynamics, ΔG tells us about the spontaneity of a process

• For a spontaneous process, ΔG is the maximum useful work that can be done by a system on the surroundings at temperature T.

∆𝐻=∆𝐺+𝑇 ∆𝑆

Energy change associated with the breakage and formation of bonds

Energy that can be converted to work

Remaining, unusable energy; disperses as heat to create disorder

Nonspontaneity

For a nonspontaneous process, ΔG is positive, and represents the minimum amount of work that needs to be done on the system to drive a process.

Now We See That Spontaneity Depends on Enthalpy AND Entropy

∆𝐺=∆𝐻−𝑇 ∆𝑆Dictates if a process is enthalpy favored

Dictates if a process is entropy favored