Temperature and Spontaneity

Fig. 19.3 pg. 805

Spontaneous Processes

• The direction of a spontaneous process can depend on temperature.
• Ice turning to water is spontaneous at T > 0 ^oC.
• Water turning to ice is spontaneous at T < 0 ^oC.
• A reversible process is one which can go back and forth between states along the same path.
  • When 1 mol of water is frozen at 1 atm at 0 ^oC to form 1 mol of ice, q = _fus = 6.008 kJ of heat is removed.
  • To reverse the process, q = _fus = 6.008 kJ must be added to the 1 mol of ice at 0 ^oC and 1 atm to form 1 mol of water at 0 ^oC.
  • Therefore, converting between 1 mol of ice and 1 mol of water at 0 ^oC is a reversible processes.
• Chemical systems in equilibrium are reversible.
• In any spontaneous process, the path between reactants and equilibrium is irreversible.
• Thermodynamics gives us the direction of a process. It cannot predict the speed at which the process will occur.
• Why are some endothermic reactions spontaneous?

Gas Molecules Confined

http://www.chem.lsu.edu/htdocs/people/jchogan/CHEM_1202/Images/Entropy01.jpg

Entropy

• Gas molecules confined to left vessel have less entropy than gas molecules allowed to spread out into both vessels.
• Most of the time entropy (S) corresponds roughly to how much "space" a substance occupies.
• At zero K in frozen pure crystalline state all substances have zero entropy. As heat is added to these substances their molecules (or atoms) start to move faster (temperature increase) and the molecules (atoms) start to overcome intermolecular forces, breaking up the perfect crystalline structure holding them together (entropy).
• Entropy can be thought of as "structure breaking" relative to absolute zero. The amount of entropy a substance has is the amount of structure which needs to be broken down to convert substance from perfect structure (zero K crystal) into its current state.

Gas Molecules Liberated

http://www.chem.lsu.edu/htdocs/people/jchogan/CHEM_1202/Images/Entropy02.jpg

Entropy

When the stopcock is opened the gas will spread out into both flasks and its entropy will increase because intermolecular forces will be diminished as gas molecules spread apart from one another; gas will become less structured (more chaotic, more spread out) and thus gain entropy.

Importance of Disorder

Fig. 19.1 pg. 804

Entropy and the Second Law of Thermodynamics

• We ask why do spontaneous processes occur?
• Consider an initial state: two flasks connected by a closed stopcock. One flask is evacuated and the other contains 1 atm of gas.
• The final state: two flasks connected by an open stopcock. Each flask contains gas at 0.5 atm.
• The expansion of the gas is isothermal (i.e. constant temperature). Therefore the gas does no work and heat is not transferred.
• Why does the gas expand?

Structure of Ice

Fig. 19.9 pg. 815

Entropy and the Second Law of Thermodynamics

Entropy

• In ice, the molecules are very well ordered because of the H-bonds.
• Therefore, ice has a low entropy.
• As ice melts, the intermolecular forces are broken (which requires energy), but the order is interrupted (so entropy increases). Water is more random than ice, so ice spontaneously melts at room temperature.
• There is a balance between energy and entropy considerations.

Frozen and Unmixed Substances

http://www.chem.lsu.edu/htdocs/people/jchogan/CHEM_1202/Images/Entropy.jpg

Melting, Vaporization, and Mixing

• In the picture shown two substances are separated and frozen to 0 K so that they form perfect crystalline structures.
• In the video which follows the substances will be heated and allowed to mix. The heating will break up the crystal structure and turn both substances into gases, while opening the stopcock will allow the resulting gases to mix. Both processes will increase the entropy of the system.

Melting, Vaporization, and Mixing

http://www.chem.lsu.edu/htdocs/people/jchogan/CHEM_1202/Images/Entropy.gif

Entropy and Mixing

• When the gases mix the entropy will increase even though the total volume of the system stays the same. Each gas will increase the amount of "space" it occupies even though it can only do so by merging with the other gas.
• There is obviously much more chaos (less structure) in mixed gases than in separated gases, so entropy increases when gases mix.

Dissolution of an Ionic Substance

Fig. 19.10 pg.816

Entropy and the Second Law of Thermodynamics

Entropy

• When an ionic solid is placed in water, two things happen:
  1. the water organizes into hydrates about the ions (so the entropy decreases), and
  2. the ions in the crystal dissociate (the hydrated ions are less ordered than the crystal, so the entropy increases).
• With very few exceptions, when a solid dissolves in a liquid usually the entropy of the system increases. Conceptually, most of the liquid doesn't change much but the solid spreads out dramatically, increasing its "space" so you expect the total entropy of the system to increase.
• Whenever an increase in entropy in one process is associated with a decrease in entropy in another, the increase in entropy has to dominate in order for the overall change to be spontaneous (second law of thermodynamics).
• Entropy is a state function.
• For a system, DS = S_final - S_initial.
• If DS > 0, the randomness increases, if DS < 0, the order increases.

Dissolution of NaCl

http://hogan.chem.lsu.edu/matter/chap26/animate1/an26_004.mov

Dissolution of NaCl

• Dissolution of NaCl in water increases the entropy of the NaCl and water mixture.
• Water molecules have to come together (lose "space") and cooperate (forming little microstructures) in order to carry ions away from the NaCl crystal lattice, but NaCl is disorganized (spread out) so much by this process that the net result is an increase in entropy.
• DS(H₂O) < 0
• DS(NaCl) > 0
• DS(overall) = DS(H₂O) + DS(NaCl)
• DS(overall) > 0

Gas Molecules and Entropy

Adapted from Fig. 19.11 pg. 816

A Molecular Interpretation of Entropy

• A gas is less ordered than a liquid, which is less ordered than a solid.
• Any process that increases the number of gas molecules leads to an increase in entropy.
• At a constant pressure any process that increases the number of gas molecules increases the amount of "space" the substance takes up proportionally.
• Gas has so much more entropy ("space") than either liquid or solid that in a chemical reaction whichever side (reactants or products) has the largest number of gas molecules almost always has the largest entropy. Solids and liquids can normally be ignored unless there is an equal number of gas molecules on both sides of a chemical equation.
• When NO(g) (red and blue) reacts with O₂(g) (red) to form NO₂(g) (second flask, b), the total number of gas molecules decreases. Therefore, the entropy decreases.
• In addition, the NO₂ molecules impose even more order on the system because the extra N-O bond restricts molecular motion.
• The NO₂ molecules are less free to move randomly.
• Therefore, NO₂(g) has fewer degrees of freedom than NO(g) and O₂(g).

Entropy Changes Upon Heating

Fig. 19.14 pg. 819

A Molecular Interpretation of Entropy

• Entropy changes dramatically at a phase change.
• As we heat a substance from absolute zero, the entropy must increase.
• If there are two different solid state forms of a substance, then the entropy increases at the solid state phase change.
• Boiling corresponds to a much greater change in entropy than melting.
• Entropy will increase when
  1. liquids or solutions are formed from solids,
  2. gases are formed from solids or liquids,
  3. the number of gas molecules increase,
  4. the temperature is increased.

Standard Molar Entropies

Table 19.2 pg. 820

Calculation of Entropy Changes

• Absolute entropy can be determined from complicated measurements.
• Absolute entropies of gases >> liquids > solids.
• Absolute entropies go up with molar mass because it is more difficult to break up structure with heavy molecules than with light molecules (dispersion forces). At room temperature ("standard" state) substances with strong intermolecular forces have more broken structure relative to 0 K than substances with weaker intermolecular forces.
• Absolute entropies of liquids and solids with H-bonding higher than those of substances without H-bonding with equal molar masses.
• Standard molar entropy, S^o: the entropy of a substance in its standard state.
• Unlike H scale normally used for chemical calculation (ie. heat of formation scale, DH_f, the most commonly used S scale is the absolute entropy scale rather than the entropy of formation scale. The absolute enthalpy scale was used at one time (called "heat content" scale) but has fallen into disuse in recent times.
• Product minus reactant differences for H or S do not depend on which scale used to calculate them. Differences between values in different scales cancel out when reactant numbers are subtracted from product numbers.
• Units: J/mol-K. Note units of DH: kJ/mol.
• Standard molar entropies of elements are not zero because absolute entropies are zero only at 0 K and "standard state" means room temperature (298 K). Formation values (including entropies using the formation scale, Ds_f^o) are zero for elements because these are differences between element values and values of interest (ie. element values).

Gibbs Free Energy I

Text slide.

Gibbs Free Energy

• G = H - TS

• For reactions at constant temperature:

• DG, DH, and DS refer to "products minus reactants" or "final minus initial" per the usual energy conventions.

• "Constant temperature" merely means that if reaction changes temperature we need to bring it back to original T before making final measurements (review state functions).

Gibbs Free Energy II

Text slide.

Gibbs Free Energy

• DG = DH - TDS is operative form of Gibbs free energy equation we will use in this course.

• Any process for which DG is negative is spontaneous (prefers to go in the "forward" direction) and any process for which DG is positive prefers to go in the reverse direction (ie. is nonspontaneous).

• G is the "instability level" of the system. Nature tries to minimize G by as many different schemes as it can. Each successful scheme reduces G and thereby makes DG (final minus initial) negative.

Gibbs Free Energy III

Text slide.

Gibbs Free Energy

What contributes to instability gain/loss (DG)?

1. Enthalpy (H). Loss of heat (negative DH) from system contributes favorably to process. Negative DH means heat balance in system is negative because system has dumped heat into the surroundings. This causes entropy of surroundings to increase.
   
2. System entropy (DS). Gain of entropy (positive DS) in system contributes favorably to a process. To put system entropy change (DS) into same units as the DH which causes surroundings entropy change (comparison purposes) we multiply DS by T (ie. TDS).

Temperature and Spontaneity

Table 19.4 pg. 828

Free Energy and Temperature

• Focus on DG = DH - TDS;
  1. If DH < 0 and DS > 0, then DG is always negative.
  2. If DH > 0 and DS < 0, then DG is always positive. (ie., reverse of 1.)
  3. If DH < 0 and DS < 0, then DG is negative (spontaneous) at low temperatures (exothermic reactions favored by removing heat, which is a product).
  4. If DH > 0 and DS > 0, then DG is negative (spontaneous) at high temperatures (endothermic reactions favored by adding heat, which is a reactant).
• Even though a reaction has a negative DG, it may occur too slowly to be observed.
• Thermodynamics gives us the direction of a spontaneous process, it does not give us the rate of the process.

Gibbs Free Energy IV

Text slide.

Gibbs Free Energy

• DH: heat energy organized from surroundings into system (unfavorable).

• TDS: Disorganization of matter in system expressed in energy units (favorable).

• DG expresses balance between organization/disorganization of energy and matter by a system.

• DG = DH - TDS

• When chemists use term "energy" generically, as in "unstable species like to lose energy to generate more stable species," they usually implicitly mean Gibbs free energy.

Gibbs Free Energy V

Text slide.

Gibbs Free Energy

• For DG to be negative (favorable) either DH must be negative (disorganize energy) or TDS must be positive (disorganize matter) or both.

• How does this relate to molecular changes?
  1. Typical reaction results in bonding changes and structure making/breaking.
  2. Making shorter bonds releases H (favorable); longer bonds absorb H (unfavorable).
  3. Making fewer bonds or more fragments results in increased entropy (more broken structure, favorable) and vice-versa.

Gibbs Free Energy VI

Text slide.

Gibbs Free Energy

Gibbs Free Energy VII

Text slide.

Gibbs Free Energy

DG and Temperature

Text slide.

DG and Temperature

DG^o_T ~ DH^o₂₉₈ - TDS^o₂₉₈

Often works at temperatures other than T = 298 K, because DH and DS are often fairly temperature-independent.

One consequence of this is it is possible to calculate temperature at which a process is at balance point between being spontaneous and nonspontaneous by assuming:

DG^o_T ~ DH^o₂₉₈ - TDS^o₂₉₈ = 0, or:

DH^o₂₉₈ ~ TDS^o₂₉₈ (ie. T ~ DH^o₂₉₈/DS^o₂₉₈)

Free Energy Changes

Fig. 19.17 pg. 823

Gibbs Free Energy

• For a spontaneous reaction, the entropy of the universe must increase.
• Reactions with large negative DH values are spontaneous.
• How do we balance DS and DH to predict whether a reaction is spontaneous?
• Gibbs free energy, G, of a state is

• For a process occurring at constant temperature

• There are three important conditions:
  1. If DG < 0 the forward reaction is spontaneous.
  2. If DG = 0 the reaction is at equilibrium and no net reaction will occur.
  3. If DG > 0 the forward reaction is not spontaneous. (However, the reverse reaction is spontaneous.) If DG > 0 energy must be supplied from the surroundings to drive the reaction.
• For a reaction to occur, the free energy of the reactants decreases as the free energy of the products increases until the products and reactants have equal G values. This state (equilibrium) corresponds to the lowest possible G value for the entire system of reactants and products.

DG and Concentration

Text slide.

DG and Concentration

• At any moment in time during a reaction at any nonstandard set of concentrations if you measure the instabilities of the product and reactant molecules and calculate the energy difference (product molecules minus reactant molecules) you get:

• The higher the Q value (the more concentrated product is relative to reactant) the higher the instability of product relative to reactant.

DG and Equilibrium Constant

Text slide.

DG and Equilibrium Constant

At equilibrium product and reactant are equally unstable (each falls apart to make the other at equal speed), so at equilibrium:

DG = DG^o + RT ln Q = 0, or:

DG^o = -RT ln Q_eq

Since Q_eq = K (equilibrium constant):

DG^o = -RT ln K;

K = e^-DG/(RT)

Driving Nonspontaneous Reactions

Fig. 19.19 pg. 833

Gibbs Free Energy

Driving Nonspontaneous Reactions

• If DG > 0 energy must be supplied from the surroundings to drive the reaction.
• Biological systems use spontaneous reactions to drive nonspontaneous reactions.
• In biology, disordered nutrients are organized into biological constituents. Therefore, DS is large and negative.
• Metabolism of food usually supplies sufficient energy to drive most nonspontaneous reactions. Example, glucose oxidation:

C₆H₁₂O₆(s) + 6O₂ 6CO₂ + 6H₂O(l); DG^o = -2880 kJ/equiv

• The free energy released by glucose oxidation is used to convert low energy ADP to high energy ATP.
• When ATP is converted back to ADP, the energy released is used to convert simple molecules into complex cell constituents.
• The low energy ADP is then available for conversion to ATP by glucose oxidation.