Chem 1310: Introduction to physical chemistry

Part 1: Thermodynamics 2

Peter H.M. Budzelaar

The direction of chemical reactions

The total energy of the universe is constant, and so is the energy of any isolated system.

But energy can change form, and this happens in both chemical and physical changes.

Thermodynamics, in its more complete and quantitative form, can tell you in which direction such changes will go.

It will not tell you how fast they will go: you'll need kinetics for that.

Free energy

The Gibbs free energy (G) is the quantity that is important for systems at constant T,p.

Free energy consists of enthalpy (see MSJ ch 6) and entropy (will be explained here).

Reactions can happen whether they are endothermic (H > 0) or exothermic (H < 0); they will not happen when they are endergonic (G > 0). This has a lot of predictive power.

Energy, enthalpy and entropy

E = energy change = q+w

At constant volume, no work done: E = qV

For constant-pressure processes, enthalpy is more appropriate:

H = qP = heat transferred at constant pressure

(where work is done only to adjust the volume so that p remains constant).

Energy, enthalpy and entropy

Enthalpy is not enough to predict the direction of a reaction.

Dissolve NaOH and NH4Cl (separately) in water. Note the temperature changes. One process is exothermic, the other endothermic, yet both occur spontaneously!

To get any further, we need the idea of "entropy".

Entropy

Entropy is a somewhat diffuse concept. It is a measure for the dispersion of energy (and matter) over a system (or over its surroundings). If it is defined in a proper, quantitative fashion, we have a rule that says the entropy of the universe cannot decrease ("second law").

Entropy and reversibilityThe concept of entropy may be diffuse, but its definition is not. For a reversible process, the entropy change is defined as:

Reversible: a process where a tiny change in conditions would reverse the process.During a reversible process, the system remains at equilibrium. You disturb it a bit, then let it respond before disturbing it further.

T

qS rev

T in Kelvin! We are dividingby an absolute temperature,not a difference,so the zero point matters.

Reversibility• Melting ice at 0°C is reversible: cooling a little bit

produces more ice, heating a bit yields more water.

• Melting ice at 10°C is not: if you cooled the system a bit, ice would not re-form.

• Even if the process you are studying in a system is irreversible, the change in the surroundings can be carried out in a reversible manner (like adding heat from something only slightly warmer than the system).

Entropy

• Entropy can often be interpreted as "disorder", and this "disorder" is zero (absent) for pure, crystalline compounds at absolute zero (0K) ("third law").

• So, we can assign an absolute entropy S, not just a relative value S, to every compound under given conditions:Heat it from 0K to R.T. in small steps, and measure the heat absorbed (at constant pressure) qrev S.

Entropy

Entropy values can be (are) tabulated just like enthalpies, and refer to standard conditions(R.T., 1 bar). They have the dimension of energy/temperature, or J K-1.

Note: energies are often tabulated in kJ; correct for the factor 1000 differences when making comparisons!

Factors affecting entropy

• State: gas >> liquid > solid(disorder between molecules)

• Rigidity: loose/floppy molecules > rigid molecules(disorder within molecules)

• Solution > pure solid+solvent (usually!)(but solute may enforce ordering of solvent)

• Solution < pure gas+solvent

Entropy does not decrease("the arrow of time")

For any process, the entropy of a system may increase or decrease, and same for surroundings, but the entropy of the universe as a whole will never decrease.

Calculating entropy changes

To use this idea, we need to be able to get/calculate Ssystem and Ssurr for any process.

A spontaneous process happening in a system is not reversible, so we cannot use eqn MSJ 18.3(S = qrev/T) directly.

Calculating entropy changes (2)

Trick: we assume the surroundings change reversibly. That means:

So, we can calculate the change in entropy of the surroundings from the change in enthalpy of the system!

For the system itself we still need to get/measure Ssys!

T

sysH

T

surrH

T

surrqS rev

surr

)()()(

Entropy and free energy

Once we have Ssys and Ssurr:

Suniverse = Ssys + Ssurr = Ssys - Hsys/T

We do not really want to work with the whole universe all the time. And Suniverse only depends on properties of the system anyway. A useful definition is:

Gsys = -T Suniverse = Hsys - T Ssys

This is the "Gibbs free energy".

Free energy andthe direction of reactions

If it is Gsys<0, a reaction is spontaneous (but might still be slow!)

If Gsys>0, the reaction will not go without "help".

This "help" must be something that at least compensates for the positive Gsys of the reaction being helped.

Any "excess" Gcomp will probably be wasted and contributes only to warming the universe as a whole.

Enthalpy and entropy contributions

What can we say about a reaction?• H < 0, S > 0: spontaneous• H > 0, S < 0: will not happen• H < 0, S < 0: don't know,• H > 0, S > 0: need a calculation

Enthalpy and entropy contributionsEntropy-driven reactions (H > 0, S > 0):• Evaporation of a liquid

• Dissolution of a solid in a solvent (NaCl in H2O)

Enthalpy-driven reactions (H < 0, S < 0):• Reaction of two gases to form a solid

NH3+HClNH4Cl

• Precipitation of an insoluble saltAg+

(aq)+Cl-(aq) AgCl

• Formation of a polymern C2H4 (-CH2CH2-)n

Using tabulated values

Enthalpies, entropies and free energies are tabulaed for standard conditions (1 bar): H°, S°, G°.

H° and S° are not too temperature-dependent, and can be used to estimate G for different conditions by using H°, S° and the new T.

For solutions/gases, H°, S° and G° are for standard concentrations (1 mol/L)/pressures (1 bar).

Free energies of reaction mixtures

For a reaction mixture under non-standard conditions, corresponding to a specific reaction with a given G° under standard conditions:

G = G° + R T ln Q

where:

Q = QC for solutions

Q = QP for gases

Free energies andequilibrium constants

At equilibrium, Q = K and G = 0, so

G = G° + R T ln K = 0

G° = - R T ln K or

where

K = KC for solutions

K = KP for gases

TR

G

eK

Equilibrium constantsdepend on the temperature

H° and S° do not vary too much with temperature, but G° = H°-TS° does, and so does

Endothermic reactions (H° > 0) become more favourable at high temperature.

Exothermic reactions (H° < 0) become less favourable at high temperature.

The entropy changes gives a kind of temperature-independent, intrinsic preference.

TR

H

R

S

eK

Equilibrium constantsdepend on the temperature

At low temperature, H° dominates strongly and the equilibrium will be very one-sided.

At high temperatures, H° becomes unimportant and S° determines the product distribution.

For chemical reactions, we are usually in an intermediate region.

TR

H

R

S

eK

The crossover temperature

There will be a temperature where K = 1:

G° = 0 H°-TS° T = H°/S°

Gibbs free energyand coupled reactions

The Gibbs free energy shows whether there is a driving or opposing force for a reaction. It also places a limit on the amount of work we could extract from this reaction.

The work could be done by coupling physical action to the chemical reaction (as happens in a coal-fired power plant or a car battery).

Gibbs free energyand coupled reactions

Chemical coupling is also common. Metabolism depends on coupling oxidation of carbohydrate etc to formation of useful chemicals in the body. The main biological energy carrier is ATP.

Muscle movement depends on the energy released in the hydrolysis of ATP to ADP. This is (again) coupling of chemical energy to physical movement.

Muscle movement

http://www.kent.ac.uk/bio/geeves/Research/myo.htm

actinfilament

myosinthick

filament

ATP bindingcauses release

of actin

ATP hydrolysis causesconformational change

release of phosphateinduces movement

myosin-ADP complexreattaches to actin

Gibbs free energyand coupled reactions

We can often write reactions as coupled systems of individual, simpler reactions. All thermodynamical conclusions reached from that will be valid, even if the reaction does not really follow the coupled path (see e.g. MSJ p654).

Gibbs free energyand coupled reactions

CH4 + ½ O2 CO + 2 H2

CO + 2 H2 CH3OH

CH4 + ½ O2 CH3OH

It would be nice if we could do this as one (coupled) reaction. In practice, the first one is spontaneous at low temperature, the second requires energy, and we lose a lot because we cannot use the energy liberated in the first step effectively.

Gibbs free energyand coupled reactions

With the right catalyst, we might eventually be able to do this better, by following a different mechanism that is more complex and directly produces the final CH3OH product without actually going through the CO and H2 intermediates. Conclusions about equlibrium will not change, but our production of CH3OH will be more efficient and produce less waste heat.

Stability

Chemists talk about "stable" and "unstable" compounds. These terms are not very well-defined.

"Stable" usually means you can put the compound in a bottle, store it for a long time, study it.

But it is also used to denote compounds that are "low in energy".

These two things are not equivalent.

Types of stability

CO2: would usually be called "stable"

CH4: all decomposition routes are endothermic, but the reaction with oxygen is highly exothermic!

C2H2: decomposition to C(s) and H2 is exothermic, but only happens on heating or compression.

CH3Na: stable under nitrogen, but inflames in air.

CH3Ag: decomposes explosively above -80°C.

Types of stability

Thermodynamically stable:if no reaction can produce a compound that is lower in free energy.We would call CO2 thermodynamically stable.

Kinetically stable:if every reaction that is exergonic has an appreciable activation barrier.We would call C2H2 kinetically stable.

Stability depends on environment

CO2 would not be called "stable" in an atmosphere of ammonia. It would form urea or ammonium carbonate.

H2O would not be stable in an atmosphere of fluorine.

CH3Na would be called stable in a nitrogen atmosphere.Magnesium and lithium should not be!

Concentration of energy

Compounds that are high in energy (relative to feasible reactions) provide a concentrated form of energy, easy to use for coupling to (endergonic) reactions.

C can be used to reduce CuO

Sn is a much weaker reductant

Just using "more" of a less "energetic" compound doesn't work because most chemistry is stoichiometric.

Not all forms of energy are the same

Mechanical and electrical energy can more easily be "concentrated".

Use pulleys to switch between one weight high up or many weights at lower height.

Use a transformer to switch between high and low voltages.

Not all forms of energy are the same

Heat is the least useful form of energy. It is already very "spread out". It can only be partially converted into other forms, and then the remainder becomes even more spread out.

When everything in the universe is at the same temperature and in chemical equilibrium, nothing can happen any more. This is called "heat death" (although is will actually be quite cold).

Light - the "ultimate" energy source

Light is important as an energy source because of its "quality".

Two photons of visible light (wavelength of 6000Å) are enough to cleave a strong single C-C bond.

To do the same thing by heating would require a temperature of thousands of K.

Light is "concentrated energy", with great potential for conversion to "useful work".

Energy content of a photon

= h = hc/ = (6.6*10-34Js)*(3*108m/s)/(6000*10-10m)= 3.3*10-19 J per photon

or 198 kJ/mol per NA photons.

A C-C bond is ca 356 kJ/mol.

Converting water back into H2 + ½O2 costs about 286 kJ/mol.

4000Å 7000Å

Photosynthesis

The "challenge" of photosynthesis is to harvest photons and convert their energy selectively into things cells need:

• short-term energy carriers (ATP)• useful chemicals: reduced species that can be used

to reduce other molecules, producing long-term energy carriers (carbohydrates, lipids)

• oxygen is only a by-product!

Photosynthesis

We would like to do something like:

H2O + CO2 + light CH2O + O2

But just shining light on a mixture of water and CO2 does not cause this to happen!

• light needs to be absorbed• its energy needs to be channeled

Chlorophyll a

PhotosynthesisLight causes ejection of an electron from chlorophyll.

The electron eventually serves to reduce NADP+ to NADPH.This can then be re-oxidized in an exothermic reaction that also

produces ATP.

The positive charge eventuallyoxidizes water to O2.

NADP+

Light - the "ultimate" energy source

Except for nuclear energy and "tidal" energy, we depend entirely on (past and present) sunlight for our energy needs.

The ultimate energy source for us would be direct conversion of light into a concentrated, useful form of energy, e.g. electricity.

This can be done now, although the cost is significant and the efficiency not yet satisfactory.

Photovoltaic cells

semiconductor

Issues:stability, yield, efficiency, (energy) cost of production.