Brad Gietman's List: 3rd part of chem

• Altering the mechanism of a reaction so that the activation energy is lower is the second major way to speed up the reaction. A catalyst can do this by participating in the activated complex for the rate-limiting step, even though the catalyst itself is neither a reactant nor a product in the overall stoichiometric equation.

• The currently accepted mechanism for this catalyzed reaction involves three steps:

  
                   ½ I₂ I

        I + cis-C₄H₈ → C₄H₈I^‡ → trans-C₄H₈ + I

                        I ½ I₂
• These last two processes involve an overall decrease in energy which is nearly the same as the increase required to achieve the activated complex.

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• Our previous discussion has concentrated on catalysts which are in the same phase as the reaction being catalyzed. This kind of catalysis is called homogeneous catalysis.
• Many important industrial processes rely on heterogeneous catalysis, in which the catalyst is in a different phase. Usually the catalyst is a solid and the reactants are gases, and so the rate-limiting step occurs at the solid surface. Thus heterogeneous catalysis is also referred to as surface catalysis.
• The detailed mechanisms of most heterogeneous reactions are not yet understood, but certain sites on the catalyst surface appear to be able to weaken or break bonds in reactant molecules. These are called active sites
• The currently accepted mechanism for this reaction involves weak bonding of both H₂ and C₂H₄ to atoms on the metal surface. This is called adsorption

• The H₂ molecules dissociate to individual H atoms, each of which is weakly bonded to a Pt atom:

  
  

  H₂ + 2Pt(surface) → 2H- - -Pt(surface)
• Because adsorption and dissociation of H₂ on a Pt surface is exothermic (ΔH_m° >= –160 kJ mol^–1), it can provide H atoms for further reaction without a large activation energy. By contrast, dissociation of gaseous H₂ molecules without a metal surface would require the full bond enthalpy (ΔH_m° = +436 kJ mol^–1). Clearly the metal surface makes a major contribution in lowering the activation energy.
• Heterogeneous catalysts are used extensively in the petroleum industry. One example is the combination of SiO₂ and Al₂O₃ used to speed up cracking of long-chain hydrocarbons into the smaller molecules needed for gasoline.

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• It does so efficiently enough that only a few kilograms of enzyme are necessary to fix about 44 × 10¹² g of nitrogen worldwide each year. Other enzymes carry out other reactions with comparable efficiencies.
• All enzymes are large protein molecules whose molar masses exceed 20 000 g mol^–1. They are condensation polymers of amino acids,
• the chain may be as long as 200 or 300 amino acid units
• The polymer chain of amino acid units in an enzyme is usually wrapped around itself in a complex fashion to form an overall shape which is approximately spherical
• essential to its operation as a catalyst. Accordingly, this region of the molecular surface is called the active site.
• An important feature of the catalytic behavior of enzymes is their specificity. Most enzymes are able to catalyze only one particular chemical reaction or at most only a few closely related reactions

• The rate law is usually found to be first order with respect to the enzyme concentration and also first order with respect to the substrate (the substance on which the enzyme acts). In other words

  Rate = k(c _enzyme)(c _substrate)
• also, it is because there is considerable lowering in the activation energy due to the ionic attraction between the enzyme and substrate.

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• The following sections are concerned with the amounts of substances which participate in chemical reactions, the quantities of heat given off or absorbed when reactions occur, and the volumes of solutions which react exactly with one another.

• 
  TABLE 1 Summary of Related Quantities and Conversion Factors.

  Related Quantities	Conversion Factor	Definition	Road Map
  Volume ↔ mass	Density, ρ
  Amount of substance ↔ mass	Molar Mass, M
  Amount of substance ↔ number of particles	Avogadro constant, NA
  Amount of X consumed or produced ↔ amount of Y consumed or produced	Stoichiometric ratio, S(Y/X)
  Amount of X consumed or produced ↔ quantity of heat absorbed during reaction	ΔHm for thermochemical equation
  Volume of solution ↔ amount of solute	Concentration of solute, cX

• thermochemical equations, such as

  
  CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)(25°C, 1 atm pressure)

  
  ΔH_m = –890 kJ mol^–1      (1)

  
  Here the ΔH_m (delta H subscript m) tells us whether heat energy is released or absorbed when the reaction occurs and also enables us to find the actual quantity of energy involved.
• By convention, if ΔH_m is positive, heat is absorbed by the reaction; i.e., it is endothermic. More commonly, ΔH_m is negative as in Eq. (1), indicating that heat energy is released rather than absorbed by the reaction, and that the reaction is exothermic.
• It is important to notice that ΔH_m is not an energy but rather an energy per unit amount.
• Its units are not kilojoules but kilojoules per mole (hence the m subscript in ΔH_m).

• Seen in this way, ΔH_m is a conversion factor enabling us to calculate the heat absorbed when a given amount of substance is consumed or produced. If q is the quantity of heat absorbed and n is the amount of substance involved, then

  
        (2)
• The quantity ΔH_m is usually referred to as an enthalpy change per mole.
• It is important to realize that the value of ΔH_m given in thermochemical equations like (1) or (3) depends on the physical state of both the reactants and the products

• hat is,

  
  ΔH_{m forward} = –ΔH_{m reverse}

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• Perhaps the most useful feature of thermochemical equations is that they can be combined to determine ΔH_m values for other chemical reactions
• On paper this net result can be obtained by adding the two chemical equations as though they were algebraic equations. The CO produced is canceled by the CO consumed since it is both a reactant and a product of the overall reaction

• Experimentally it is found that the enthalpy change for the net reaction is the sum of the enthalpy changes for steps 1 and 2:

  
  ΔH_net = –110.5 kJ mol^–1 + (–283.0 kJ mol^–1) + –393.5 kJ mol^–1 = ΔH₁ + ΔH₂

  
  That is, the thermochemical equation

  
  C(s) + O₂(g) → CO₂(g)      ΔH_m = –393.5 kJ mol^–1

• n the general case it is always true that whenever two or more chemical equations can be added algebraically to give a net reaction, their enthalpy changes may also be added to give the enthalpy change of the net reaction.

  This principle is known as Hess' law. If it were not true, it would be possible to think up a series of reactions in which energy would be created but which would end up with exactly the same substances we started with.

• .Hess’ law enables us to obtain ΔH_m values for reactions which cannot be carried out experimentally, as the next example shows.

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• By now chemists have measured the enthalpy changes for so many reactions that it would take several large volumes to list all the thermochemical equations. Fortunately Hess' law makes it possible to list a single value, the standard enthalpy of formation ΔH_f, for each compound
• The standard enthalpy of formation is the enthalpy change when 1 mol of a pure substance is formed from its elements. Each element must be in the physical and chemical form which is most stable at normal atmospheric pressure and a specified temperature (usually 25°C).
• Note also that 285.8 kJ are given off per mole of H₂O(l) formed.
• Quite often, however, elements do not react directly with each other to form the desired compound, and ΔH_f must be calculated by combining the enthalpy changes for other reactions.
• . The standard enthalpy of formation for an element in its most stable state must be zero.

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• the law of conservation of energy is therefore referred to as the first law of thermodynamics.
• The total of translational, rotational, vibrational, and electronic energies is the internal energy of an atom or molecule.
• When chemical reactions occur, the internal energy of the products is usually different from that of the reactants, and the difference appears as heat energy in the surroundings
• When a chemical reaction occurs at constant pressure, as in a coffee-cup calorimeter, there is a change in potential energy of the atmosphere (given by P ΔV) as well as a change in heat energy of the surroundings. Because the heat energy absorbed can be measured more easily than P ΔV, it is convenient to define the enthalpy as the internal energy plus the increased potential energy of the atmosphere. Thus the enthalpy increase equals the heat absorbed at constant pressure.
• Enthalpy changes for a variety of reactions may be calculated from standard enthalpies of formation
• However, it has the advantage that enthalpy changes for reactions of a particular compound can be estimated even if the compound has not yet been synthesized.
• The enthalpy change for a reaction depends on the relative strengths of the bonds broken and formed and on the relative number of bonds broken and formed. A good fuel is a substance which can combine with oxygen from the air, forming more bonds and/or stronger bonds than were originally present. The fossil fuels, coal, petroleum, and natural gas consist mainly of carbon and hydrogen. When they burn in air, strong O—H and C=O bonds are formed in the resulting H₂O and CO₂ molecules

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• Here we must consider changes in the kinetic and potential energies of electrons in the atoms and molecules involved, that is, changes in the electronic energy.

• As a simple example of a chemical change, let us consider an exothermic reaction involving only one kind of atom, the decomposition of ozone, O₃:
• What makes a gaseous reaction exothermic or endothermic is the change in the bonding. Changes in the energies of molecular motion can usually be neglected by comparison.
• The sum of all the different kinds of energy which the molecules of a substance can possess is called the internal energy and given the symbol U

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• System. The term system is used to describe any sample of matter in which we are particularly interested
• Initial and final states. In thermodynamics our principal concern is with the initial state before any changes begin, and the final state, when no more changes occur

• The delta convention. When a chemical or physical change occurs, many of the properties of the system change. We conventionally refer to a change in a property with the symbol Δ (delta). In the O₃–O₂ reaction, for example, the pressure P increases by 101.3 kPa, and we can indicate this fact by writing
• Heat energy. Our final convention refers to the heat energy q absorbed by the system. If the heat change occurs at constant volume, the symbol q_V is used, if at constant pressure, q_p.

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• When a change occurs at constant pressure, there is another energy factor we must consider in addition to the heat absorbed and the change in internal energy. This is the expansion work w_exp which the system does as its volume expands against the external pressure.
• q_p = ΔU + w_exp 

• where      q_p = heat absorbed

               ΔU = change in internal energy

              w_exp = expansion work, i.e., work done in lifting the weight
• However, when a reaction is carried out at constant atmospheric pressure, it is necessary to measure P, V₁ and V₂ (as in Example 1) as well as q_p in order to calculate the change in internal energy from the equation ΔU = q_p – P ΔV.
• This extra energy is added to take account of the fact that whenever a body of volume V is introduced into the atmosphere, the potential energy of the atmosphere is increased by PV
• Enthalpy = internal energy + potential energy of atmosphere 
• In other words, the heat energy absorbed by a system in any change at constant pressure is equal to the increase in its enthalpy. The change in enthalpy ΔH can be obtained from a single experimental measurement: the heat energy absorbed at constant pressure.

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• t is therefore often necessary to convert a measured ΔU value to a ΔH value.
• Though enthalpies of formation are easy to find, equivalent tables of internal energies are nonexistent. In many ways this insistence on ΔH rather than on ΔU is a pity. In particular, it suggests that somehow the enthalpy H has more fundamental significance on the molecular level than the internal energy U. It is important to realize that this is not the case. It is the internal energy which has a simple molecular interpretation, namely, the total energy of all the molecules in the system. By contrast the enthalpy includes not only the total energy of the molecules in the system but the potential energy of the atmosphere outside the system as well. We use the enthalpy so often because of its convenience rather than because of its molecular significance.
• Both enthalpy and the internal energy are often described as state functions. This means that they depend only on the state of the system, i.e., on its pressure, temperature, composition, and amount of substance, but not on its previous history
• he entropy, symbol S, and the free energy, symbol G, are discussed in other sections. These are quite sensitive to pressure, and the inclusion of this superscript is important. For reasons of consistency therefore we will indicate standard enthalpy changes as ΔH° from now on.

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• The bond enthalpy D_X–Y of a diatomic molecule X—Y is the enthalpy change for the (usually hypothetical) process:

  
  XY(g) → X(g) + Y(g)      ΔH°(298 K) = D_X―Y      (1)
• We have already used the term bond energy to describe this quantity, though strictly speaking the bond energy is a measure of ΔU rather than ΔH. As we have already seen, ΔU and ΔH are nearly equal, and so either term may be used.
• we must expect to obtain only approximate results, accurate only to about ± 50 kJ mol^–1, from the use of bond enthalpies

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• If less energy is needed to break up the reactant molecules into their constituent atoms than is released when these atoms are reconstituted into product molecules, then the reaction will be exothermic
• In summary, there are two factors which determine whether a gaseous reaction will be exothermic or not: (1) the relative strengths of the bonds as measured by the bond enthalpies, and (2) the relative number of bonds broken and formed. An exothermic reaction corresponds to the formation of more bonds, stronger bonds, or both
• A second generalization is that the strengths of bonds usually increase with polarity.
• A third factor affecting the strength of bonds is the size of the atoms.

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• Chemical reactions which proceed downhill, are said to be spontaneous
• A spontaneous process corresponds to a rearrangement of atoms and molecules from a less probable to a more probable situation, as measured by the thermodynamic probability W of
• he reactants and products. W is defined as the number of alternative microscopic arrangements which correspond to the same macroscopic state.
• According to the second law of thermodynamics, when a spontaneous process occurs, there must be an increase in total entropy.
• The entropy of a perfectly ordered crystal at absolute zero is zero according to the third law of thermodynamics. Increasing the temperature, volume, or amount of substance increases the entropy. For a given amount of substance, the heavier and more complex the molecules, the greater the entropy, while weaker forces between atoms or molecules result in lower entropy. In general the greater the randomness or disorder of the atoms or molecules the greater the entropy of a substance.
• For a spontaneous reaction occurring at constant temperature and pressure, ΔG° must be negative. Since ΔG° = ΔH° – T ΔS°, a negative enthalpy change is the most important factor governing spontaneity of a reaction at low temperatures.

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• The entropy of a substance depends on two things: first, the state of a substance—its temperature, pressure, and amount; and second, how the substance is structured at the molecular level.
•    As we saw in the last section, there should be only one way of arranging the energy in a perfect crystal at 0 K. If W = 1, then S = k ln W = 0; so that the entropy should be zero at the absolute zero of temperature. This rule, known as the third law of thermodynamics, is obeyed by all solids unless some randomness of arrangement is accidentally “frozen” into the cryst
• Without exception the entropy of any pure substance always increases with temperature.
• e argued earlier that when a gas doubles its volume, the number of ways in which the gas molecules can distribute themselves in space is enormously increased and the entropy increases by 5.76 J K^–1
• More generally the entropy of a gas always increases with increasing volume and decreases with increasing pressure.
• Thus the entropy of 2 mol of a given substance is twice as large as the entropy of 1 mol. Properties which behave in this way are said to be extensive properties

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• There are two aspects of the molecular structure of a substance which affect the value of its entropy: (1) The degree to which the movement of the atoms and molecules in the structure is restricted—the less restricted this movement, the greater the entropy. (2) The mass of the atoms and molecules which are moving—the greater the mass, the larger the entropy.

• Thus when a solid melts, the molar entropy of the substance increases. When a liquid vaporizes, the restrictions on the molecules’ ability to move around are relaxed almost completely and a further and larger increase in the entropy occurs. When 1 mol of ice melts, for example, its entropy increases by 22 J K^–1, while on boiling the entropy increase is 110 J K^–1
• we still find an increase of entropy with complexity when we compare molecules of very similar masses:
• Another trend in entropy, most noticeable in the case of solids, is the decrease in the entropy as the forces between the atoms, molecules, or ions increases.
• Since there is very little difference in the molar masses, the entropy decrease can only be attributed to the increase in the coulombic attraction between the ions as we move from the singly charged ions Na⁺ and F^– through the doubly charged ions Mg²⁺ and O^2–, to the triply charged ions A1³⁺ and N^3–. (While it is true that there is a fair degree of covalent character to the bonding in AIN, the effect of this will be to

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