Energy Gibbs’ free

Gibbs free energy, also known as free energy, provides a way to predict the spontaneity of a reaction using a combination of the enthalpy and entropy of a reaction. Free energy is defined as 

The value of A G will tell us if the reaction is spontaneous. There are three possible values for AG  

A G 0 The forward reaction is nonspontaneous, but the reverse reaction is spontaneous. 

Since we already have tables of standard enthalpies and standard entropies, we can substitute these values into the free energy equation and determine the standard free energies of formation for substances. The standard free energies of formation tell you if a substance will form spontaneously if the constituent atoms are combined. The formula to determine the standard free energy change for a reaction is the same as Equation 17.8 for the enthalpy change (except Gs are substituted for the Hs)  

Sample Calculate the standard free energy change for the complete combustion of methane, CH4, at 25°C. 

The Gibbs free energy G is a central thermodynamic quantity in understanding chemistry. The Gibbs free energy determines whether a reaction, or perhaps its reverse reaction, will proceed spontaneously. It provides for the location of chemical equilibrium, at which there is no net forward or reverse reaction. The free-energy change of a reaction determines the equilibrium constant, which also determines the reverse rate constant for a reaction, if the forward rate constant is known. 

AG is change in the free energy as the process proceeds. It is calculated from the sum of the free energies of all the reaction product species minus the sum of the free energies of all the reactant species. These quantities depend on the temperature, pressure, and concentrations of each of the species. The changes in the enthalpy, AH, and entropy, A5, are similarly defined as the difference between the product and reactant values. 

For a certain set of chemical species concentrations, temperature, and pressure, a chemical process will proceed in the direction that decreases the free energy. If AG 0 for that set of concentrations, and so forth, the process will proceed spontaneously in the direction of the forward reaction, although thermodynamics says nothing about the rate at which it will proceed. If AG 0, the reaction will proceed in the reverse direction spontaneously. The process proceeds in the direction to minimize the free energy of the system until AG = 0, at which point equilibrium has been attained. Stated another way, natural processes always proceed in the direction that decreases the free energy, until equilibrium is reached. 

The free-energy change in forming a compound at temperature T in its standard state from its elements in their standard states (also at temperature T) is defined as AG°p the standard free energy of formation for a chemical compound. The standard state for a gaseous species is a pressure of 1 bar, denoted p°. 

For a general chemical reaction, where a is the stoichiometric coefficient of species A, for example, 

Ratio of the enthalpy of fusion AH to the binding energy of various crystalline solids. This ratio is only 4% for most metals. 

The Gibbs free energy is constructed such that it will be a minimum when the system is at equilibrium, or we might say that nature tends to want to minimize the free energy of a system. Whichever phase has the lowest free energy will be the stable phase. 

Entropy of fusion for various crystalline solids. For most metals, AS is only a few calories per mole. 

Schematic of the free energy whose slope becomes discontinuous during a first-order phase transition. 

4 Isothermal isobaric systems 1.4.1 Gibbs free energy 

The relative probability of a state in an NPT system is expressed as a function of thermodynamic quantity enthalpy, which is defined as H = E + PV. From Equation (1.1) we have 

Thus in an NPT system enthalpy takes the place of internal energy in an NVT system. The probability law for an NPT system is 

The Gibbs free energy is defined as G = E — TS + PV or G = H — TS. Following logic analogous to that of Section 1.3.1, we have 

To complete the analogy to Helmholtz free energy in NVT systems  

Recall that the square brackets in the equilibrium relationship given in Eq. 2.2 designate concentration, measured in mol / L. We are using kcal / mol as the standard unit of energy in this text. The unit kj/mol is also commonly used, and the conversion is 1 kcal/mol = 4.184 kj/mol. 

The free energy has two components, the enthalpy (AFT) and the entropy (AS°), related by the Gibbs-Helmholtz equation (Eq. 2.3). Typically, enthalpy is measured in kcal/mol, and entropy in entropy units (eu), which are equivalent to cal/mol K. Therefore, for entropy to be an energy value, it must be multiplied by the temperature. This has an important consequence. Changes in temperature affect the free energy between A and B, and therefore 

Composition of an A/B Mixture as a Function of Gibbs Free Energy Difference and Temperature 

The thermodynamic term of widest use in soil chemistry is the free energy, or more explicidy, the Gibbs free energy. This is the energy of a substance or a reaction that, at constant temperature and pressure, is available for subsequent use. Energy drives chemical reactions and AG is the most widely useful. It is directiy related to (1) the activity or chemical potential, (2) the energy of formation of compounds, (3) the equilibrium constant of a reaction, and (4) the electrode potential. The first three are discussed here the electrode potential is discussed in Chapter 4. 

The most useful concentration unit for solutions is the chemical activity a (Section 3.2). The change in free energy with the amount of solute is 

Reactions that release energy and leave the system in a lower energy state, a more stable state, than before are spontaneous. The second law states that systems will strive to reach the lowest energy level. Thermodynamics says only that a reaction will proceed and not what die reaction rate, will be. The hydrogen and oxygen in reaction, 3.36 can coexist for centuries without reacting until a catalyst or spark is introduced. 

The free energies of formation of many compounds and ions have been measured and compiled. Table 3.7 contains values for the AG° of formation of some compounds relevant to soil chemistry. 

The change of free energy during a reaction is the difference between the free energies of the products and those of the reactants. An important energy reaction in nature is photosynthesis, the formation of glucose  

A system at constant temperature and pressure is at disequilibrium until all of its Gibbs free energy, G, is used up. In the equilibrium condition the Gibbs free energy equals zero. 

The Gibbs free energy is a measure of the probability that a reaction occurs. It is composed of the enthalpy, H, and the entropy, S° (Eq. 5). The enthalpy can be described as the thermodynamic potential, which ensues H = U + p V. where U is the internal energy, p is the pressure, and V is the volume. The entropy, according to classical definitions, is a measure of molecular order of a thermodynamic system and the irreversibility of a process, respectively. 

A positive value for G means that additional energy is required for the reaction to happen, and a negative value that the process happens spontaneously thereby releasing energy. 

The change in free energy of a reaction is directly related to the change in energy of the activities of all reactants and products under standard conditions. 

G° equals G, if all reactants occur with unit activity, and thus the argument of the logarithm in Eq. 6 being 1 and consequently the logarithm becoming zero. 

If the process occurs at a constant pressure, but 6w 0, one may add PV to A, as in the case of enthalpy, and thereby obtain Gibbs free energy, which is also a state function. We obtain 

The thermodynamic functions U, S, A, and G may thus be written with the help of the partition function. From this, it follows that they are state functions and that variations of them, dU, dS, dA, and dG, are exact differentials. 

G is Gibbs free energy. Since chemical reactions often occur at a constant pressure, G is perhaps the most important state function in chemistry. If H is constant and there is no heat exchange with the environment, a spontaneous reaction at constant temperature (AS 0) means that 

If the product side of a chemical reaction has a lower value of G than the reactant side (AG 0), the chemical reaction occurs spontaneously. Equation 5.33 implies 

Consider a process where ammonium chloride (NH4CI) (salmiac) is formed from ammonia and hydrochloric add  

He realized that changes in this function could predict whether or not a process is spontaneous under conditions of constant pressure and temperature. This constraint is not that demanding because many laboratory processes occur under these conditions (or approximately so). Now, if we focus on the change in the Gibbs free energy for a process at constant temperature, we have the following result  

From a practical viewpoint, this could be the most important equation in this chapter. 

An alternative function called the Helmholtz free energy is useful for constant volume conditions. This is less common in engneering applications, so we will not consider it 

One of the goals of chemists is to be able to predict if a reaction will be spontaneous. A reaction may be spontaneous if its AH is negative or if its AS is positive, but neither one is a reliable predictor by itself about whether or not a reaction will be spontaneous. Temperature also plays a part. A thermodynamic factor that takes into account the entropy, enthalpy, and temperature of the reaction would be the best indicator of spontaneity. This factor is the Gibbs free energy. 

Like most thermodynamic functions, it is only possible to measure the change in Gibbs free energy, so the relationship becomes  

If there is a AG associated with a reaction and we reverse that reaction, the sign of the AG changes. 

AG is the best indicator chemists have as to whether or not a reaction is spontaneous  

Just like with the enthalpy and entropy, the standard Gibbs free energy change, (AG°), is calculated  

Recall that equilibrium is achieved by maximizing the entropy of the universe. We can restate this relationship in terms of only the system by using the equation  

ASsurmundillgs = dqr /T. We know that at constant pressure the change in enthalpy is equal to the heat thus, ASsutIDUlldinss = AHsimmmdm s/T. Also, since AHslul.ounditlgs = 

If we multiply through by -T, and substitute AG for -ASuniveiseT, we have the important MCAT equation for Gibbs free energy G  

ASuniver5e be positive under any conditions. For the MCAT however, a negative AG A negative AG indicates a spontaneous from the Gibbs function is good enough for spontaneity. reation, 

You must know the Gibbs function, and, most importantly, that a negative AG indicates a spontaneous reaction. Realize that the Gibbs function deals with the change in enthalpy and entropy of a system. 

Disorder increases with time because we measure time in the direction in which disorder increases. 

Physical parameters involved are heat, mechanical work, and the state of disorder (or structure). Any of these can be used to drive a process to completion. Many experimental measurements have been made to quantify the components of Gibbs free energy. Thus, calculations can indicate to the engineer if the process can be expected to yield energy or require energy. 

Energy level of source (Gibb s free energy) 

FIGURE 2.5.1 Gibbs free energy consists of the ability of a system to do usefnl work on the environment or to add heat to the environment. If the Gibbs free energy is negative, the environment will be able to affect the system and the process will thns happen spontaneously. 

Water will freeze spontaneously at absolute temperatures less than 273 K. Therefore, the Gibbs free energy of freezing water will be negative. 

We should recognize that the surroundings for any system serve essentially as a large, constant-temperature heat source (or heat sink if the heat flows from the system to the surroundings). The change in entropy of the surroundings depends on how much heat is absorbed or given off by the system. 

For an isothermal process, the entropy change of the surroundings is given by 

Because in a constant-pressure process, is simply the enthalpy change for the reaction, AH, we can write 

For the reaction in Sample Exercise 19.5, is the enthalpy change for the reaction under standard conditions, AH°, so the changes in entropy will be standard entropy changes, AS°. Therefore, using the procedures described in Section 5.7, we have 

The negative value tells us that at 298 K the formation of ammonia from H2(g) and N2(g) is exothermic. The surroundings absorb the heat given off by the system, which means an increase in the entropy of the surroundings  

Notice that the magnitude of the entropy gained by the surroundings is greater than that lost by the system, calculated as —198.3 J/K in Sample Exercise 19.5. 

Because AS°njv is positive for any spontaneous reaction, this calculation indicates that when NH3( ), H2( ), and N2( ) are together at 298 K in their standard states (each at 1 atm pressure), the reaction moves spontaneously toward formation of NH3( ). 

The second law of thermodynamics tells us that a spontaneous reaction increases the entropy of the universe that is, A5umv 0. In order to determine the sign of A univ for a reaction, however, we would need to calculate both ASsys and ASsan- In general, we are usually concerned only with what happens in a particular system. Therefore, we need another thermodynamic function to help us determine whether a reaction will occnr spontaneonsly if we consider only the system itself. 

From Eqnation (18.4), we know that for a spontaneous process, we have 

Now we have a criterion for a spontaneons reaction that is expressed only in terms of the properties of the system (AHsys and A5sys) and we can ignore the surroundings. 

Heat transfers during the operation of a heat engine. 

Analysis based on the second law shows that efficiency can also be expressed as 

The change in G, that is, the difference in G between G now and G yesterday, is given as 

When a problem looks difficult you should try to break it into smaller parts and take a look at each of them. This may be easier said than done as you probably do not know how to break a problem into smaller pieces. This is an art - and we will master it together. Making a list, like a list of the words mentioned, or a list of the quantities and numbers given, or a list of the questions asked, can help us move ahead. 

This question may look a little convoluted and we will translate it to symbols and formulas. We have chemical potential, that is, G per one mole, G (or p), and we also have a change this means AGm- Since both ice and water are present on the skating surface we will have to account for changes of two chemical potentials AGm(ice) and AGm(water). Not bad for a start. 

The riddle states that the changes in G are due to the change in pressure. Check your textbook and under the section Dependence on Gibbs Energy on Temperature and Pressure you will find this formula  

The difference. A, in (4-7) means the following G(final state) minus G(initial state). The same applies to the pressure change. The previous equation can then be written as 

In the previous section, we saw that entropy is the one and only criterion that determines whether or not a chemical reaction will be spontaneous. But it is not enough to consider AS of the system alone we must also take into account AS of the surroundings  

The total change in entropy (system plus surroundings) must be positive in order for the process to be spontaneous. It is fairly straightforward to assess AS using tables of standard entropy values (a skill that you likely learned in your general chemistry course). However, the assessment of A5ju presents more of a challenge. It is certainly not possible to observe the entire universe, so how can we possibly measure A5 su Fortunately, there is a clever solution to this problem. Under conditions of constant pressure and temperature, it can be shown that  

Notice that is now defined in terms of the system. Both AH and T (temperature in 

Kelvin) are easily measured, which means that A55 can in fact be measured. Pluming this expression for into the equation for we arrive at a new equation for A5,q, for which 

This expression is still the ultimate criterion for spontaneity (A5jqj must be positive). As a final step, we multiply the entire equation by —T, which gives us a new term, called Gibbs free energy  

According to the second law of thermodynamics, A5 iv 0 for a spontaneous process. We are usually concerned with and usually measure, however, the properties of the system rather than those of the surroundings or those of the universe overall. Therefore, it is convenient to have a thermodynamic function that enables us to determine whether or not a process is spontaneous by considering the system alone. 

Now we have an equation that expresses the second law of thermodynamics (and predicts whether or not a process is spontaneous) in terms of only the system. We no longer need to consider the surroundings. For convenience, we can rearrange the preceding equation, multiply through by — 1, and replace the sign with a sign  

According to this equation, a process carried out at constant pressure and temperature is spontaneous if the changes in enthalpy and entropy of the system are such that — TAS ys is less than zero. 

To express the spontaneity of a process more directly, we introduce another thermodynamic function called the Gibbs free energy (G), or simply free energy. 

Each of the terms in Equation 18.10 pertains to the system. G has units of energy just as H and TS do. Furthermore, like enthalpy and entropy, free energy is a state function. The change in free energy, AG, of a system for a process that occurs at constant temperature is 

Equation 17.3 establishes a relationship between the enthalpy change in a system and the entropy change in the surroundings. Recall that for any process the entropy change of the universe is the sum of the entropy change of the system and the entropy change of the surroundings  

Combining Equation 17.4 with Equation 17.3 gives us the following relationship at constant temperature and pressure  

Using Equation 17.5, we can calculate AAuniv while focusing only on the system. If we multiply Equation 17.5 by -T, we arrive at the expression  

If we drop the subscript sys—from now on AH and AS without subscripts mean AH ys and AS sys—we get the expression  

The right hand side of Eqnation 17.7 represents the change in a thermodynamic function called Gibbs free energy. The formal definition of Gibbs free energy (G) is  

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Gibbs function (see Gibbs free energy, free energy) gram... 

The relations which permit us to express equilibria utilize the Gibbs free energy, to which we will give the symbol G and which will be called simply free energy for the rest of this chapter. This thermodynamic quantity is expressed as a function of enthalpy and entropy. This is not to be confused with the Helmholtz free energy which we will note sF (L" j (j, > )... 

Gibbs free energy or Gibbs molar free energy molar flow of gas phase acceleration of gravity enthalpy, molar enthalpy, weight enthalpy Henry s constant Planck s constant height horsepower radiation intensity molar flux... 

For spontaneous processes at constant temperature and pressure it is the Gibbs free energy G that decreases, while at equilibrium under such conditions dG = 0. 

Equation ( A2.1.39) is the generalized Gibbs-Diihem equation previously presented (equation (A2.1.27)). Note that the Gibbs free energy is just the sum over the chemical potentials. 

Of these the last eondition, minimum Gibbs free energy at eonstant temperahire, pressure and eomposition, is probably the one of greatest praetieal importanee in ehemieal systems. (This list does not exhaust the mathematieal possibilities thus one ean also derive other apparently ununportant eonditions sueh as tliat at eonstant U, S and Uj, Fisa minimum.) However, an experimentalist will wonder how one ean hold the entropy eonstant and release a eonstraint so that some other state fiinetion seeks a minimum. 

We have seen that equilibrium in an isolated system (dt/= 0, dF= 0) requires that the entropy Sbe a maximum, i.e. tliat dS di )jjy = 0. Examination of the first equation above shows that this can only be true if. p. vanishes. Exactly the same conclusion applies for equilibrium under the other constraints. Thus, for constant teinperamre and pressure, minimization of the Gibbs free energy requires that dGId Qj, =. p. =... 

Figure A2.5.2 shows schematically the behaviour of several thennodynamic fiinctions along a constant-pressure line (shown as a dotted line in Figure A2.5.1 )—the molar Gibbs free energy G(for a one-component system the same as...

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

Figure A2.5.4 shows for this two-component system the same thennodynamic fimctions as in figure A2.5.2, the molar Gibbs free energy (i= + V2P2> the molar enthalpy wand the molar heat capacity C. , again all at...

Figure A2.5.15. The molar Gibbs free energy of mixing versus mole fraetionxfor a simple mixture at several temperatures. Beeause of the synuuetry of equation (A2.5.15) the tangent lines indieating two-phase equilibrium are horizontal. The dashed and dotted eiirves have the same signifieanee as in previous figures.

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

Since equation (A3.6.4) is equal to the difference between the Gibbs free energy of... 

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Kirkwood generalized the Onsager reaction field method to arbitrary charge distributions and, for a spherical cavity, obtained the Gibbs free energy of solvation in tenns of a miiltipole expansion of the electrostatic field generated by the charge distribution [12, 1 3]... 

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

Finally, exchange is a kinetic process and governed by absolute rate theory. Therefore, study of the rate as a fiinction of temperature can provide thennodynamic data on the transition state, according to equation (B2.4.1)). This equation, in which Ids Boltzmaim s constant and h is Planck s constant, relates tlie observed rate to the Gibbs free energy of activation, AG. ... 

Thermodynamics shows that equilibrium constants can be related to Gibbs free energies, AG, by Eq. (3). 

This shows that Eqs. (1) and 2) are basically relationships between the Gibbs free energies of the reactions under consideration, and explains why such relationships have been termed linear free energy relationships (LEER). 

Our discussion so far has considered the calculation of Helmholtz free energies, which a obtained by performing simulations at constant NVT. For proper comparison with expe inental values we usually require the Gibbs free energy, G. Gibbs free energies are obtaini trorn a simulation at constant NPT. 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

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