Enthalpy standard, of formation

For a reaction studied under conditions of constant pressure, we can obtain the enthalpy change by using a calorimeter. However, this process can be very difficult. In fact, in some cases it is impossible, since certain reactions do not lend themselves to such study. An example is the conversion of solid carbon from its graphite form to its diamond form  

The value of AH for this process cannot be obtained readily by measurement in a calorimeter. We will show next how to calculate AH for chemical reactions and physical changes by using standard enthalpies of formation. 

The standard enthalpy of formation (AH°) of a compound is defined as the change in enthalpy that accompanies the formation of 1 mole of a cor -pound from its elements with all substances in their standard states. 

Standard state is not the same as standard temperature and pressure (STP) for a gas. 

Recently, the International Union of Pure and Applied Chemistry (IUPAC) has adopted l bar (100,000. Pa) as the standard pressure instead of 1 atm (101,325 Pa). Both standards are now widely used. 

Unless Otherwise noted, all art on this page Is C) Cengage Learning 2014. 

The value of AH for this process cannot be obtained by direct measurement in a calorimeter becanse the process is mnch too slow under normal conditions. However, as we saw in Example 6.7, AH for this process can be calculated from heats of combustion. This is only one example of how nsefnl it is to be able to calculate AH values for chemical reactions. We will next show how to do this using standard enthalpies of formation. 

A degree symbol on a thermodynamic fnnction, for example, AH°, indicates that the corresponding process has been carried ont nnder standard conditions. The standard state for a substance is a precisely defined reference state. Because thermodynamic functions often depend on the concentrations (or pressures) of the substances involved, we must use a common reference state to properly compare the thermodynamic properties of two substances. This is especially important because, for most thermodynamic properties, we can measnre only changes in the property. For example, we have no method for determining absolnte valnes of enthalpy. We can measure enthalpy changes (AH values) only by performing heat-flow experiments. 

Standard enthalpies of formation of chemical compoundsf are of great practical value to chemists. They give an easy method of determining the 

The International Union of Pure and Applied Chemistry (lUPAC) recommends that the standard pressure be 1 bar (1 X 10 Pa).Thermodynamic tables are becoming available for 1 bar pressure, and in the future such tables will probably replace those for 1 atm. 

Although the reference form is usually the stablest allotrope of an element, the choice is essentially arbitrary as long as one is consistent. 

Because Hess s law relates the enthalpy changes of some reactions to the enthalpy changes of others, we only need to tabulate the enthalpy changes of certain types of reactions. We also generally list enthalpy changes only for certain standard thermodynamic conditions (which are not identical to the standard conditions for gases, STP). 

The term standard state refers to the standard thermodynamic conditions chosen for substances when listing or comparing thermodynamic data 1 atm pressure and the specified temperature (usually 25° C). These standard conditions are indi- 

As we will show, it is sufficient to tabulate just the enthalpy changes for formation reactions—that is, for reactions in which compounds are formed from their elements. To specify the formation reaction precisely, however, we must specify the exact form of each element. 

We need to simplify even further the process of predicting reaction enthalpies of biochemical reactions. 

The standard reaction enthalpy, A,H-, is the difference between the standard molar enthalpies of the reactcuits cuid the products, with each term weighted by the stoichiometric coefficient, v (nu), in the chemical equation 

The problem with eqn 1.22 is that we have no way of knowing the absolute enthalpies of the substances. To avoid this problem, we can imagine the reaction as taking place by an indirect route, in which the reactants are first broken down into the elements and then the products are formed from the elements (Fig. 1.24). Specifically, the standard enthalpy of formation, AfH, of a substance is the standard enthalpy (per mole of the substance) for its formation from its elements in their reference states. The reference state of an element is its most stable form under the prevailing conditions (Table 1.7). Don t confuse reference state with standard state the reference state of carbon at 25 C is graphite (not diamond) the standard state of carbon is any specified phase of the element at 1 bar. For example, the standard enthalpy of formation of liquid water (at 25 C, as always in this text) is obtained from the thermochemical equation 

With the introduction of standard enthalpies of formation, we can write 

The first term on the right is the enthalpy of formation of all the products from their elements the second term on the right is the enthalpy of formation of all the reactants from their elements. The fact that the enthalpy is a state function means that a reaction enthalpy calculated in this way is identical to the value that would 

Calculations involving Hess s law typically require that several reactions be manipulated and combined to finally give the reaction of interest. In doing this procedure you should 

This process involves some trial and error, but it can be very systematic if you always allow the final reaction to guide you. 

Appendix 2 lists the standard enthalpies of formation for a number of elements and compounds. By convention, the standard enthalpy of formation of any element in its most stable form is zero. Again, using the element oxygen as an example, we can write Af/f(O2) = 0, but A/f f(O3) 0 and A// 0) 0. Similarly, graphite is a more stable allotropic form of carbon than diamond under standard conditions and 25°C, so we have A//f (graphite) = 0 and A// (diamond) 0. 

The importance of the standard enthalpies of formation is that once we know their values, we can readily calculate the standard enthalpy of reaction (A//, defined as the enthalpy of a reaction carried out under standard conditions. For example, consider the hypothetical reaction 

The direct method of measuring AHf works for compounds that can be synthesized from their elements easily and safely. Suppose we want to know the enthalpy of formation of carbon dioxide. We must measure the enthalpy of the reaction when carbon (graphite) and molecular oxygen in their standard states are converted to carbon dioxide in its standard state  

We know from experience that this combustion goes to completion. Thus, from Equation 5.19 we can write 

Because graphite and O2 are the most stable allotropic forms of their respective elements, A//f(graphite) and A//f(02) are both zero. Therefore, 

In the enthalpy diagrams we have drawn, we have not written any numerical values on the enthalpy axis. This is because we caimot determine absolute values of enthalpy, H. However, enthalpy is a function of state, so changes in enthalpy, AH, have unique values. We can deal just with these changes. Nevertheless, as with many other properties, it is still useful to have a starting point, a zero value. 

Consider a map-making analogy What do we list as the height of a mountain Do we mean by this the vertical distance between the mountaintop and the center of Earth Between the mountaintop and the deepest trench in the ocean No. By agreement, we mean the vertical distance between the mountaintop and mean sea level. We arbitrarily assign to mean sea level an elevation of zero, and all other points on Earth are relative to this zero elevation. The elevation of Mt. Everest is +8848 m that of Badwater, Death Valley, California, is -86 m. We do something similar with enthalpies. We relate our zero to the enthalpies of certain forms of the elements and determine the enthalpies of other substances relative to this zero. 

The standard enthalpy of formation (AfJT ) of a substance is the enthalpy 

The standard enthalpy of formation is 0 for a pure element in its reference form. 

Listed here are the most stable forms of several elements at 298.15 K, the temperature at which thermochemical data are commonly tabulated. 

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Table 1.5. Standard Enthalpies of Formation of Some Hydrocarbons (kcal/mol) ...

The amonnt of energy that can be released from a given chemical reaction is determined from the energies (enthalpies of formation) of the individnal reactants and prodncts. Enthalpies are nsnally given for snbstances in their standard states, which are the stable states of pnre snbstances at atmospheric pressnre and at 25°C. The overall heat of reaction is the difference between the snms of the standard enthalpies of formation of the prodncts... 

Figure 4,4 Standard enthalpies of formation (A// and lattice energies (plotted as —t/O for alkali metal halides and hydrides.

Figure 7.7 Trends in the standard enthalpies of formation AH] for Groups 3 and 13 trihalides as illustrated by data for MF3 and MBrj.

The atom and bond concepts dominate chemistry. Dalton postulated that atoms retained their identities even when in chemical combinations with other atoms. We know that their properties are sometimes transferable from one molecule to another for example, the incremental increase in the standard enthalpy of formation of a normal hydrocarbon per CHj group is —20.6 1.3 kJmol . We also know that more often there are subtle modifications to the electron density. 

The standard enthalpies of formation of ions in aqueous solution listed at the bottom of Table 8.3 are relative values, established by taking... 

The standard enthalpy change, Aff°, for a given thermochemical equation is equal to the sum of the standard enthalpies of formation of the product compounds minus the sum of the standard enthalpies of formation of the reactant compounds. 

Enthalpy changes for reactions in solution can be determined using standard enthalpies of formation of aqueous ions, applying the general relation... 

Table 4.3 summarizes values taken from the JANAF tables for the Gibbs free energy functions and standard enthalpies of formation for a few common substances. The JANAF tables provide a more complete tabulation. 

This value is the standard enthalpy of formation of glycerol dissolved in water in a hypothetical m = 1 solution that obeys Henry s law. 

Combining this result with the standard enthalpies of formation of SF6 and GeF4... 

Extensive tabulations of standard enthalpies of formation and related thermodynamic data can be found in the literature.5 Table 9.1 summarizes selected values from these sources. 

There are millions of possible reactions, and it is impractical to list every one with its standard reaction enthalpy. However, chemists have devised an ingenious alternative. First, they report the standard enthalpies of formation of substances. Then they combine these quantities to obtain the standard enthalpy of reaction needed. Let s look at these two stages in turn. 

The standard enthalpy of formation, AH°, of a substance is the standard reaction enthalpy per mole of formula units for the formation of a substance from its elements in their most stable form, as in the reaction... 

A note on good practice You should always be alert to the difference between a quantity per mole of molecules and the same quantity for or of a mole of molecules. Standard enthalpies of formation are expressed per mole of molecules, as in —277.69 kj-mol the standard enthalpy of forming 1 mol C2H5OH(l) is —277.69 kj. The point might seem picky, but it will help you to keep units straight. 

It follows from the definition just given that the standard enthalpy of formation of an element in its most stable form is zero. For instance, the standard enthalpy of formation of C(gr) is zero because C(gr) — C(gr) is a null reaction (that is, nothing changes). We write, for instance, AHf°(C, gr) = 0. However, the enthalpy of formation of an element in a form other than its most stable one is nonzero. For example, the conversion of carbon from graphite (its most stable form) into diamond is endothermic ... 

The standard enthalpy of formation of diamond is therefore reported as AHt°(C, diamond) = + 1.9 kj-mol l. Values for a selection of other substances are listed in Table 6.5 and Appendix 2A. 

Now let s see how to combine standard enthalpies of formation to calculate a standard reaction enthalpy. To do so, we imagine carrying out the reaction in two steps we reverse the formation of the reactants from the elements, then combine the elements to form the products. The first step is usually to calculate the reaction enthalpy for the formation of all the products from their elements. For this step, we use the enthalpies of formation of the products. Then, we calculate the reaction enthalpy for the formation of all the reactants from their elements. The difference between these two totals is the standard enthalpy of the reaction (Fig. 6.31) ... 

In this expression, the n are the amounts of each substance in the chemical equation and the symbol X (sigma) means a sum. The first sum is the total standard enthalpy of formation of the products. The second sum is the similar total for the reactants. 

EXAMPLE e.ll Using standard enthalpies of formation to calculate a standard enthalpy of reaction... 

STRATEGY We expect a strongly negative value because all combustions are exothermic and this oxidation is like an incomplete combustion. First, add up the individual standard enthalpies of formation of the products, multiplying each value by the appropriate number of moles from the balanced equation. Remember that the standard enthalpy of formation of an element in its most stable form is zero. Then, calculate the total standard enthalpy of formation of the reactants in the same way and use Eq. 20 to calculate the standard reaction enthalpy. 

Standard enthalpies of formation are commonly determined from combustion data by using Eq. 20. The procedure is the same, but the standard reaction enthalpy is known and the unknown value is one of the standard enthalpies of formation. 

Self-Test 6.16A Calculate the standard enthalpy of formation of ethyne, the fuel used in oxyacetylene welding torches, from the information in Tables 6.4 and 6.5. 

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