Enthalpy, bond

Click Coached Problems for a self-study module on enthalpy change. 

For many reactions, AH is a large negative number the reaction gives off a lot of heat In other cases, AH is positive heat must be absorbed for the reaction to occur. You may well wonder why the enthalpy change should vary so widely from one reaction to another. Is there some basic property of the molecules involved in the reaction that determines the sign and magnitude of AH  

These questions can be answered on a molecular level in terms of a quantity known as bond enthalpy. (More commonly but less properly it is called bond energy.) The bond enthalpy is defined as AH when one mole of bonds is broken in the gaseous state. From the 

Using bond enthalpies, it is possible to explain why certain gas phase reactions are endothermic and others are exothermic. In general, a reaction is expected to be endothermic (Le., heat must be absorbed) if— 

A measure of the stability of a molecule is its bond enthalpy, which is the enthalpy change required to break a particular bond in 1 mole of gaseous molecules. (Bond enthalpies in soUds and liquids are affected by neighboring molecules.) The experimentally determined bond enthalpy of the diatomic hydrogen molecule, for example, is 

This equation tells us that breaking the covalent bonds in 1 mole of gaseous H2 molecules requires 436.4 kJ of energy. For the less stable chlorine molecule. 

Bond enthalpies can also be directly measured for diatomic molecules containing unlike elements, such as HCl, 

Measuring the strength of covalent bonds in polyatomic molecules is more complicated. For example, measurements show that the energy needed to break 

In each case, an O—H bond is broken, but the first step is more endothermic than the second. The difference between the two values suggests that the second O—H bond itself has undergone change, because of the changes in the chanical environment. 

Bond enthalpies for a variety of single and multiple bonds are listed in Table 8.4 (page 247). Note that bond enthalpy is always a positive quantity heat is always absorbed when chemical bonds are broken. Conversely, heat is given off when bonds are formed from gaseous atoms. Thus 

You will note from Table 8.4 that the bond enthalpy is larger for a multiple bond than for a single bond between the same two atoms. Thus 

the double bond enthalpy is less than twice that for a single bond. 

The direct conversion of a soHd to a vapor is called sublimation. The reverse process is called vapor deposition. Sublimation can be observed on a cold, frosty morning, when frost vanishes as vapor without first melting. The frost itself forms by vapor deposition from cold, damp air. The vaporization of solid carbon dioxide ( dry ice ) is another example of sublimation. The standard molar enthalpy change accompanying sublimation is called the standard enthalpy of sublimation, AsubH. Because enthalpy is a state property, the same change in enthcdpy must b e obtained b oth in the direct conversion of soHd to vapor cuid in the indirect conversion, in which the solid first melts to the Hquid cUid then that liquid vaporizes (Fig. 1.23)  

This result is an example of a more general statement that will prove useful time and again during our study of thermochemistry  

The enthalpy change of an overall process is the sum of the enthalpy changes for the steps (observed or hypothetical) into which it maybe divided. 

To use eqn 1.20 correctly, the two enthalpies that are added together must be for the same temperature, so to get the enthalpy of sublimation of water at 0°C, we must add together the enthalpies of fusion (6.01 kJ mol ) and vaporization (45.07 kJ mol ) for this temperature. Adding together enthalpies of transition for different temperatures gives a meaningless result. It follows that 

To understand bioenergetics at a moiecuiar ievei we need to account for the flow of energy during chemicai reactions as individuai chemicai bonds are broken and made. 

In which species does the central atom obey the octet rule (Select all that apply.) 

How many lone pairs are there on the central atom in the Lewis structure of ICI2  

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Strictly, these values are bond enthalpies, but the term energies is commonly used. Other descriptions are average standard bond energies, mean bond energies . 

Derivation of bond enthalpies from themioehemieal data involves a system of simultaneous equations in which the sum of unknown bond enthalpies, each multiplied by the number of times the bond appears in a given moleeule, is set equal to the enthalpy of atomization of that moleeule (Atkins, 1998). Taking a number of moleeules equal to the number of bond enthalpies to be determined, one ean generate an n x n set of equations in whieh the matrix of eoeffieients is populated by the (integral) number of bonds in the moleeule and the set of n atomization enthalpies in the b veetor. (Obviously, eaeh bond must appear at least onee in the set.)... 

Procedure. Run one or more simultaneous equation programs to determine the C—C and C—H bond energies and interpret the results. The error veetor is the veetor of ealeulated values minus the veetor of bond enthalpies taken as tme from an aeeepted source. Caleulate the enor veetor using a standard souree of bond enthalpies (e.g., Laidler and Meiser, 1999 or Atkins, 1994). Expand the method for 2-butene (2-butene) = —11 kJ mol ] and so obtain the C—H, C—C,... 

What is the average enthalpy of atomization of the four C—H bonds in methane Compare this value with the accepted value of the C—H bond enthalpy. 

Calculate the bond enthalpy of the C—C bond in ethane using only the enthalpies of atomization of methane and ethane. Compare this result with the accepted result. 

BOND ENTHALPY (BE) AND STRAINLESS BOND ENTHALPY (SBE) CONSTANTS AND SUMS... 

At the top of File Segment 5-1 is a heat of fomiation information block. Two sums are listed One is a sum of nomial bond enthalpies for ethylene, and the other is a sum selected from a parameter set of stiainless bonds. Both sets of bond enthalpies have been empirically chosen. A group of molecules selected as nomial generates one parameter set, and a group supposed to be strainless is selected to generate a second set of str ainless bond enthalpies designated SBE in Eile Segment 5-1. The subject of parameterization has been treated in detail in Chapter 4. See Computer Projects 3-6 and 3-7 for the specific problem of bond enthalpies. 

Once the BEs and SBEs have been decided upon, the normal functioning of the MM program causes each bond to be multiplied by the number of times it appears in the computed molecule to find its contribution to the total bond enthalpy. In ethylene, 26.43 + 4(—4.59) = 8.07kcalmol . In Eile Segment 5-1, this sum is denoted BE. This whole procedure is essentially a conventional bond energy calculation. 

A force field that can produce vibrational spectra has a second advantage in that the Ay// calculations can be put on a much more satisfactory theoretical base by calculating an enthalpy of formation at 0 K as in ab initio procedures and then adding various thermal energies by more r igorous means than simply lumping them in with empirical bond enthalpy contributions to Ay//-. The stronger the theoretical base, the less likely is an unwelcome surprise in the output. 

Bond Bond order Bond length /pm Mean bond enthalpy /(k J moi" )... 

Table 6.3 Some enthalpies of atomization (Af/j, 298 K) and comparative bond-enthalpy contributions, E...

We should point out a serious limitation of the bond enthalpies listed in Table 8.4. Whenever the bond involves two different atoms (e.g., O—H) the value listed is approximate rather than exact, because it represents an average taken over two or more different species. Consider, for example, the O—H bond where we find... 

Both of these reactions involve breaking a mole of O—H bonds, yet the experimental values of AH are quite different The bond enthalpy listed in Table 8.4,464 kj/mol, is an average of these two values. 

This limitation explains why, whenever possible, we use enthalpies of formation (AFff) rather than bond enthalpies to calculate the value of AH for a reaction. Calculations involving enthalpies of formation are expected to be accurate within 0.1 kj the use of bond enthalpies can result in an error of 10 kj or more. 

Which statements) is/are true about bond enthalpy ... 

The transition-state model is generally somewhat more accurate than the collision model (at least with p = 1). Another advantage is that it explains why the activation energy is ordinarily much smaller than the bond enthalpies in the reactant molecules. Consider, for example, the reaction... 

The difference in Ka values is due largely to the difference in bond strength. The H—F bond (bond enthalpy = 565 kj/mol) is much stronger than the H—Cl bond (bond enthalpy = 431 kj/mol). 

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