c04 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come
GROUP ADDITIVITY 63If we were asked to predictcH^298 (n-pentane(g)), a reasonable answer would be to
add another negative change just like the last two:cH^298 (n-pentane(g))=− 2877. 6 − 658. 4 =−3536 kj mol−^1.The experimental value is 3535.4±1.0.
Even simpler, we can note that, given the reference pointcH^298 (ethane(g))=
−1560.7 kJ mol−^1 , the heats of combustion ofn-alkanes (except for methane) obey a
linear function of thenumberof additional hydrogen atoms over those in the reference
compound with slope equal to –658.5/2=−329.2 kJ mol−^1. These CH 2 hydrogen
atoms are calledsecondaryhydrogens as distinct from CH 3 , hydrogens, which are
primary, and isolated C H atoms, which aretertiary.NowanycH^298 (n-alkane(g))
can be found by counting secondary hydrogen atoms and adding the count times
−329.2 to the base value of−1560.7.
Because the enthalpies of formationfH^298 ofn-alkanes(g) are proportional
tocH^298 , one can estimatefH^298 values in the same way that we used in the
combustion case. Simply count hydrogen atoms and add to a base value for ethane:Ethane Propane n-ButanefH^298 (g) −84.0 −104.7 −125.6
Difference −20.7 −20.9Counting secondary hydrogens forn-octane and multiplying by−20.8/2=−10.4
gives 12(−10.4)=−124.8. Adding the base value,−84.0 gives−208.8 kJ mol−^1.
The experimental value is− 208. 4 ± 0 .8kJmol−^1.
Zavitsas et al. (2008) have extended this method to cover primary, secondary, and
tertiary hydrogens by the equationfH◦=− 14. 0 np+(− 10. 4 ns)+(− 6. 65 nt)=∑
ciniwherenp,ns,andntare the numbers of primary, secondary, and tertiary hydrogen
atoms in any alkane or cycloalkane. By this system, the enthalpy of formation of
4-methylheptane, an isomer ofn-octane, isH
|
CH 3 CH 2 CH 2 CCH 2 CH 2 CH 3
|
CH 3fH◦=− 14. 0 np+(− 10. 4 ns)+(− 6. 65 nt)
fH^298 (4−methylheptane(g))=− 14 .0(9)+(− 10 .4(8))+− 6 .65(1)
=− 215 .8kJmol−^1The experimental value is−212.1.