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Question 6.PS.13: Using Standard Molar Enthalpies of Formation Benzene, C6H6, ......

Using Standard Molar Enthalpies of Formation

Benzene, C_6H_6, is a commercially important hydrocarbon that is present in gasoline, where it enhances the octane rating. Calculate its enthalpy of combustion per mole; that is, find the value of ΔH° for the reaction

C_6H_6(\ell ) + \frac{15}{2} O_2(g) → 6 CO_2(g) + 3 H_2O(\ell )

For benzene, ΔH^\circ_f\left\{ C_6H_6(\ell)\right\}= 49.0  kJ/mol. Use Table 6.2 for any other values you may need.

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ΔH° = – 3267.5  kJ

Strategy and Explanation To calculate ΔH° you need standard molar enthalpies of formation for all compounds (and elements, if they are not in their standard states) involved in the reaction. (Since O_2(g) is in its standard state, it is not included.) From Table 6.2,

C(graphite) + O_2(g) → CO_2(g)              ΔH^\circ_f = – 393.509  kJ/mol

H_2(g) + \frac{1}{2} O_2(g) → H_2O(\ell)              ΔH^\circ_f = – 285.830  kJ/mol

Using Equation 6.11,

ΔH° = \sum\left\{(moles  of  product) × ΔH^\circ_f (product)\right\} – \sum\left\{(moles  of  reactant) × ΔH^\circ_f (reactant)\right\}              [6.11]

ΔH° = [6  mol× ΔH^\circ_f \left\{ CO_2(g)\right\}+  3  mol × ΔH^\circ_f \left\{H_2O(\ell)\right\} ] – [1  mol  C_6H_6(\ell) × ΔH^\circ_f \left\{C_6H_6(\ell)\right\}

= [6  mol × (- 393.509  kJ/mol) +  3  mol × (- 285.830  kJ/mol)]

– [1  mol × (49.0  kJ/mol)] = – 3267.5  kJ

Reasonable Answer Check As expected, the enthalpy change for combustion of a fuel is negative and large.

Table 6.2    Selected Standard Molar Enthalpies of Formation at 25 °C*
Formula Name Standard Molar  Enthalpy of Formation  (kJ/mol) Formula Name Standard Molar  Enthalpy of Formation  (kJ/mol)
 Al_2O_3(s) Aluminum oxide -1675.7  HI(g) Hydrogen iodide 26.48
 BaCO_3(s) Barium carbonate -1216.3  KF(s) Potassium fluoride -567.27
 CaCO_3(s) Calcium carbonate -1206.92  KCl(s) Potassium chloride -436.747
 CaO(s) Calcium oxide -635.09  KBr(s) Potassium bromide -393.8
 C( s, diamond) Diamond 1.895  MgO(s) Magnesium oxide -601.7
 CCl_4(\ell) Carbon tetrachloride -135.44  MgSO_4(s) Magnesium sulfate -1284.9
 CH_4(g) Methane -74.81  Mg(OH)_2(s) Magnesium hydroxide -924.54
 C_2H_5OH(\ell) Ethyl alcohol -277.69  NaF(s) Sodium fluoride -573.647
 CO(g) Carbon monoxide -110.525  NaCl(s) Sodium chloride -411.153
 CO_2(g) Carbon dioxide -393.509  NaBr(s) Sodium bromide -361.062
 C_2H_2(g) Acetylene (ethyne) 226.73  NaI(s) Sodium iodide -287.78
 C_2H_4(g) Ethylene (ethene) 52.26  NH_3(g) Ammonia -46.11
 C_2H_6(g) Ethane -84.68  NO(g) Nitrogen monoxide 90.25
 C_3H_8(g) Propane -103.8  NO_2(g) Nitrogen dioxide 33.18
 C_4H_{10}(g) Butane -126.148  O_3(g) Ozone 142.7
 C_6H_{12}O_6(s)  \alpha-D-Glucose -1274.4  PCl_3(\ell) Phosphorus trichloride -319.7
 CuSO_4(s) Copper(II) sulfate -771.36  PCl_5(s) Phosphorus pentachloride -443.5
 H_2O(g) Water vapor -241.818  SiO_2(s) Silicon dioxide (quartz) -910.94
 H_2O(\ell) Liquid water -285.830  SnCl_2(s) Tin(II) chloride -325.1
 HF(g) Hydrogen fluoride -271.1  SnCl_4(\ell) Tin(IV) chloride -511.3
 HCl(g) Hydrogen chloride -92.307  SO_2(g) Sulfur dioxide -296.83
 HBr(g) Hydrogen bromide -36.40  SO_3(g) Sulfur trioxide -395.72
*From Wagman, D. D., Evans, W. H., Parker, V. B., Schuman, R. H., Halow, I., Bailey, S. M., Churney, K. L., and Nuttall, R. The NBS Tables of Chemical Thermodynamic Properties. Journal of Physical and Chemical Reference Data, Vol. 11, Suppl. 2, 1982. (NBS, the National Bureau of Standards, is now NIST, the National Institute for Standards and Technology.)

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