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Question 6.PS.14: Standard Molar Enthalpy of Formation from Enthalpy of Combus......

Standard Molar Enthalpy of Formation from Enthalpy of Combustion

Octane, C_8H_{18}, is a hydrocarbon that is present in gasoline. At 25 °C the enthalpy of combustion per mole for octane is – 5116.0 kJ/mol. Use data from Table 6.2 to calculate the standard molar enthalpy of formation of octane. (Assume that water vapor is produced by the combustion reaction.)

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ΔH_f^\circ =- 208.4  kJ

Strategy and Explanation Write a balanced equation for the target reaction whose ΔH° you want to calculate. Also write a balanced equation for combustion of octane, for which you know the standard enthalpy change. By studying these two equations, decide what additional information is needed to set up a Hess’s law calculation that will yield the standard molar enthalpy of formation of octane.

( target reaction)   8 C( s ) + 9 H_2(g) → C_8H_{18}(\ell)          ΔH_f^\circ = ??  kJ/mol

(a) C_8H_{18}(\ell) + \frac{25}{2} O_2(g) → 8 CO_2(g)  +  9 H_2O(g)     ΔH_{combustion}^\circ = – 5116.0  kJ

Notice that the combustion equation involves 1 mol C_8H_{18}(\ell) as a reactant and the target equation (for enthalpy of formation) involves 1 mol C_8H_{18}(\ell) as a product. Therefore, it seems reasonable to reverse the combustion equation and see where that leads.

(a’) 8 CO_2(g) + 9 H_2O(g) → C_8H_{18}(\ell)  +  \frac{25}{2} O_2(g)    ΔH° = + 5116.0  kJ

On the reactant side of the target equation we have 8 C(s) and 9 H_2(g). These elements, combined with O_2(g), are on the left side of equation (a’), so perhaps it would be reasonable to use the equations corresponding to standard molar enthalpies of formation of carbon dioxide and water. From Table 6.2, we have

(b)  C( s ) + O_2(g) → CO_2(g)            ΔH_f^\circ = – 393.509  kJ/mol

(c)  H_2(g) + \frac{1}{2} O_2(g) → H_2O(g)            ΔH_f^\circ = + 241.818 kJ/mol

Multiplying equation (b) by 8 and equation (c) by 9 gives the correct number of moles of C(s) and of H_2(g) on the reactant side of the target equation. This gives

(a’) 8 CO_2(g) + 9 H_2O(g) → C_8H_{18}(\ell)  +  \frac{25}{2} O_2(g)       ΔH° = + 5116.0  kJ

(b’) 8 C( s ) + 8  O_2(g) → 8  CO_2(g)                         ΔH° = – 3148.072  kJ

(c’) \underline{9 H_2(g) + \frac{9}{2}  O_2(g) → 9 H_2O(g)                                        ΔH° =- 2176.362  kJ/mol}

 8 C( s ) + 9 H_2(g) → C_8H_{18}(\ell)        ΔH_f^\circ = ΔH_{a'}^\circ + ΔH_{b'}^\circ + ΔH_{c'}^\circ = – 208.4  kJ/mol

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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