## Q. 6.PS.14

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.)

## Verified Solution

$ΔH_f^\circ =- 208.4 kJ$

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.)