# 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.

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
$ΔH° = – 3267.5 kJ$

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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