Write an equation for the combustion of one mole of benzene, C6H6(l), and use data from Appendix D to determine delta G degrees (which is 124.5) at 298K if the products of the combustion are (a) CO2(g) and H2O(l), and (b)CO2(g) and H2O(g). Describe how you might determine the difference between the values obtained in (a) and (b) without having either to write the combustion equation or to determine delta G degrees values for the combustion reactions.
To write the equation for the combustion of one mole of benzene (C6H6) and determine the delta G degrees at 298K, we first need to know the balanced chemical equation for the combustion reaction.
The combustion of benzene can be represented by the equation:
C6H6(l) + 15/2 O2(g) → 6 CO2(g) + 3 H2O(l) (a)
To determine the value of delta G degrees for this reaction, we can use the standard free energy of formation (delta Gf degrees) values for each reactant and product from Appendix D.
The standard free energy change can be calculated using the formula:
delta G degrees = Σn delta Gf degrees (products) - Σn delta Gf degrees (reactants)
where n represents the stoichiometric coefficients in the balanced equation.
For equation (a):
delta G degrees = (6 * delta Gf degrees (CO2(g))) + (3 * delta Gf degrees (H2O(l))) - (delta Gf degrees (C6H6(l))) - (15/2 * delta Gf degrees (O2(g)))
Given that delta G degrees = 124.5 kJ/mol, we can look up the standard free energy of formation values for each of the compounds involved in the reaction in Appendix D and substitute them into the equation. Note that delta Gf degrees (O2(g)) is zero since it is the reference and not listed in the table.
To determine the difference between the values obtained in (a) and (b) without explicitly calculating the values or writing the combustion equations, we can use the concept of Hess's Law.
Hess's Law states that the standard enthalpy and entropy change for a reaction are independent of the pathway and depend only on the initial and final states. Since delta G degrees is related to delta H degrees and delta S degrees through the equation delta G degrees = delta H degrees - T delta S degrees, it follows that the difference between the delta G degrees values in (a) and (b) can be determined by examining the differences in delta H degrees and delta S degrees between the two reactions.
By comparing the given data, it can be observed that the only difference in the products between (a) and (b) is the phase change of H2O from liquid to gas. This phase change will affect the value of delta H degrees but not delta S degrees, as the number and type of molecules remain the same.
Thus, the difference between the values obtained in (a) and (b) can be attributed solely to the difference in the enthalpy change (delta H degrees) due to the phase change of H2O from liquid to gas.
Therefore, to determine the difference between the values obtained in (a) and (b), one does not need to explicitly calculate delta G degrees values or write the combustion equations. Instead, the difference can be inferred by comparing the changes in delta H degrees caused by the phase change of H2O.