Free Energy and Chemical Reactions

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    In this section we will show you how to calculate standard free energy.  Standard free energy
(wpe5.jpg (740 bytes)G) is the change in free energy that will occur if the reactants in their standadrd states are converted to the products in their standard states.  For example, the reaction

                C(s) + O2(g) --> CO2(g)

wpe3.gif (856 bytes)H = -393.5 kJ, wpe5.jpg (740 bytes)S = 3.05 J/K, and the temperature is at 298 K.

                                wpe5.jpg (740 bytes)G = wpe5.jpg (740 bytes)H - wpe5.jpg (740 bytes)TS
                               = -3.935 * 105 J - (298 K)(3.05 J/K)
                               = -3.944 * 105 J
                               = -394.4 kJ (per mole of CO
2)

It is very important to convert everything to joules first.  The answer will not be correct if wpeC.jpg (740 bytes)S is in kilojoules and wpe5.jpg (740 bytes)H is in joules.
        A second way of calculating wpe5.jpg (740 bytes)G is similar to calculating the wpe5.jpg (740 bytes)H by using Hess' law.  For example, using this method to find the wpe5.jpg (740 bytes)G of

                    2CO(g) + O2(g) --> 2CO2(g)

We are given

                    2CH4(g) + 3O2(g) --> 2CO(g) + 4H2O(g)             wpe5.jpg (740 bytes)G = -1088 kJ
                      CH4(g) + 2O2(g) --> CO2(g) + 2H2O(g)              wpe5.jpg (740 bytes)G = -801 kJ

The first equation needs to be reversed and the second equation needs to be multiplied by two.

                    2CO(g) + 4H2O(g) --> 2CH4(g) + 3O2(g)             wpe5.jpg (740 bytes)G = -(-1088 kJ)
                     2CH4(g) + 4O2(g) --> 2CO2(g) + 4H2O(g)          wpe5.jpg (740 bytes)G = 2(-801 kJ) 
                                                                                                                              
                            2CO(g) + O2 --> 2CO2(g)                             wpe5.jpg (740 bytes)G = -514 kJ

 

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