The value of ^G for the following reaction is -5490 kJ. Use this value and data to calculate the standard free energy of formation for C4H10 (g).
2 C4H10 (g) + 13 O2 (g) --> 8 CO2 (g) + 10 H2o (l)
To calculate the standard free energy of formation (∆G°f) for C4H10 (g), we need to use the equation:
∆G° = Σn∆G°f(products) - Σn∆G°f(reactants)
Where ∆G° is the standard free energy change of the reaction, ∆G°f(products) is the standard free energy of formation of the products, ∆G°f(reactants) is the standard free energy of formation of the reactants, and n represents the stoichiometric coefficients of each substance.
First, we need to determine the standard free energy change (∆G°) for the given reaction using the value of ∆G° provided:
∆G° = -5490 kJ
Now, we need to determine the standard free energy of formation for each compound involved in the reaction. We can refer to a table or database that provides standard free energy of formation values (∆G°f) for various compounds at standard conditions.
Let's calculate the ∆G°f for each substance:
∆G°f(CO2) = -394 kJ/mol (from table)
∆G°f(H2O) = -286 kJ/mol (from table)
Now, we need to calculate the ∆G°f for C4H10. As C4H10 (butane) is not available in the table, we can use the ∆G°f values of its constituent elements and apply the following formula:
∆G°f(C4H10) = Σn∆G°f(elements)
In this case, C4H10 consists of carbon (C) and hydrogen (H) atoms.
∆G°f(C) = 0 kJ/mol (for carbon)
∆G°f(H2) = 0 kJ/mol (for hydrogen gas)
Since C4H10 contains four carbon atoms and ten hydrogen atoms, we multiply the respective ∆G°f values by their stoichiometric coefficients:
∆G°f(C4H10) = (4 * ∆G°f(C)) + (10 * ∆G°f(H2))
Now we can substitute the known values into the equation to calculate the ∆G°f for C4H10:
∆G°f(C4H10) = (4 * 0 kJ/mol) + (10 * 0 kJ/mol)
∆G°f(C4H10) = 0 kJ/mol
Therefore, the standard free energy of formation (∆G°f) for C4H10 (g) is 0 kJ/mol.