From the reaction below, calculate the free energy of formation for CH4(g) at 25°C, if ΔGfo(C8H8(g)) is 214.417 kJ/mol.
8CH4(g) ↔ C8H8(g) + 12H2(g) ΔGo = 620.735 kJ/mol
I don't understand what equation to use. I thought it was dGfo-dGo but that doesn't give the right answer.
I believe you forgot the coefficients (e.g. 8).
8CH4 ==> C8H8+ 12H2
dGfrxn = (n*dGfC8H8 + n*dGfH2)-(n*dGfCH4)
620.735 = [(1*214.417) + (12*0)] - (8*dGfCH4)
620.735 = 214.417 + 0 - 8x
Solve for x.
To calculate the free energy of formation (ΔGfo) for CH4(g) at 25°C using the given reaction and data, you need to apply the concept of Hess's law. It allows you to calculate the overall free energy change (ΔGo) of a reaction in terms of the free energy changes of individual reactions.
Hess's law states that if a reaction can be expressed as a sum of two or more reactions, then the change in enthalpy (ΔH) or free energy (ΔG) for the overall reaction is equal to the sum of the changes for the individual reactions.
In this case, you have the following reaction:
8CH4(g) ↔ C8H8(g) + 12H2(g)
The ΔGo for this reaction is given as 620.735 kJ/mol. However, you also need to know the ΔGfo for C8H8(g), which is given as 214.417 kJ/mol.
Now, you can break down the overall reaction into its constituent reactions:
C8H8(g) + 12H2(g) ↔ 8CH4(g)
Notice that this reaction is the reverse of the given reaction. Therefore, the ΔGo for this reaction is equal in magnitude but opposite in sign, so it is (-620.735 kJ/mol).
Now, using the concept of Hess's law, you can calculate the ΔGo for the formation of CH4(g) using the given ΔGfo for C8H8(g) and the ΔGo for the reverse reaction:
ΔGo = Σ ΔGfo(products) - Σ ΔGfo(reactants)
Since you have only one product (CH4(g)) and one reactant (C8H8(g) + 12H2(g)), the equation becomes:
ΔGo = ΔGfo(CH4(g)) - [ΔGfo(C8H8(g)) + 12ΔGfo(H2(g))]
Substituting the given values:
620.735 kJ/mol = ΔGfo(CH4(g)) - [214.417 kJ/mol + 12×ΔGfo(H2(g))]
Now, you need the ΔGfo value for H2(g) at 25°C to proceed with the calculation. If you have that value, you can substitute it into the equation and solve for ΔGfo(CH4(g)).
Please note that the ΔGfo values are typically given in tables or can be calculated using thermodynamic data for individual species at standard conditions (25°C and 1 atm pressure).