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 (ΔGf) for C4H10 (g), we need to use the standard free energy change (ΔG) for the reaction and the standard free energy of formation values for the other substances involved in the reaction.
First, we can write the balanced equation for the reaction:
2 C4H10 (g) + 13 O2 (g) --> 8 CO2 (g) + 10 H2O (l)
In this reaction, we have 2 moles of C4H10 (g) on the reactant side.
The standard free energy change (ΔG) for the reaction is given as -5490 kJ. Note that the standard free energy change for a reaction is equal to the sum of the free energy of formation of the products minus the sum of the free energy of formation of the reactants:
ΔG = Σ[nΔGf(products)] - Σ[nΔGf(reactants)]
ΔG = [8ΔGf(CO2)] + [10ΔGf(H2O)] - [2ΔGf(C4H10)] - [13ΔGf(O2)]
We want to solve for ΔGf(C4H10), so let's rearrange the equation:
ΔGf(C4H10) = ([8ΔGf(CO2)] + [10ΔGf(H2O)]) - ΔG + [13ΔGf(O2)]
Now we need the standard free energy of formation values for CO2, H2O, and O2.
The standard free energy of formation values at 298 K (25°C) can be found from reference materials or databases. Let's assume the following:
ΔGf(CO2) = -394 kJ/mol
ΔGf(H2O) = -286 kJ/mol
ΔGf(O2) = 0 kJ/mol (since elemental oxygen is in its standard state)
Now we can plug in the values:
ΔGf(C4H10) = ([8(-394 kJ/mol)] + [10(-286 kJ/mol)]) - (-5490 kJ) + [13(0 kJ/mol)]
Simplifying the equation:
ΔGf(C4H10) = (-3152 kJ) + (-2860 kJ) + 5490 kJ
ΔGf(C4H10) = -522 kJ/mol
Therefore, the standard free energy of formation for C4H10 (g) is -522 kJ/mol.
To calculate the standard free energy of formation for C4H10 (g), we can use the equation:
ΔG°f = ΣnΔG°f(products) - ΣmΔG°f(reactants)
Where:
- ΔG°f is the standard free energy of formation.
- Σn is the coefficient of the species in the products.
- Σm is the coefficient of the species in the reactants.
- ΔG°f(products) is the standard free energy of formation for each product.
- ΔG°f(reactants) is the standard free energy of formation for each reactant.
First, let's look up the standard free energy of formation for each species involved in the reaction:
- ΔG°f(CO2) = -394 kJ/mol
- ΔG°f(H2O) = -288 kJ/mol
- ΔG°f(O2) = 0 kJ/mol
Using these values, we can calculate the standard free energy change for the reaction:
ΔG° = ΣnΔG°f(products) - ΣmΔG°f(reactants)
= [8(-394 kJ/mol) + 10(-288 kJ/mol)] - [2(0 kJ/mol) + 13(0 kJ/mol)]
= -3152 kJ/mol
Now, we can use the given value of ΔG° (-5490 kJ) to calculate the standard free energy of formation for C4H10 (g):
ΔG°f(C4H10) = ΔG° - [2ΔG°f(CO2) + 10ΔG°f(H2O) - 2ΔG°f(O2)]
= -5490 kJ - [2(-394 kJ/mol) + 10(-288 kJ/mol) - 2(0 kJ/mol)]
= -5490 kJ - [-788 kJ/mol - 2880 kJ/mol]
= -5490 kJ + 3668 kJ/mol
= -1822 kJ/mol
Therefore, the standard free energy of formation for C4H10 (g) is -1822 kJ/mol.