Question

a) Calculate ΔG for the process below, the combustion of methane. Standard free energies of formation, △G°, in kJ/mol, are given below each reactant and product in the process shown below.
CH4(g) + O2(g) → CO2(g) + H2O(g) (not balanced!)

– 50.8 – 394.4 – 228.6
b) Coal gasification can be represented by the balanced equation:
2 C(s) + 2 H2O(g) → CH4(g) + CO2(g)
Using the free energies from part a), calculate ΔG for this reaction.
c) Write the equation that shows the overall process for gasification of coal, and burning the methane produced. What is the net energy to be obtainedby this process?
d) What is the net energy to be obtained by direct combustion of 2 moles of carbon? Use △G° values for the products from part a).
e) Compare your results from parts c) and d). In the light of your results, comment on the thermodynamic efficiency of goal gasification, and why (or not) the process may be economically or environmentally advantageous.

Answer 1

a)

dG = Gpoducts - Greactants

balance equation

CH4 + O2 = CO2 + H2O

balance C, H and finally O

CH4 + 2O2 = CO2 + 2H2O

this is now balanced, get dG

dG = G-CO2 + 2*G-H2O - (G-CH4 + 2G-O2)

dG = (-384.4 + 2*-228.6) - (-50.8 + 0)

dG = -790.8 kJ/mol

b)

2 C(s) + 2 H2O(g) → CH4(g) + CO2(g)

this is now balanced

dG =G products - G reactants

dG = -50.8 + -394.4 - (2*0 + 2*(-228.6))

dG = 12 kJ/mol

c)

Overall process:

CH4(g) + 2O2(g) = CO2(g) + 2H2O(g)

2C(s) + 2H2O(g) → CH4(g) + CO2(g)

add all

CH4(g) + 2O2(g) + 2C(s) + 2H2O(g) → CH4(g) + CO2(g)+CO2(g) + 2H2O(g)

cancel common terms

2O2(g) + 2C(s) → CO2(g)+CO2(g)

2O2(g) + 2C(s) = 2CO2(g)

or per unit mol:

O2(g) + C(s) = CO2(g)

d)

Apply Hess Law, we can addd simultaneous equation such as:

dG total = dG1 + dG2 = (  -790.8 kJ/mol) + (12 kJ/mol) = - 778.8 kJ/mol

e)

Overall process seems to be possible

for

2C(s) + 2H2O(g) → CH4(g) + CO2(g)

this seems to be impossible to do in spontaneous process, therefore, this will not be efficient enough

The environment advantages/disadvantages

- C(s) is converted to CO2(g), which pollutes the environment

This is convenient for energy geneartion, specially from fuel (coal) mines