Assume that the complete combustion of one mole of ethanol to carbon dioxide and water liberates 1370 kJ/mol (?G°\' = –1370 kJ/mol). If the energy generated by the combustion of ethanol is entirely converted to the synthesis of a hypothetical compound X, calculate the number of moles of the compound that could theoretically be generated. Use the value ?G°\'compound X = –71.3 kJ/mol.
You must know how many mols ethanol. Assuming 1 mol ethanol, then
713 kJ/molX x # mols X = 1370 kJ
m, kjb k,
To calculate the number of moles of compound X that could theoretically be generated, we need to use the concept of Gibbs free energy (ΔG°).
The ΔG° for the combustion of ethanol, which is -1370 kJ/mol, tells us the amount of energy released during the reaction. We can assume that this energy is used to synthesize the compound X.
The ΔG° for the synthesis of compound X is -71.3 kJ/mol, which tells us the energy required for the synthesis reaction.
The net change in Gibbs free energy (ΔG°) for the entire process can be calculated by subtracting the energy required for the synthesis of compound X from the energy released during the combustion of ethanol.
ΔG°net = ΔG°combustion + ΔG°synthesis
= -1370 kJ/mol + (-71.3 kJ/mol)
= -1441.3 kJ/mol
We have the value of ΔG° as -1441.3 kJ/mol.
Now, one mole of compound X can be formed when the net change in Gibbs free energy is equal to -RT ln(K), where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and K is the equilibrium constant.
To convert -1441.3 kJ to J:
ΔG°net in J/mol = -1441.3 kJ/mol × 1000 J/kJ = -1441300 J/mol
We can plug in the values for ΔG°net and R to calculate the equilibrium constant K:
-1441300 J/mol = -8.314 J/(mol·K) × T × ln(K)
To simplify the equation, we can divide both sides by -8.314 J/(mol·K):
174035.87 mol·K = T × ln(K)
Now, we need to know the temperature (T) to solve for the equilibrium constant K. If you have the temperature information, substitute the value to calculate K.