Final answer:
Using the standard Gibbs free energy equation and the given equilibrium constant, the calculation indicates the formation of ammonia is exergonic. The calculated value does not match the provided answers, suggesting potential issues with unit conversions or logarithm calculations.
Step-by-step explanation:
To calculate the standard Gibbs free energy (AGo) associated with the formation of ammonia (NH3), the standard free energy change formula AGo = -RT ln K can be used, where R is the ideal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and K is the equilibrium constant.
Given that the equilibrium constant K for the reaction is 0.2 and R is generally considered as 8.314 J/(mol·K), and presuming the standard temperature of 298 K is applied to reflect standard conditions (25 °C), the calculation would be:
AGo = -8.314 J/(mol·K) * 298 K * ln(0.2)
First, we calculate the natural logarithm of the Keq value:
ln(0.2) = -1.6094
Then, multiply by -8.314 and 298:
AGo = -8.314 * 298 * (-1.6094) = 4002.77 J/mol = 4.00277 kJ/mol
The exact value provided in the question isn't clearly matched; the student should ensure they have calculated the natural logarithm correctly and converted all units properly. The calculated value for AGo with respect to the formation of ammonia indicates that the reaction is exergonic, as a negative value of AGo signifies that the process is spontaneous under standard conditions.