For the reaction:
2 NO(g) + 1 O2(g) <--> 2 NO2(g)
Calculate K, the equilibrium constant, from thermodynamic data at 281 K.
(Hint #1: Assume that S and H do not change with temperature.)
(Hint #2: Work in J/mol)
I would determine DGo from
DGo rxn = (n*DGo products) - (n*DGo reactants)
Then since DG = 0 at equilibrium,
DGo = -RT*lnK
To calculate the equilibrium constant (K) from thermodynamic data at a given temperature, we need to use the equation:
ΔG° = -RTln(K)
where ΔG° is the standard Gibbs free energy change, R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and ln is the natural logarithm.
Hint #1 suggests assuming that entropy (S) and enthalpy (H) do not change with temperature. This simplifies the calculation because we can use standard thermodynamic data.
Hint #2 suggests working in J/mol. This is the common unit for thermodynamic calculations.
Given that we are working at 281 K, we need to find the standard thermodynamic data (ΔG°) for the reaction. The ΔG° can be determined using the following equation:
ΔG° = ΔH° - TΔS°
where ΔH° is the standard enthalpy change and ΔS° is the standard entropy change.
The standard enthalpy change (ΔH°) and standard entropy change (ΔS°) can be found in standard thermodynamic tables or databases for the given reaction. However, we'll need this data to proceed further with the calculation.
Once you have these values, you can substitute them into the equation ΔG° = ΔH° - TΔS°, calculate ΔG°, and then use the equation ΔG° = -RTln(K) to solve for K.