Spontaneity of the Reaction of Nitrogen and Oxygen to form Nitrogen Monoxide
Introduction
Nitrogen reacts with oxygen as follows.
N2 (g) + O2 (g) → 2 NO (g)
This application will calculate the temperature at which this reaction becomes spontaneous.
Using the ThermophysicalData:-Chemicals package, the application first defines a temperature-dependent function that describes the Gibbs Energy of the reaction
This function is then numerically solved for the temperature at which the Gibbs Energy is zero. The reaction is spontaneous at or above this temperature.
Physical Properties
with(ThermophysicalData:-Chemicals):
Enthalpies
h_NO := Property("Hmolar", "NO(g)", "temperature" = T): h_N2 := Property("Hmolar", "N2(g)", "temperature" = T): h_O2 := Property("Hmolar", "O2(g)", "temperature" = T):
Entropies
s_NO := Property("Smolar", "NO(g)", temperature = T): s_N2 := Property("Smolar", "N2(g)", temperature = T): s_O2 := Property("Smolar", "O2(g)", temperature = T):
Gibbs Energy of Reaction
Gibbs := proc(temp) local DeltaS, DeltaH, DeltaG: uses Units:-Simple: # Change in entropy DeltaS := 2 * s_NO - (s_N2 + s_O2): # Change in enthalpy DeltaH := 2 * h_NO - (h_N2 + h_O2): # Gibbs free energy DeltaG := 0.5 * eval(DeltaH - temp * DeltaS, T = temp): return DeltaG: end proc:
At 298 K, the Gibbs Energy per mole of NO is
Gibbs(298 * Unit(K))
87.59kJmol
The reaction is spontaneous when the Gibbs Energy is zero or negative. Hence the reaction is spontaneous at a temperature of
fsolve(Gibbs(T) = 0, T = 300 * Unit(K))
7571.23K
plot(Gibbs, 298 * Unit(K) .. 10000 * Unit(K), numpoints = 5, title = "Gibbs Energy of the Reaction of Nitrogen and Oxygen to Form Nitrogen Monoxide", labels = ["Temperature (K)", "Gibbs Free Energy (J/mol/K)"], labeldirections = [horizontal, vertical], size = [800,400])
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