Spontaneity of the Reaction of Nitrogen and Oxygen to form Nitrogen Monoxide - Maple Programming Help

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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))

87.58553545kJmol

(3.1)

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))

7571.230267K

(3.2)

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])