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Spontaneity of the Reaction of Nitrogen and Oxygen to form Nitrogen Monoxide
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Introduction
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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 empirical data in the ThermophysicalData:-Chemicals package, the application first defines a function that describes the Gibbs Energy of the reaction at an arbitrary temperature.
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.
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Physical Properties
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with(ThermophysicalData:-Chemicals):
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Enthalpies
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h_NO := Property("Hmolar", "NO", "temperature" = T):
h_N2 := Property("Hmolar", "N2", "temperature" = T):
h_O2 := Property("Hmolar", "O2", "temperature" = T):
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Entropies
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s_NO := Property("Smolar", "NO", temperature = T):
s_N2 := Property("Smolar", "N2", temperature = T):
s_O2 := Property("Smolar", "O2", temperature = T):
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Gibbs Energy of Reaction
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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:
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At 298 K, the Gibbs Energy per mole of NO is
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(3.1) |
The reaction is spontaneous when the Gibbs Energy is zero or negative. Hence the reaction is spontaneous at a temperature of
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fsolve(Gibbs(T) = 0, T = 300 * Unit(K))
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(3.2) |
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plot(Gibbs, 298 * Unit(K) .. 10000 * Unit(K), numpoints = 5, title = "Gibbs Free 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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