Over what range of temperatures is each of the following processes spontaneous?

Question

Over what range of temperatures is each of the following processes spontaneous? Assume that all occur at a pressure of 1 atm. a. The rusting of iron, a complex reaction that can be approximated as: 4 Fe(s) + 3 O_2(g) rightarrow 2 Fe_2O_3(s). b. The preparation of SO_3(g) from SO_2(g), a step in the manufacture of sulfuric acid: SO_2(g) + 1/2O_2(g) rightarrow SO_3(g). c. The production of the anesthetic dinitrogen oxide through the decomposition of ammonium nitrate: NH_4NO_3(s) rightarrow N_2O(g) + 2H_2O(g).

Explanation / Answer

a)   4 Fe(s) + 3O2 (g) ----------> 2 Fe2O3 (s)

H

H = Hof of products - Hof of reactants

    = 2x Hof Fe2O3 (s) - [ 4 x  Hof Fe(s) + 3 Hof O2(g) ]

   = 2 x -824.2 - [ 4 x 0 + 3 x 0] kJ/mol

= - 1648.4 kJ/mol

= -1648400 J/mol

S = So (products) - So(reactants)

= 2xSo Fe2O3 (s) - [ 4 x  So Fe(s) + 3 SoO2(g) ]

   = 2 x 87.4 - [ 4 x 27.28 + 3 x 205.1 ] J/K/mol

= - 549.6 J/K/mol

  S   = - 549.6 J/K/mol

--------------------------------

H= -1648400 J/mol
S= - 549.6 J/K/mol

For any reaction to be spontaneous, G < 0

The relation between G, H, S is

G = H - TS

G < 0 ( condition for spontaneity)

H - TS < 0

H < TS

TS > H

T > H/S

T > ( -1648400 J/mol) / ( -549.6 J/K/mol )

T > 2999 K

To become spontaneous, temperature should be greater than 2999 K.

Therefore,

For temperatures above 2999 K, the given reaction will become spontaneous.

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