Question

4. Classify each of the following reactions as one of these four types: • spontaneous at all temperatures • not spontaneous at any temperature • spontaneous below a certain temperature but not above • spontaneous above a certain temperature but not below See Table 17.1 in Tro, Fridgen and Shaw. (a) CaH2 () + 2 H2O (1) + Ca(OH)2 (s) + 2 H2(g); AH = -230 kJ; (b) 2 NO(g) + Cl, (g) → 2 NOCI (g); AH= -78.4 kJ; (c) CH. (g) → C H2(g) + 2 H2 (g); AH=311.4 kJ; (d) AgCl (s) +2 H2O (g) + CO (g) → AgCIO, (s) + CH, (g); J/K AS= 163 J/K AS=-121.0 J/K AS-232.7 J/K AH=616 kJ; AS=-343

Answer 1

If a reaction to be spontaneous the change in Gibbs free energy must be negative(∆G < 0 ).

We can determine ∆G by using a relation, ΔG​=ΔH​−TΔS​, where ΔH is change in enthalpy, ΔS is change in entropy and T is temperature in Kelvin.

In all reaction ΔS is in J/K so we have to convert into kJ/K by dividing it by 1000 as ΔH is in kJ.

• For reaction (a) :- ΔG​=ΔH​−TΔS = -230 - (0.163)T as T is always greater than 0, ΔG of this reaction will always be less than zero. Therefore reaction(a) is spontaneous at all temperature.
• For reaction (b) :- ΔG​=ΔH​−TΔS = -78.4 -(-0.121)T = -78.4 + (0.121)T , for ΔG to be negative, -78.4+0.121T<0 ⇒ T<(78.4/0.121) ⇒ T < 647.93K. Therefore reaction(b) is spontaneous below a certain temperature not above.
• For reaction (c) :- ΔG​=ΔH​−TΔS = 311.4 -(0.2327)T, for ΔG to be negative, 311.4 -(0.2327)T<0 ⇒ T>(311.4/0.2327) ⇒ T > 1338.2K. Therefore reaction(c) is spontaneous above a certain temperature not below.
• For reaction (d) :- ΔG​=ΔH​−TΔS = 616 - (-0.343)T= 616+0.343T as T is always greater than 0, ΔG of this reaction will always be greater than zero. Therefore reaction(d) is not spontaneous at any temperature.

Note - We cannot obtain temperature which less than 0 Kelvin, that's why T is always greater than 0.