Based on the standard free energies of formation, which of the following reactions represent a feasible way to synthesize the product?
a. n2(g)+h2(g)→n2h4(g); δg∘f=159.3 kj/mol
b. 2na(s)+o2(g)→na2o2(s); δg∘f=−447.7kj/mol
c. c(s)+2s(s)→cs2(g); δg∘f=67.1 kj/mol
d. ca(s)+12o2(g)→cao(s); δg∘f=−604.0 kj/mol

Explanation:

According the equation of Gibb's free energy -

∆G = ∆H -T∆S

∆G = is the change in gibb's free energy

∆H = is the change in enthalpy

T = temperature

∆S = is the change in entropy .

And , the sign of the  ΔG , determines whether the reaction is Spontaneous or non Spontaneous or at equilibrium ,

i.e. ,

if

•ΔG < 0 , the reaction is Spontaneous

•ΔG > 0 , the reaction is non Spontaneous

•ΔG = 0 , the reaction is at equilibrium

a.

N₂(g) + H₂(g)  → N₂H₄ (g)   ; ΔG⁰f = 159.3 kJ/mol

ΔG > 0 , the reaction is non Spontaneous  , the reaction is not feasible in the forward direction

b.

2Na(s) + O₂(g) → Na₂O₂ (s)   ; ΔG⁰ f = − 447.7kJ/mol

ΔG < 0 , the reaction is Spontaneous  , the reaction is feasible in the forward direction .

c.

C(s) + 2S(s)  →  CS₂ (g)   ; ΔG⁰f = 67.1 kJ/mol

ΔG > 0 , the reaction is non Spontaneous  , the reaction is not feasible in the forward direction

d.

Ca(s) + 12 O₂ (g) → CaO (s) ;  ΔG⁰f = −604.0 kJ/mol

ΔG < 0 , the reaction is Spontaneous  , the reaction is feasible in the forward direction .