## Thermodynamics

38) (a) N2H4(g) + H2(g) 2NH3(g)

ΔS° = ΣΔS°(products) - ΣΔS°(reactants)

ΔS° = [2S°(NH3(g))] - [S°(N2H4(g)) + S°(H2(g))]

ΔS° = [2 mol NH3(g) x 192.5 J/1 mol NH3(g)•K] - [1 mol N2H4(g) x 238.5 J/1 mol N2H4(g)•K + 1 mol H2(g) x 130.58 J/1 mol H2(g)•K]

ΔS° = 15.9 J/K

The value of ΔS° is relatively small because there are 2 moles of reactant gases and 2 moles of product gases. The slight increase results from H2(g) having fewer degrees of freedom than more complicated structures.

(b) Al(s) + 3Cl2(g) 2AlCl3(s)

ΔS° = ΣΔS°(products) - ΣΔS°(reactants)

ΔS° = [2S°(AlCl3(s))] - [S°(Al(s)) + 3S°(Cl2(g))]

ΔS° = [2 mol AlCl3(s) x 109.3 J/1 mol AlCl3(s)•K] - [1 mol Al(s) x 28.32 J/1 mol Al(s)•K + 3 mol Cl2(g) x 222.96 J/1 mol Cl2(g)•K]

ΔS° = -478.6 J/K

The value of ΔS° is negative because there 3 moles of reactant gases and 0 moles of product gas.

(c) Mg(OH)2(s) + 2HCl(g) MgCl2(s) + 2H2O(l)

ΔS° = ΣΔS°(products) - ΣΔS°(reactants)

ΔS° = [S°(MgCl2(s)) + 2S°(H2O(l))] - [S°(Mg(OH)2(s)) + 2S°(HCl(g))]

ΔS° = [1 mol MgCl2(s) x 89.6 J/1 mol MgCl2(s)•K + 2 mol H2O(l) x 69.91 J/1 mol H2O(l)] - [1 Mg(OH)2(s) x 63.24 J/1 Mg(OH)2(s)•K + 2 mol HCl(g) x 186.69 J/1 mol HCl(g)•K]

ΔS° = -207.2 J/K

The value of ΔS° is negative because there 2 moles of reactant gases and 0 moles of product gas.

(d) 2CH4(g) C2H6(g) + H2(g)

ΔS° = ΣΔS°(products) - ΣΔS°(reactants)

ΔS° = [S°(C2H6(g)) + S°(H2(g))] - [2S°(CH4(g))]

ΔS° = [1 mol C2H6(g) x 229.5 J/1 mol C2H6(g)•K + 1 mol H2(g) x 130.58 J/1 mol H2(g)] - [2 mol CH4(g) x 186.3 J/1 mol CH4(g)•K]

ΔS° = -12.5 J/K

The value of ΔS° is relatively small because there are 2 moles of reactant gases and 2 moles of product gases. The slight decrease results from H2(g) having fewer degrees of freedom than more complicated structures.