5.8 Free energy  (Page 7/12)

Among other things, an ideal fuel for the control thrusters of a space vehicle should decompose in a spontaneous exothermic reaction when exposed to the appropriate catalyst. Evaluate the following substances under standard state conditions as suitable candidates for fuels.

(a) Ammonia: ${\text{2NH}}_3(g)⟶{\text{N}}_2(g)+{\text{3H}}_2(g)$

(b) Diborane: ${\text{B}}_2{\text{H}}_6(g)⟶\text{2B}(g)+{\text{3H}}_2(g)$

(c) Hydrazine: ${\text{N}}_2{\text{H}}_4(g)⟶{\text{N}}_2(g)+{\text{2H}}_2(g)$

(d) Hydrogen peroxide: ${\text{H}}_2{\text{O}}_2(l)⟶{\text{H}}_2\text{O}(g)+\frac{1}{2}{\text{O}}_2(g)$

Calculate Δ G ° for each of the following reactions from the equilibrium constant at the temperature given.

(a) ${\text{N}}_2(g)+{\text{O}}_2(g)⟶\text{2NO}(g)\text{T}=2000\text{°C}{K}_p=4.1\times {10}^{\text{−4}}$

(b) ${\text{H}}_2(g)+{\text{I}}_2(g)⟶\text{2HI}(g)\text{T}=400\text{°C}{K}_p=50.0$

(c) ${\text{CO}}_2(g)+{\text{H}}_2(g)⟶\text{CO}(g)+{\text{H}}_2\text{O}(g)\text{T}=980\text{°C}{K}_p=1.67$

(d) ${\text{CaCO}}_3(s)⟶\text{CaO}(s)+{\text{CO}}_2(g)\text{T}=900\text{°C}{K}_p=1.04$

(e) $\text{HF}(aq)+{\text{H}}_2\text{O}(l)⟶{\text{H}}_3{\text{O}}^{\text{+}}(aq)+{\text{F}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_p=7.2\times {10}^{\text{−4}}$

(f) $\text{AgBr}(s)⟶{\text{Ag}}^{\text{+}}(aq)+{\text{Br}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_p=3.3\times {10}^{\text{−13}}$

Calculate Δ G ° for each of the following reactions from the equilibrium constant at the temperature given.

(a) ${\text{Cl}}_2(g)+{\text{Br}}_2(g)⟶\text{2BrCl}(g)\text{T}=25\text{°C}{K}_p=4.7\times {10}^{\text{−2}}$

(b) ${\text{2SO}}_2(g)+{\text{O}}_2(g)\rightleftharpoons {\text{2SO}}_3(g)\text{T}=500\text{°C}{K}_p=48.2$

(c) ${\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)\text{T}=60\text{°C}{K}_p=\text{0.196 atm}$

(d) $\text{CoO}(s)+\text{CO}(g)\rightleftharpoons \text{Co}(s)+{\text{CO}}_2(g)\text{T}=550\text{°C}{K}_p=4.90\times {10}^2$

(e) ${\text{CH}}_3{\text{NH}}_2(aq)+{\text{H}}_2\text{O}(l)⟶{\text{CH}}_3{\text{NH}}_3{}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_p=4.4\times {10}^{\text{−4}}$

(f) ${\text{PbI}}_2(s)⟶{\text{Pb}}^{\mathrm{2+}}(aq)+{\text{2I}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_p=8.7\times {10}^{\text{−9}}$

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of Δ G ° given.

(a) ${\text{O}}_2(g)+{\text{2F}}_2(g)⟶{\text{2OF}}_2(g)\text{Δ}G\text{°}=\text{−9.2 kJ}$

(b) ${\text{I}}_2(s)+{\text{Br}}_2(l)⟶\text{2IBr}(g)\text{Δ}G\text{°}=\text{7.3 kJ}$

(c) $\text{2LiOH}(s)+{\text{CO}}_2(g)⟶{\text{Li}}_2{\text{CO}}_3(s)+{\text{H}}_2\text{O}(g)\text{Δ}G\text{°}=\text{−79 kJ}$

(d) ${\text{N}}_2{\text{O}}_3(g)⟶\text{NO}(g)+{\text{NO}}_2(g)\text{Δ}G\text{°}=\text{−1.6 kJ}$

(e) ${\text{SnCl}}_4(l)⟶{\text{SnCl}}_4(l)\text{Δ}G\text{°}=\text{8.0 kJ}$

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of Δ G ° given.

(a) ${\text{I}}_2(s)+{\text{Cl}}_2(g)⟶\text{2ICl}(g)\text{Δ}G\text{°}=\text{−10.88 kJ}$

(b) ${\text{H}}_2(g)+{\text{I}}_2(s)⟶\text{2HI}(g)\text{Δ}G\text{°}=\text{3.4 kJ}$

(c) ${\text{CS}}_2(g)+{\text{3Cl}}_2(g)⟶{\text{CCl}}_4(g)+{\text{S}}_2{\text{Cl}}_2(g)\text{Δ}G\text{°}=\text{−39 kJ}$

(d) ${\text{2SO}}_2(g)+{\text{O}}_2(g)⟶{\text{2SO}}_3(g)\text{Δ}G\text{°}=\text{−141.82 kJ}$

(e) ${\text{CS}}_2(g)⟶{\text{CS}}_2(l)\text{Δ}G\text{°}=\text{−1.88 kJ}$

Calculate the equilibrium constant at the temperature given.

(a) ${\text{O}}_2(g)+{\text{2F}}_2(g)⟶{\text{2F}}_2\text{O}(g)(\text{T}=100\text{°C})$

(b) ${\text{I}}_2(s)+{\text{Br}}_2(l)⟶\text{2IBr}(g)(\text{T}=0.0\text{°C})$

(c) $\text{2LiOH}(s)+{\text{CO}}_2(g)⟶{\text{Li}}_2{\text{CO}}_3(s)+{\text{H}}_2\text{O}(g)(\text{T}=575\text{°C})$

(d) ${\text{N}}_2{\text{O}}_3(g)⟶\text{NO}(g)+{\text{NO}}_2(g)(\text{T}=\mathrm{-10.0}\text{°C})$

(e) ${\text{SnCl}}_4(l)⟶{\text{SnCl}}_4(g)(\text{T}=200\text{°C})$

Calculate the equilibrium constant at the temperature given.

(a) ${\text{I}}_2(s)+{\text{Cl}}_2(g)⟶\text{2ICl}(g)(\text{T}=100\text{°C})$

(b) ${\text{H}}_2(g)+{\text{I}}_2(s)⟶\text{2HI}(g)(\text{T}=0.0\text{°C})$

(c) ${\text{CS}}_2(g)+{\text{3Cl}}_2(g)⟶{\text{CCl}}_4(g)+{\text{S}}_2{\text{Cl}}_2(g)(\text{T}=125\text{°C})$

(d) ${\text{2SO}}_2(g)+{\text{O}}_2(g)⟶{\text{2SO}}_3(g)(\text{T}=675\text{°C})$

(e) ${\text{CS}}_2(g)⟶{\text{CS}}_2(l)(\text{T}=90\text{°C})$

Consider the following reaction at 298 K:
${\text{N}}_2{\text{O}}_4(g)\rightleftharpoons {\text{2NO}}_2(g)K_P=0.142$

What is the standard free energy change at this temperature? Describe what happens to the initial system, where the reactants and products are in standard states, as it approaches equilibrium.