Chapter 12: ThermodynamicsContent check — Chemistry: Atoms First, Chapter 12: Thermodynamics

(a) ${\text{NaNO}}_3(s)⟶$ ${\text{Na}}^{\text{+}}(aq)+$ ${\text{NO}}_3{}^{\text{−}}(aq)$

(b) the freezing of liquid water

(c) ${\text{CO}}_2(s)⟶$ ${\text{CO}}_2(g)$

(d) ${\text{CaCO}}_3(s)⟶$ $\text{CaO}(s)+$ ${\text{CO}}_2(g)$

Indicate whether the following processes are spontaneous or nonspontaneous.

(a) Liquid water freezing at a temperature below its freezing point

(b) Liquid water freezing at a temperature above its freezing point

(c) The combustion of gasoline

(d) A ball thrown into the air

(e) A raindrop falling to the ground

(f) Iron rusting in a moist atmosphere

Indicate which substance in the given pairs has the higher entropy value. Explain your choices.

(a) C₂H₅OH(l) or C₃H₇OH(l)

(b) C₂H₅OH(l) or C₂H₅OH(g)

(c) 2H(g) or H(g)

Predict the sign of the entropy change for the following processes. Give a reason for your prediction.

(a) ${\text{Na}}^{\mathrm{+}}(aq)+$ ${\text{Cl}}^{\mathrm{-}}(aq)⟶$ $\text{NaCl}(s)$

(b) $2\text{Fe}(s)+$ $\frac{3}{2}{\text{O}}_2(g)⟶$ ${\text{Fe}}_2{\text{O}}_2(s)$

(c) $2{\text{C}}_6{\text{H}}_{14}(l)+$ $19{\text{O}}_2(g)⟶$ $14{\text{H}}_2\text{O}(g)+$ $12{\text{CO}}_2(g)$

Calculate $\text{Δ}S\text{°}$ for the following changes.

(a) ${\text{SnCl}}_4(l)⟶$ ${\text{SnCl}}_4(g)$

(b) ${\text{CS}}_2(g)⟶$ ${\text{CS}}_2(l)$

(c) $\text{Cu}(s)⟶\text{Cu}(g)$

(d) ${\text{H}}_2\text{O}(l)⟶$ ${\text{H}}_2\text{O}(g)$

(e) $2{\text{H}}_2(g)+$ ${\text{O}}_2(g)⟶$ $2{\text{H}}_2\text{O}(l)$

(f) $2\text{HCl}(g)+$ $\text{Pb}(s)⟶$ ${\text{PbCl}}_2(s)+$ ${\text{H}}_2(g)$

(g) $\text{Zn}(s)+$ ${\text{CuSO}}_4(s)⟶$ $\text{Cu}(s)+$ ${\text{ZnSO}}_4(s)$

Using the relevant $S\text{°}$ values listed in Appendix G, calculate ${\text{Δ}S\text{°}}_{298}$ for the following changes:

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

(b) ${\text{N}}_2(g)+$ $\frac{5}{2}{\text{O}}_2(g)⟶$ ${\text{N}}_2{\text{O}}_5(g)$

By calculating ΔS_univ at each temperature, determine if the melting of 1 mole of NaCl(s) is spontaneous at 500 °C and at 700 °C.
$S_{\text{NaCl}(s)}^{°}=$ $72.11\frac{\text{J}}{\text{mol·K}}$ $S_{\text{NaCl}(l)}^{°}=$ $95.06\frac{\text{J}}{\text{mol·K}}$ $\text{Δ}{H}_{\text{fusion}}^{°}=$ $\text{27.95 kJ/mol}$

What assumptions are made about the thermodynamic information (entropy and enthalpy values) used to solve this problem?

Use the standard entropy data in Appendix G to determine the change in entropy for each of the following reactions. All the processes occur at the standard conditions and 25 °C.

(a) $\text{C}(s\text{, graphite})+$ ${\text{O}}_2(g)⟶$ ${\text{CO}}_2(g)$

(b) ${\text{O}}_2(g)+$ ${\text{N}}_2(g)⟶$ $\text{2NO}(g)$

(c) $\text{2Cu}(s)+$ $\text{S}(g)⟶$ ${\text{Cu}}_2\text{S}(s)$

(d) $\text{CaO}(s)+$ ${\text{H}}_2\text{O}(l)⟶$ $\text{Ca}{(\text{OH})}_2(s)$

(e) ${\text{Fe}}_2{\text{O}}_3(s)+$ $\text{3CO}(g)⟶$ $\text{2Fe}(s)+$ ${\text{3CO}}_2(g)$

(f) ${\text{CaSO}}_4\text{·}{\text{2H}}_2\text{O}(s)⟶$ ${\text{CaSO}}_4(s)+$ ${\text{2H}}_2\text{O}(g)$

Use the standard free energy of formation data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.

(a) ${\text{MnO}}_2(s)⟶$ $\text{Mn}(s)+$ ${\text{O}}_2(g)$

(b) ${\text{H}}_2(g)+$ ${\text{Br}}_2(l)⟶$ $\text{2HBr}(g)$

(c) $\text{Cu}(s)+$ $\text{S}(g)⟶$ $\text{CuS}(s)$

(d) $\text{2LiOH}(s)+$ ${\text{CO}}_2(g)⟶$ ${\text{Li}}_2{\text{CO}}_3(s)+$ ${\text{H}}_2\text{O}(g)$

(e) ${\text{CH}}_4(g)+$ ${\text{O}}_2(g)⟶$ $\text{C}(s,\text{graphite})+$ ${\text{2H}}_2\text{O}(g)$

(f) ${\text{CS}}_2(g)+$ ${\text{3Cl}}_2(g)⟶$ ${\text{CCl}}_4(g)+$ ${\text{S}}_2{\text{Cl}}_2(g)$

Given:
$$\begin{array}{cccc}{\text{P}}_4(s)+{\text{5O}}_2(g)⟶{\text{P}}_4{\text{O}}_{10}(s)\hfill & & & \text{Δ}G\text{°}=\text{−2697.0 kJ/mol}\hfill \\ {\text{2H}}_2(g)+{\text{O}}_2(g)⟶{\text{2H}}_2\text{O}(g)\hfill & & & \text{Δ}G\text{°}=\text{−457.18 kJ/mol}\hfill \\ {\text{6H}}_2\text{O}(g)+{\text{P}}_4{\text{O}}_{10}(s)⟶{\text{4H}}_3{\text{PO}}_4(l)\hfill & & & \text{Δ}G\text{°}=\text{−428.66 kJ/mol}\hfill \end{array}$$

(a) Determine the standard free energy of formation, $\text{Δ}{G}_{\text{f}}^{°},$ for phosphoric acid.

(b) How does your calculated result compare to the value in Appendix G? Explain.

Consider the decomposition of red mercury(II) oxide under standard state conditions.
$\text{2HgO}(s,\text{red})⟶$ $\text{2Hg}(l)+$ ${\text{O}}_2(g)$

(a) Is the decomposition spontaneous under standard state conditions?

(b) Above what temperature does the reaction become spontaneous?

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

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

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

$$\begin{array}{cccc}\text{(a)}{\text{O}}_2(g)+{\text{2F}}_2(g)⟶{\text{2OF}}_2(g)\hfill & & & \text{Δ}G\text{°}=\text{−9.2 kJ}\hfill \\ \text{(b)}{\text{I}}_2(s)+{\text{Br}}_2(l)⟶\text{2IBr}(g)\hfill & & & \text{Δ}G\text{°}=\text{7.3 kJ}\hfill \\ \text{(c)}\text{2LiOH}(s)+{\text{CO}}_2(g)⟶{\text{Li}}_2{\text{CO}}_3(s)+{\text{H}}_2\text{O}(g)\hfill & & & \text{Δ}G\text{°}=\text{−79 kJ}\hfill \\ \text{(d)}{\text{N}}_2{\text{O}}_3(g)⟶\text{NO}(g)+{\text{NO}}_2(g)\hfill & & & \text{Δ}G\text{°}=\text{−1.6 kJ}\hfill \\ \text{(e)}{\text{SnCl}}_4(l)⟶{\text{SnCl}}_4(l)\hfill & & & \text{Δ}G\text{°}=\text{8.0 kJ}\hfill \end{array}$$

Determine ΔGº for the following reactions.

(a) Antimony pentachloride decomposes at 448 °C. The reaction is:
${\text{SbCl}}_5(g)⟶$ ${\text{SbCl}}_3(g)+$ ${\text{Cl}}_2(g)$

An equilibrium mixture in a 5.00 L flask at 448 °C contains 3.85 g of SbCl₅, 9.14 g of SbCl₃, and 2.84 g of Cl₂.

(b) Chlorine molecules dissociate according to this reaction:
${\text{Cl}}_2(g)⟶$ $2\text{Cl}(g)$

1.00% of Cl₂ molecules dissociate at 975 K and a pressure of 1.00 atm.

The evaporation of one mole of water at 298 K has a standard free energy change of 8.58 kJ.
${\text{H}}_2\text{O}(l)\rightleftharpoons$ ${\text{H}}_2\text{O}(g)$ $\text{Δ}G\text{°}=$ $\text{8.58 kJ}$

(a) Is the evaporation of water under standard thermodynamic conditions spontaneous?

(b) Determine the equilibrium constant, K_P, for this physical process.

(c) By calculating ∆G, determine if the evaporation of water at 298 K is spontaneous when the partial pressure of water, $P_{{\text{H}}_2\text{O}},$ is 0.011 atm.

(d) If the evaporation of water were always nonspontaneous at room temperature, wet laundry would never dry when placed outside. In order for laundry to dry, what must be the value of $P_{{\text{H}}_2\text{O}}$ in the air?

One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate (G6P) to form fructose-6-phosphate (F6P):
$\text{G6P}\rightleftharpoons$ $\text{F6P}$ $\text{Δ}G\text{°}=$ $\text{1.7 kJ}$

(a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?

(b) Standard thermodynamic conditions imply the concentrations of G6P and F6P to be 1 M, however, in a typical cell, they are not even close to these values. Calculate ΔG when the concentrations of G6P and F6P are 120 μM and 28 μM respectively, and discuss the spontaneity of the forward reaction under these conditions. Assume the temperature is 37 °C.

What happens to $\text{Δ}G\text{°}$ (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?

(a) $\text{S}(s)+$ ${\text{O}}_2(g)⟶$ ${\text{SO}}_2(g)$

(b) ${\text{2SO}}_2(g)+$ ${\text{O}}_2(g)⟶$ ${\text{SO}}_3(g)$

(c) $\text{HgO}(s)⟶$ $\text{Hg}(l)+$ ${\text{O}}_2(g)$