19. Chemical Thermodynamics

Gibbs Free Energy

Gibbs free energy and spontaneity | Chemistry | Khan Academy

Predict the conditions (high temperature, low temperature, all
temperatures, or no temperatures) under which each reaction is
spontaneous.
d. 2 NO2( g) ¡ 2 NO( g) + O2( g) (endothermic)

Use standard free energies of formation to calculate ΔG° at 25 °C
for each reaction in Problem 61. How do the values of ΔG°
calculated this way compare to those calculated from ΔH° and
ΔS°? Which of the two methods could be used to determine
how ΔG° changes with temperature?

For each reaction, calculate ΔHrxn ° , ΔSrxn ° , and ΔGrxn ° at 25 °C and
state whether or not the reaction is spontaneous. If the reaction
is not spontaneous, would a change in temperature make it
spontaneous? If so, should the temperature be raised or lowered
from 25 °C?
c. N2( g) + O2( g) ¡ 2 NO( g)

Consider the unbalanced equation:  
(b) Use the data in Appendix B and ΔG°f for IO3 
-1aq2= 
-128.0 kJ>mol to calculate ΔG° for the reaction at 25 °C.

Consider this reaction occurring at 298 K:
N2O( g) + NO2( g) ∆ 3 NO( g)
a. Show that the reaction is not spontaneous under standard
conditions by calculating ΔGrxn ° .

To determine if a compound will either freeze or vaporize we must first determine their normal freezing and boiling point by assuming Gibbs Free Energy is zero.&#160;

Consider the reaction:
CO2( g) + CCl4( g) ∆ 2 COCl2( g)
Calculate ΔG for this reaction at 25 °C under the following
conditions:
i. PCO2 = 0.112 atm
ii. PCCl4 = 0.174 atm
iii. PCOCl2 = 0.744 atm

Dinitrogen tetroxide decomposes to nitrogen dioxide: 
N2O4( g) ¡ 2 NO2( g) ΔHrxn ° = 55.3 kJ 
At 298 K, a reaction vessel initially contains 0.100 atm of N2O4. 
When equilibrium is reached, 58% of the N2O4 has decomposed 
to NO2. What percentage of N2O4 decomposes at 388 K? Assume 
that the initial pressure of N2O4 is the same (0.100 atm).

Living organisms use energy from the metabolism of food to
create an energy-rich molecule called adenosine triphosphate
(ATP). The ATP acts as an energy source for a variety of reactions
that the living organism must carry out to survive. ATP provides
energy through its hydrolysis, which can be symbolized as follows:
ATP(aq) + H2O(l ) ¡ ADP(aq) + Pi(aq) ΔGrxn ° = -30.5 kJ
where ADP represents adenosine diphosphate and Pi represents
an inorganic phosphate group (such as HPO42 - ).
b. The free energy obtained from the oxidation (reaction with 
oxygen) of glucose (C6H12O6) to form carbon dioxide and 
water can be used to re-form ATP by driving the given reaction in reverse. Calculate the standard free energy change for 
the oxidation of glucose and estimate the maximum number 
of moles of ATP that can be formed by the oxidation of one 
mole of glucose.

Ethyl alcohol has ΔHfusion = 5.02 kJ>mol and melts at - 114.1 °C. What is the value of ΔSfusion for ethyl alcohol?

Consider the dissociation reaction A21g2 S 2A1g2. The following pictures represent two possible initial states and the equilibrium state of the system:<img src="https://lightcat-files.s3.amazonaws.com/problem_images/812d1cf4b7f486b2-1673625872854.jpg" alt="" />
(b) What are the signs ( + , - , or 0) of ∆H, ∆S, and ∆G when the system goes from initial state 1 to the equilibrium state? Explain. Is this a spontaneous process?

Consider a reaction A21g2 + B21g2Δ2 AB1g2, with atoms of A shown in red in the diagram and atoms of B shown in blue.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/816d1730b32ca815-1667324713251.jpg" alt="" />
(a) If Kc = 1, which box represents the system at equilibrium?

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system?

Use data in Appendix C to calculate ΔH°, ΔS°, and ΔG° at 25 °C for each of the following reactions.
(c) 2 P1s2 + 10 HF1g2¡2 PF51g2 + 5 H21g2

The following reaction is exothermic:
(c) Is the reaction likely to be spontaneous at lower temperatures only, at higher temperatures only, or at all temperatures?

The reaction SO21g2 + 2 H2S1g2Δ3 S1s2 + 2 H2O1g2 is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (b) In principle, is this reaction a feasible method of removing SO2?

Consider the following endothermic reaction of gaseous AB3 molecules with A2 molecules. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/c4e3cbea645de813-1673560821980.jpg" alt="" /> Identify the true statement about the spontaneity of the reaction. 
(a) The reaction is likely to be spontaneous at high temperatures. 
(b) The reaction is likely to be spontaneous at high temperatures. 
(c) The reaction is always spontaneous.
(d) The reaction is always spontaneous.

The following reaction of A3 molecules is spontaneous. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/60275c74f7d8bdf2-1673534943776.jpg" alt="" />(b) What are the signs of ∆H, ∆S, and ∆G for the reaction? Explain.

The accompanying diagram shows how ΔH (red line) and TΔS (blue line) change with temperature for a hypothetical reaction.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/35cead1f90081413-1667325253213.jpg" alt="" />
(b) In what temperature range is this reaction spontaneous?

The reaction SO21g2 + 2 H2S1g2Δ3 S1s2 + 2 H2O1g2 is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (c) If PSO2 = PH2S and the vapor pressure of water is 25 torr, calculate the equilibrium SO2 pressure in the system at 298 K.

Using Gibbs Free Energy

The oxidation of glucose 1C6H12O62 in body tissue produces CO2 and H2O. In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol 1C2H5OH2 and CO2. (b) Compare the maximum work that can be obtained from these processes under standard conditions.
C6H12O61s2 + 6 O21g2Δ6 CO21g2 + 6 H2O1l2
C6H12O61s2Δ2 C2H5OH1l2 + 2 CO21g2

Consider the Haber synthesis of gaseous NH3 (∆H°f = -46.1 kJ/mol; ∆G°f = -16.5 kJ/mol:  
(d) What are the equilibrium constants Kp and Kc for the reaction at 350 K? Assume that ∆H° and ∆S° are independent of temperature.

Under nonstandard conditions the pressure, temperature and molarities will be different from 1.0 atm, 25oC and 1.0 M respectively and so we use the following equation for Gibbs Free Energy:

Methanol (CH3OH) burns in oxygen to form carbon dioxide
and water. Write a balanced equation for the combustion of liquid methanol and calculate ΔH°
rxn, ΔSrxn ° , and ΔGrxn ° at 25 °C. Is
the combustion of methanol spontaneous?

Methanol 1CH3OH2 can be made by the controlled oxidation of methane: CH41g2 + 12O21g2¡CH3OH1g2
(b) Will ΔG for the reaction increase, decrease, or stay unchanged with increasing temperature?

Consider a twofold expansion of 1 mol of an ideal gas at 25 °C in the isolated system shown in Figure 18.1. <QUESTION REFERENCES FIGURE 18.1> 
(a) What are the values of ∆H, ∆S, and ∆G for the process?

For each reaction, calculate ΔHrxn ° , ΔSrxn ° , and ΔGrxn ° at 25 °C and
state whether or not the reaction is spontaneous. If the reaction
is not spontaneous, would a change in temperature make it
spontaneous? If so, should the temperature be raised or lowered
from 25 °C?
a. N2O4( g) ¡ 2 NO2( g)

∆Go = - 332 kJ; the reaction favors the formation of reactants.

∆Go = - 166 kJ; the reaction favors the formation of products.

∆Go = - 166 kJ; the reaction favors the formation of reactants.

∆Go = - 332 kJ; the reaction favors the formation of products.

Nitrogen gas combines with fluorine gas to form nitrogen trifluoride according to the reaction below at 25oC:N2 (g) &nbsp;+ &nbsp;3 F2 (g) &nbsp;→ &nbsp;2 NF3 (g) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ΔHo = -249.0 kJ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ΔSo = -278 J/KCalculate ΔGo and state if the reaction favors reactants or products at standard conditions.

Consider the following graph of total free energy of reactants and products versus reaction progress for the general reaction, Reactants -> Products. At which of the four points (labeled a, b, c, and d) is Q < K? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/4c0d107085b51990-1673536435722.jpg" alt="" />
(a) Point a
(b) Point c and d
(c) Point a, c, and d
(d) Point b

Ethanol is manufactured in industry by the hydration of ethylene: Using the data in Appendix B, calculate ∆G° and show that this reaction is spontaneous at 25 °C. Why does this reaction become nonspontaneous at higher temperatures? Estimate the temperature at which the reaction becomes nonspontaneous. <QUESTION REFERENCES APPENDIX B>

Cytochrome, a complicated molecule that we will represent
as CyFe2+, reacts with the air we breathe to supply energy
required to synthesize adenosine triphosphate (ATP). The
body uses ATP as an energy source to drive other reactions
(Section 19.7). At pH 7.0 the following reduction potentials
pertain to this oxidation of CyFe2+:
O21g2 + 4 H+1aq2 + 4 e- ¡ 2 H2O1l2 Ered ° = +0.82 V
CyFe3+1aq2 + e- ¡ CyFe2+1aq2 E°red = +0.22 V
(a) What is ∆G for the oxidation of CyFe2+ by air? (b) If the
synthesis of 1.00 mol of ATP from adenosine diphosphate
(ADP) requires a ∆G of 37.7 kJ, how many moles of ATP are
synthesized per mole of O2?

Using data from Appendix C, calculate ΔG° for the following reactions. Indicate whether each reaction is spontaneous at 298 K under standard conditions.
(a) 2 SO21g2 + O21g2¡2 SO31g2

Consider the reaction 3 CH41g2¡C3H81g2 + 2 H21g2.
(a) Using data from Appendix C, calculate ΔG° at 298 K.

Use data from Appendix IIB to calculate the equilibrium
constants at 25 °C for each reaction.
a. 2 CO( g) + O2( g) ∆ 2 CO2( g)

Nitrogen dioxide, a pollutant in the atmosphere, can combine
with water to form nitric acid. One of the possible reactions is
shown here. Calculate ΔG° and K
p for this reaction at 25 °C and
comment on the spontaneity of the reaction.
3 NO2( g) + H2O(l ) ¡ 2 HNO3(aq) + NO( g)

The crystalline hydrate Cd1NO322 #4H2O1s2 loses water when placed in a large, closed, dry vessel at room temperature: Cd1NO322 #4H2O1s2¡Cd1NO3221s2 + 4 H2O1g2
This process is spontaneous and ΔH° is positive at room temperature. (b) If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does ΔS° change for this reaction at room temperature?

Is it possible for a reaction to be nonspontaneous yet exo-thermic? Explain.

Compare the values of ∆G and ∆G° when: 
(a) Q < 1.
(b) Q = 1.
(c) Q > 1.
Does the thermodynamic tendency for the reaction to occur increase or decrease as Q increases?

Consider the following equilibrium: N2O41g2Δ2 NO21g2
Thermodynamic data on these gases are given in Appendix C. You may assume that ΔH° and ΔS° do not vary with temperature. (a) At what temperature will an equilibrium mixture contain equal amounts of the two gases?

Consider the evaporation of methanol at 25.0 °C :
CH3OH(l ) ¡ CH3OH( g)
b. Find ΔG 
r at 25.0 °C under the following nonstandard 
conditions: 
i. PCH3OH = 150.0 mmHg 
ii. PCH3OH = 100.0 mmHg 
iii. PCH3OH = 10.0 mmHg

Consider the evaporation of methanol at 25.0 °C :
CH3OH(l ) ¡ CH3OH( g)
a. Find ΔG°
r at 25.0 °C.

The potassium-ion concentration in blood plasma is about 5.0 * 10-3 M, whereas the concentration in muscle-cell fluid is much greater (0.15 M ). The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to K+. (a) What is ΔG for the transfer of 1 mol of K+ from blood plasma to the cellular fluid at body temperature 37 °C? (b) What is the minimum amount of work that must be used to transfer this K+?

Consider the decomposition of barium carbonate: BaCO31s2ΔBaO1s2 + CO21g2
Using data from Appendix C, calculate the equilibrium pressure of CO2 at (b) 1100 K.

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/124b0d235df3f9c2-1673551237055.jpg" alt="" />
(b) What are the signs ( + , - , or 0) of ∆H, ∆S, and ∆G for this process? Explain.

The reaction SO21g2 + 2 H2S1g2Δ3 S1s2 + 2 H2O1g2 is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (d) Would you expect the process to be more or less effective at higher temperatures?

Consider the reaction:
I2( g) + Cl2( g) ∆ 2 ICl( g)
K
p = 81.9 at 25 °C
Calculate ΔG
rxn for the reaction at 25 °C under each of the
following conditions:
a. standard conditions

A metal salt with the formula MCl2 crystallizes from water 
to form a solid with the composition MCl2 # 6 H2O. The equilibrium vapor pressure of water above this solid at 298 K is 
18.3 mmHg. What is the value of ΔG for the reaction 
MCl2 # 6 H2O(s) ∆ MCl2(s) + 6 H2O( g) when the pressure 
of water vapor is 18.3 mmHg? When the pressure of water 
vapor is 760 mmHg?

Living organisms use energy from the metabolism of food to
create an energy-rich molecule called adenosine triphosphate
(ATP). The ATP acts as an energy source for a variety of reactions
that the living organism must carry out to survive. ATP provides
energy through its hydrolysis, which can be symbolized as follows:
ATP(aq) + H2O(l ) ¡ ADP(aq) + Pi(aq) ΔGrxn ° = -30.5 kJ
where ADP represents adenosine diphosphate and Pi represents
an inorganic phosphate group (such as HPO42 - ).
a. Calculate the equilibrium constant, K, for the given reaction
at 298 K.

Consider the evaporation of methanol at 25.0 °C :
CH3OH(l ) ¡ CH3OH( g)
c. Explain why methanol spontaneously evaporates in open air 
at 25.0 °C

Using the data in Appendix C and given the pressures listed, calculate Kp and ΔG for each of the following reactions:
(c) N2H41g2¡N21g2 + 2 H21g2 PN2H4 = 0.5 atm, PN2 = 1.5 atm, PH2 = 2.5 atm

The value of Ka for nitrous acid 1HNO22 at 25 °C is given in Appendix D. (b) By using the value of Ka, calculate ΔG° for the dissociation of nitrous acid in aqueous solution.

If Gibbs Free Energy is less than zero then a reaction will be spontaneous and favor both products and the forward direction.&#160;

In photosynthesis, plants form glucose (C6H12O6) and oxygen 
from carbon dioxide and water. Write a balanced equation for 
photosynthesis and calculate ΔHrxn ° , ΔSrxn ° , and ΔGrxn ° at 25 °C. 
Is photosynthesis spontaneous?

At what temperatures is the following reaction, the 
reduction of magnetite by graphite to elemental iron, 
spontaneous? 
Fe3O41s2 + 2 C1s, graphite2¡2 CO21g2 + 3 Fe1s2

For each reaction, calculate ΔHrxn ° , ΔSrxn ° , and ΔGrxn ° at 25 °C and
state whether or not the reaction is spontaneous. If the reaction
is not spontaneous, would a change in temperature make it
spontaneous? If so, should the temperature be raised or lowered
from 25 °C?
d. N2( g) + 3 H2( g) ¡ 2 NH3( g)

Use data from Appendix IIB to calculate the equilibrium
constants at 25 °C for each reaction.
b. 2 H2S( g) ∆ 2 H2( g) + S2( g)

The lead storage battery uses the reaction  
(b) Calculate ∆G for this reaction on a cold winter’s day (10 °F) in a battery that has run down to the point where the sulfuric acid concentration is only 0.100 M.

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (d) At what temperature are the two phases in equilibrium?

Free Energy

Consider the conversion of 1,2-dichloroethane to vinyl chloride, the starting material for manufacturing poly(vinyl chloride) (PVC) plastics:  Is this reaction spontaneous under standard-state conditions? Would it help to carry out the reaction in the presence of base to remove HCl? Explain. Is it possible to synthesize vinyl chlo-ride from graphite, gaseous H2, and gaseous Cl2 at 25 °C and 1 atm pressure?

Consider the following reaction between oxides of nitrogen: NO21g2 + N2O1g2¡3 NO1g2
(b) Calculate ΔG at 800 K, assuming that ΔH° and ΔS° do not change with temperature. Under standard conditions is the reaction spontaneous at 800 K?

Consider the following three reactions:
(i) Ti1s2 + 2 Cl21g2¡TiCl41g2
(a) For each of the reactions, use data in Appendix C to calculate ΔH°, ΔG°, K, and ΔS ° at 25 °C.

Consider the sublimation of iodine at 25.0 °C :
I2(s) ¡ I2( g)
c. Explain why iodine spontaneously sublimes in open air at
25.0 °C

Sulfur dioxide reacts with strontium oxide as follows: SO21g2 + SrO1g2¡SrSO31s2
(a) Without using thermochemical data, predict whether ΔG° for this reaction is more negative or less negative than ΔH°.

Consider the following three reactions:
(i) Ti1s2 + 2 Cl21g2¡TiCl41g2
(ii) C2H61g2 + 7 Cl21g2 ¡2 CCl41g2 + 6 HCl1g2
(iii) BaO1s2 + CO21g2¡BaCO31s2
(c) For each of the reactions, predict the manner in which the change in free energy varies with an increase in temperature.

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/7ae692800521c7c3-1673541546743.jpg" alt="" />
(a) Sketch the final (equilibrium) state of the system.

Chlorine can be prepared in the laboratory by the reaction of hydrochloric acid and potassium permanganate.
(b) Calculate E° and ∆G° for the reaction

A mixture of 14.0 g of N2 and 3.024 g of H2 in a 5.00 L container is heated to 400 °C. Use the data in Appendix B to calculate the molar concentrations of N2, H2, and NH3 at equilibrium. Assume that ∆H° and ∆S° are independent of temperature, and remember that the standard state of a gas is defined in terms of pressure. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/b0fb8fb4a2dccd43-1673562376415.jpg" alt="" />

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (b) In what temperature range is it a spontaneous process?

Consider the decomposition of barium carbonate: BaCO31s2ΔBaO1s2 + CO21g2
Using data from Appendix C, calculate the equilibrium pressure of CO2 at (a) 298 K.

The value of Ka for nitrous acid 1HNO22 at 25 °C is given in Appendix D. (c) What is the value of ΔG at equilibrium?

Consider the reaction:
I2( g) + Cl2( g) ∆ 2 ICl( g)
K
p = 81.9 at 25 °C
Calculate ΔG
rxn for the reaction at 25 °C under each of the
following conditions:
b. at equilibrium

What is the melting point of benzene in kelvin if ΔHfusion = 9.95 kJ>mol and ΔSfusion = 35.7 J> 1K mol2?

Consider the following reaction between oxides of nitrogen: NO21g2 + N2O1g2¡3 NO1g2
(c) Calculate ΔG at 1000 K. Is the reaction spontaneous under standard conditions at this temperature?

The oxidation of glucose 1C6H12O62 in body tissue produces CO2 and H2O. In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol 1C2H5OH2 and CO2. (a) Using data given in Appendix C, compare the equilibrium constants for the following reactions:
C6H12O61s2 + 6 O21g2Δ6 CO21g2 + 6 H2O1l2
C6H12O61s2Δ2 C2H5OH1l2 + 2 CO21g2

Methanol 1CH3OH2 is made industrially in two steps from CO and H2. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane 1CH42:
Step 1. CO1g2 + 2 H21g2 S CH3OH1l2
ΔS° = - 332 J>K
Step 2. CH3OH1l2 S CH41g2 + 1>2 O21g2
ΔS° = 162 J>K (k) Calculate an overall ΔG°, ΔH°, and ΔS° for the forma- tion of CH4 from CO and H2.


















Gibbs
Free Energy and Calculations



The value of Ka for nitrous acid 1HNO22 at 25 °C is given in Appendix D. (d) What is the value of ΔG when 3H+4 = 5.0 * 10-2 M, 3NO2 -4 = 6.0 * 10-4 M, and 3HNO24 = 0.20 M?

Consider the reaction 2 NO21g2¡N2O41g2. (a) Using
data from Appendix C, calculate ΔG° at 298 K. (b) Calculate
ΔG at 298 K if the partial pressures of NO2 and N2O4
are 0.40 atm and 1.60 atm, respectively.

The following pictures represent equilibrium mixtures for the interconversion of A molecules (red) and X, Y, or Z molecules (blue):<img src="https://lightcat-files.s3.amazonaws.com/problem_images/32bdbff2cf9c9a74-1673562385404.jpg" alt="" /> What is the sign of ∆G° for each of the three reactions?

Without doing any calculations, determine the signs of ΔSsys
and ΔS
surr for each chemical reaction. In addition, predict under
what temperatures (all temperatures, low temperatures, or high
temperatures), if any, the reaction is spontaneous.
c. 2 N2( g) + O2( g) ¡ 2 N2O( g) ΔHrxn ° = +163.2 kJ

Consider the sublimation of iodine at 25.0 °C :
I2(s) ¡ I2( g)
b. Find ΔG
rxn at 25.0 °C under the following nonstandard conditions:
i. PI2 = 1.00 mmHg
ii. PI2 = 0.100 mmHg

Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low T but not spontaneous at high T; (iv) spontaneous at high T but not spontaneous at low T.
(c) N2F41g2¡2 NF21g2 ΔH° = 85 kJ; ΔS° = 198 J>K

Suppose that a reaction has ΔH = - 33 kJ and ΔS = - 58 J>K. At what temperature will it change from spontaneous to nonspontaneous?

Tell whether the free-energy changes, ΔG, for the processes listed in Problem 9.127 are likely to be positive, negative, or zero.

Reduction of mercury(II) oxide with zinc gives metallic mercury: 
(b) Estimate at what temperature, if any, the reaction will become nonspontaneous

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly?

Given the following reduction half-reactions: 
Fe3+1aq2 + e- ¡ Fe2+1aq2 E°red = +0.77 V 
S2O62 - 1aq2 + 4 H+1aq2 + 2 e- ¡ 2 H2SO31aq2 E°red = +0.60 V 
N2O1g2 + 2 H+1aq2 + 2 e- ¡ N21g2 + H2O1l2 Ered ° = -1.77 V 
VO2+1aq2 + 2 H+1aq2 + e- ¡ VO2+ + H2O1l2 E°red = +1.00 V 

(b) Calculate ∆G° for each reaction at 298 K.

For each reaction, calculate ΔHrxn ° , ΔSrxn ° , and ΔGrxn ° at 25 °C and
state whether or not the reaction is spontaneous. If the reaction
is not spontaneous, would a change in temperature make it
spontaneous? If so, should the temperature be raised or lowered
from 25 °C?
d. 2 KClO3(s) ¡ 2 KCl(s) + 3 O2( g)

Calculate the change in Gibbs free energy for each of the sets of 
ΔH 
rxn, ΔSrxn, and T given in Problem 42. Predict whether or not 
each reaction is spontaneous at the temperature indicated. 
(Assume that all reactants and products are in their standard 
states.)

Carbon disulfide 1CS22 is a toxic, highly flammable substance. The following thermodynamic data are available for CS21l2 and CS21g2 at 298 K: 
<TABLE> 
(e) Use the data in the table to calculate ΔS° at 298 K for the vaporization of CS21l2. Is the sign of ΔS° as you would expect for a vaporization?

Without doing any calculations, determine the signs of ΔSsys
and ΔS
surr for each chemical reaction. In addition, predict under
what temperatures (all temperatures, low temperatures, or high
temperatures), if any, the reaction is spontaneous.
a. C3H8( g) + 5 O2( g) ¡ 3 CO2( g) + 4 H2O( g)
ΔH°
rxn = -2044 kJ

Consider the reaction:
2 NO( g) + O2( g) ∆ 2 NO2( g)
The following data show the equilibrium constant for this reaction measured at several different temperatures. Use the data to
find ΔH°
rxn and ΔSrxn ° for the reaction. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/416e467bee3409ec-1661446316695.jpg" alt="" />

Determine ΔG° for the reaction: 
Fe2O3(s) + 3 CO( g) ¡ 2 Fe(s) + 3 CO2( g) 
Use the following reactions with known ΔGrxn ° values: 
2 Fe(s) + 3 2 O2( g) ¡ Fe2O3(s) ΔGrxn ° = -742.2 kJ 
CO( g) + 1 2 O2( g) ¡ CO2( g) ΔGrxn ° = -257.2 kJ

Consider this reaction occurring at 298 K:
N2O( g) + NO2( g) ∆ 3 NO( g)
c. Can the reaction be made more spontaneous by an increase or
decrease in temperature? If so, what temperature is required to
make the reaction spontaneous under standard conditions?

From the values given for ΔH° and ΔS°, calculate ΔG° for each of the following reactions at 298 K. If the reaction is not spontaneous under standard conditions at 298 K, at what temperature (if any) would the reaction become spontaneous?
(a) 2 PbS1s2 + 3 O21g2¡2 PbO1s2 + 2 SO21g2 ΔH ° = -844 kJ; ΔS° = -165 J>K

Besides our standard equation for Gibbs Free Energy we have another that connects it to our equilibrium constant K:&#160;

The normal freezing point of n-octane 1C8H182 is -57 °C. (b) In what temperature range is the freezing of n-octane a spontaneous process?

Calculate the free energy change for this reaction at 25 °C. Is the 
reaction spontaneous? (Assume that all reactants and products 
are in their standard states.) 
2 Ca(s) + O2( g) ¡ 2 CaO(s) 
ΔH° 
rxn = -1269.8 kJ; ΔSrxn ° = -364.6 J>K

Consider this reaction occurring at 298 K:
N2O( g) + NO2( g) ∆ 3 NO( g)
b. If a reaction mixture contains only N2O and NO2 at partial
pressures of 1.0 atm each, the reaction will be spontaneous
until some NO forms in the mixture. What maximum partial
pressure of NO builds up before the reaction ceases to be
spontaneous?

Consider the reaction 3 CH41g2¡C3H81g2 + 2 H21g2.
(b) Calculate ΔG at 298 K if the reaction mixture consists of 40.0 atm of CH4, 0.0100 atm of C3H81g2, and 0.0180 atm of H2.

Consider this reaction occurring at 298 K:
BaCO3(s) ∆ BaO(s) + CO2( g)
b. If BaCO3 is placed in an evacuated flask, what is the partial 
pressure of CO2 when the reaction reaches equilibrium?

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane 1C2H62, is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen:
2 CH41g2¡C2H61g2 + H21g2
In practice, this reaction is carried out in the presence of oxygen:
2 CH41g2 + 12O21g2¡C2H61g2 + H2O1g2
(b) Is the difference in ΔG° for the two reactions due primarily to the enthalpy term 1ΔH2or the entropy term (-TΔS)?

The forward reaction is spontaneous and the system is far from equilibrium.

The forward reaction is spontaneous and the system is near equilibrium.

The reverse reaction is spontaneous and the system is far from equilibrium.

The reverse reaction is spontaneous and the system is near equilibrium.

If ∆G is small and positive which of the following statements is true?

Use tabulated electrode potentials to calculate ∆G°rxn for each reaction at 25 °C.
c. Br2(l) + 2 I-(aq) ¡ 2 Br-(aq) + I2(s)

How is it possible for a reaction to be spontaneous yet endothermic?

Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds according to: 
CH3COOH1l2¡CH3OH1g2 + CO1g2 
By using data from Appendix C, calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that ΔH° and ΔS° do not vary with temperature.

Elemental sulfur is formed by the reaction of zinc sulfide with oxygen: 
(b) At what temperature, if any, the reaction will become nonspontaneous?

The following reaction, sometimes used in the laboratory to generate small quantities of oxygen gas, has ∆G° = -224.4 kJ/mol at 25°C: <img src="https://lightcat-files.s3.amazonaws.com/problem_images/0022184bf3d0ddd6-1673476704843.jpg" alt="" /> Use the following additional data at 25 °C to calculate the standard molar entropy S° of O2 at 25°C: ∆H°f(KClO3) = -397.7 kJ/mol, ∆H°f(KCl) = -436.5 kJ/mol, S°(KClO3) = 143.1 J/(K*mol), and S°(KCl) = 82.6 J/(K*mol).

These reactions are important in catalytic converters in
automobiles. Calculate ΔG° for each at 298 K. Predict the effect
of increasing temperature on the magnitude of ΔG°.
b. 5 H2( g) + 2 NO( g) ¡ 2 NH3( g) + 2 H2O( g)

18.3 Gibbs Free Energy and the Relationship between Delta G, Delta H, and Delta S

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane 1C2H62, is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen:
2 CH41g2¡C2H61g2 + H21g2
In practice, this reaction is carried out in the presence of oxygen:
2 CH41g2 + 12O21g2¡C2H61g2 + H2O1g2
(c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the “Chemistry and Life” box in Section 19.7.

Ammonium nitrate is dangerous because it decomposes (sometimes explosively) when heated: 
(a) Using the data in Appendix B, show that this reaction is spontaneous at 25 °C.
<QUESTION REFERENCES APPENDIX B>

Consider this reaction occurring at 298 K:
BaCO3(s) ∆ BaO(s) + CO2( g)
a. Show that the reaction is not spontaneous under standard
conditions by calculating ΔGrxn ° .

(a) Using data in Appendix C, estimate the temperature 
at which the free-energy change for the transformation 
from I21s2 to I21g2 is zero. (b) Use a reference source, 
such as Web Elements (www.webelements.com), to 
find the experimental melting and boiling points of I2. 
(c) Which of the values in part (b) is closer to the value 
you obtained in part (a)?

For each reaction, calculate ΔHrxn ° , ΔSrxn ° , and ΔGrxn ° at 25 °C and
state whether or not the reaction is spontaneous. If the reaction
is not spontaneous, would a change in temperature make it
spontaneous? If so, should the temperature be raised or lowered
from 25 °C?
a. 2 CH4( g) ¡ C2H6( g) + H2( g)

Consider the reaction:
I2( g) + Cl2( g) ∆ 2 ICl( g)
K
p = 81.9 at 25 °C
Calculate ΔG
rxn for the reaction at 25 °C under each of the
following conditions:
c. PICl = 2.55 atm; PI2 = 0.325 atm; PCl2 = 0.221 atm

Ammonium hydrogen sulfide, a stink bomb ingredient, decomposes to ammonia and hydrogen sulfide:  Calculate the standard free-energy change for the rection at 25 °C if the total pressure resulting from the solid NH4S placed in an evacuated container is 0.658 atm at 25 °C.
(a) -43.8 kJ
(b) +1.04 kJ
(c) -462 kJ
(d) +5.51 kJ

Given the data in Problem 18.78, calculate ∆G for the vaporization of benzene at:
(a) 70 °C
Predict whether benzene will boil at each of these temperatures and 1 atm pressure. <QUESTION REFERENCES PROBLEM 18.78>

The Laws of Thermodynamics, Entropy, and Gibbs Free Energy

Assuming that gaseous reactants and products are present at 1 atm partial pressure, which of the following reactions are spontaneous in the forward direction? 
(a) 
(b) 
(c) 
(d)

Use the data in Appendix B to calculate the equilibrium pressure of CO2 in a closed 1 L vessel that contains each of the following samples: <PROBLEM REFERENCES APPENDIX B> 
(a) 15 g of MgCO3 and 1.0 g of MgO at 25 °C
Assume that ∆H° and ∆S° are independent of temperature.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/e9b08a582a567c1d-1673476025001.jpg" alt="" />

(c) In general, under which condition is ΔG°f more positive (less negative) than ΔH°f ? (i) When the temperature is high, (ii) when the reaction is reversible, (iii) when ΔS°f is negative.

Use tabulated electrode potentials to calculate ∆Gr°xn for each reaction at 25 °C.
c. MnO2(s) + 4 H+(aq) + Cu(s) ¡
Mn2+(aq) + 2H2O(l) + Cu2+(aq)

Which of the following processes are spontaneous: (a) the melting of ice cubes at -10 °C and 1 atm pressure; (b) separating a mixture of N2 and O2 into two separate samples, one that is pure N2 and one that is pure O2; (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor at room temperature; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?

The values of ΔGf° for the hydrogen halides become less negative with increasing atomic number. The ΔGf° of HI is slightly
positive. However, the trend in ΔSf° is to become more positive
with increasing atomic number. Explain.

If our Gibbs Free Energy is less than zero then a reaction is spontaneous. &#160;

Nitrogen reacts with fluorine to form nitrogen trifluoride:  Calculate ∆G°, and determine whether the equilibrium composition should favor reactions or products at 25 °C
(a) ∆G° = -6.7 kJ; the equilibrium composition should favor products. 
(b) ∆G° = -332 kJ; the equilibrium composition should favor reactants 
(c) ∆G° = -166 kJ; the equilibrium composition should favor products 
(d) ∆G° = +82.6 kJ; the equilbirum composiiton should favor reactants.

A reaction has an equilibrium constant of 8.5 * 103 at 298 K. 
At 755 K, the equilibrium constant is 0.65. Find ΔHrxn ° for the 
reaction.

The Haber process is the principal industrial route for converting nitrogen into ammonia:
N21g2 + 3 H21g2 ¡ 2 NH31g2
(b) 
Using the thermodynamic data in Appendix C, calculate 
the equilibrium constant for the process at room temperature.

The fuel in high-efficiency natural-gas vehicles consists primarily of methane 1CH42. (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

Use the data in Appendix B to calculate ∆G for the decom-position of nitrosyl chloride at 25 °C when the partial pressures are 2.00 atm of NOCl, 1.00 * 10^-3 atm of NO, and 1.00 * 10^-3 atm of Cl2: <QUESTION REFERENCES APPENDIX B> Is the reaction spontaneous in the forward or the reverse direction under these conditions?

"Methanol 1CH3OH2 is made industrially in two steps from CO and H2. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane 1CH42:
Step 1. CO1g2 + 2 H21g2 S CH3OH1l2
ΔS° = - 332 J>K
Step 2. CH3OH1l2 S CH41g2 + 1>2 O21g2
ΔS° = 162 J>K
(e) In what temperature range is step 1 spontaneous?

Consider again the dissociation reaction <img src="https://lightcat-files.s3.amazonaws.com/problem_images/c22647a08e050a1e-1673559328767.jpg" alt="" /> <QUESTION REFERENCES QUESTION 32>
(e) What is the value of ∆G for the dissociation reaction when the system is at equilibrium?

An ideal gas is compressed at constant temperature. What are the signs ( + , - , or 0) of ∆H, ∆S, and ∆G for the process? Explain. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/e80ab61bc9eb02ca-1673544881144.jpg" alt="" />

The normal freezing point of n-octane 1C8H182 is -57 °C. (d) Is there any temperature at which liquid n-octane and solid n-octane are in equilibrium? Explain.

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/e8905075c03550f9-1673549852012.jpg" alt="" /> 
(d) Relate each of the pictures to the graph in Figure 18.11. <REFERENCES FIGURE 18.11>

Consider the following reaction between oxides of nitrogen: NO21g2 + N2O1g2¡3 NO1g2
(a) Use data in Appendix C to predict how ΔG for the reaction varies with increasing temperature.

A certain constant-pressure reaction is barely nonspontaneous at 45 °C. The entropy change for the reaction is 72 J>K. Estimate ΔH.

Entropy: Embrace the Chaos! Crash Course Chemistry #20

Phosphorus pentachloride forms from phosphorus trichloride and chlorine:
(b) Estimate the temperature at which the reaction will become nonspontaneous.

Calculate ΔG° at 298 K for these reactions and predict the effect
on ΔG° of lowering the temperature.
b. CaCO3(s) ¡ CaO(s) + CO2( g)

The entropy change for a certain nonspontaneous reaction at 50 °C is 104 J/K. 
(a) Is the reaction endothermic or exothermic? 
(b) What is the minimum value of ∆H (in kJ) for the reaction?

Using data from Appendix C, write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free-energy change for these reactions at 298 K:
(a) NaHCO31s2ΔNaOH1s2 + CO21g2

Consider the reaction:
2 NO( g) + O2( g) ¡ 2 NO2( g)
Estimate ΔG° for this reaction at each temperature and predict
whether or not the reaction is spontaneous. (Assume that ΔH°
and ΔS° do not change too much within the given temperature
range.)
b. 715 K

Fill in the blanks in the table. Both ΔH and ΔS refer to the
system.

Consider this reaction occurring at 298 K:
BaCO3(s) ∆ BaO(s) + CO2( g)
c. Can the reaction be made more spontaneous by an increase
or decrease in temperature? If so, at what temperature is the
partial pressure of carbon dioxide 1.0 atm?

The normal boiling point of bromine is 58.8 °C, and the standard entropies of the liquid and vapor are S°[Br2(l) = 152.2 J/(K*mol); S°[Br2(g) = 245.4 J/(K*mol). At what temperature does bromine have a vapor pressure of 227 mmHg?

Urea (NH2CONH2), an important nitrogen fertilizer, is produced industrially by the reaction  
Given that ∆G° = -13.6 kJ, calculate ∆G at 25 °C for the following sets of conditions. .
(a) 10 atm NH3, 10 atm CO2, 1.0 M NH2CONH2
(b) 0.10 atm NH3, 0.10 atm CO2, 1.0 M NH2CONH2
Is the reaction spontaneous for the conditions in part (a) and/or part (b)?

Magnesium m#etal has ΔHfusion = 9.037 kJ>mol and ΔSfusion = 9.79 J>1K mol2. What is the melting point of magnesium in °C? (LO 11.4)
(a) 0.923 °C (b) 923 °C
(c) 650 °C (d) 1.08 * 103 °C

The solubility of AgCl(s) in water at 25 °C is 1.33 * 10 - 5 mol>L 
and its ΔH° of solution is 65.7 kJ>mol. What is its solubility at 
50.0 °C?

Use the values of of ∆G°f in Appendix B to calculate the stan-dard free-energy change for the synthesis of dichloroethane from ethylene and chlorine:
C2H41g2 + Cl21g2S CH2ClCH2Cl1l2
Is it possible to synthesize dichloroethane from gaseous C2H4 and Cl2, each at 25 °C and 1 atm pressure?

Consider the reaction PbCO31s2ΔPbO1s2 + CO21g2
Using data in Appendix C, calculate the equilibrium pressure of CO2 in the system at (a) 400 °C.

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