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- What is the relationship between the free-energy change under nonstandard-state conditions, ∆G, the free-energy change under standard-state conditions, ∆G°, and the reaction quotient, Q?
Problem 106
- 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?
Problem 107
- 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:
Problem 108
Is the reaction spontaneous in the forward or the reverse direction under these conditions? - 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)?
Problem 111
- What is the relationship between the standard free-energy change, ∆G°, for a reaction and the equilibrium constant, K? What is the sign of ∆G° when: (a) K > 1? (b) K = 1? (c) K < 1?
Problem 112
- Do you expect a large or small value of the equilibrium constant for a reaction with the following values of ∆G°? (a) ∆G° is positive. (b) ∆G° is negative.
Problem 113
- 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.
Problem 120
Problem 122a,b
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:
(a) 15 g of MgCO3 and 1.0 g of MgO at 25 °C
(b) 15 g of MgCO3 and 1.0 g of MgO at 280 °C .
Assume that ∆H° and ∆S° are independent of temperature.
Problem 124d
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.
- Is it possible for a reaction to be nonspontaneous yet exo-thermic? Explain.
Problem 125
Problem 126a
Trouton's rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids: ∆Hvap/Tbp ≈ 88 J/(K*mol) (a) Check the reliability of Trouton's rule for the liquids listed in the following table.
Problem 126b
Trouton's rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids: ∆Hvap/Tbp ≈ 88 J/(K*mol) (b) Explain why liquids tend to have the same value of ∆Hvap/Tbp.
- 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?
Problem 128
- Tell whether reactions with the following values of ΔH and ΔS are spontaneous or nonspontaneous and whether they are exothermic or endothermic. (a) ΔH = - 48 kJ; ΔS = + 135 J>K at 400 K (b) ΔH = - 48 kJ; ΔS = - 135 J>K at 400 K (c) ΔH = + 48 kJ; ΔS = + 135 J>K at 400 K (d) ΔH = + 48 kJ; ΔS = - 135 J>K at 400 K
Problem 132
- The following reaction, sometimes used in the laboratory to generate small quantities of oxygen gas, has ∆G° = -224.4 kJ/mol at 25°C:
Problem 133
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).
- Suppose that a reaction has ΔH = - 33 kJ and ΔS = - 58 J>K. At what temperature will it change from spontaneous to nonspontaneous?
Problem 134
- 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.
Problem 136
Problem 138b
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.
- Chloroform has ΔHvaporization = 29.2 kJ>mol and boils at 61.2 °C. What is the value of ΔSvaporization for chloroform?
Problem 139
Problem 141a
Consider the unbalanced equation: (a) Balance the equation for this reaction in basic solution.
Problem 141b
Consider the unbalanced equation: (b) Use the data in Appendix B and ΔG°f for IO3-(aq)= -128.0 kJ/mol to calculate ΔG° for the reaction at 25 °C.
Problem 141d
Consider the unbalanced equation: I2(s) → I-(aq) + IO3-(aq) (d) What pH is required for the reaction to be at equilibrium at 25°C when [I-] = 0.10M and [IO3-] = 0.50 M?
Problem 143k
Methanol (CH3OH) 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 (CH4):
Step 1. CO(g) + 2 H2(g) S CH3OH(l) ΔS° = - 332 J/K
Step 2. CH3OH1l2 → CH4(g) + 1/2 O2(g) ΔS° = 162 J/K
(k) Calculate an overall ΔG°, ΔH°, and ΔS° for the formation of CH4 from CO and H2.
Problem 143l
Methanol (CH3OH) 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 (CH4):
Step 1. CO(g) + 2 H2(g) S CH3OH(l) ΔS° = - 332 J/K
Step 2. CH3OH1l2 → CH4(g) + 1/2 O2(g) ΔS° = 162 J/K
(l) Is the overall reaction spontaneous at 298 K?
Problem 143m
Methanol (CH3OH) 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 (CH4):
Step 1. CO(g) + 2 H2(g) S CH3OH(l) ΔS° = - 332 J/K
Step 2. CH3OH1l2 → CH4(g) + 1/2 O2(g) ΔS° = 162 J/K
(m) If you were designing a production facility, would you plan on carrying out the reactions in separate steps or together? Explain.
- For a process to be spontaneous, the total entropy of the system and its surroundings must increase; that is ΔStotal = ΔSsystem + ΔSsurr 7 0 for a spontaneous process Furthermore, the entropy change in the surroundings, ΔSsurr, is related to the enthalpy change for the process by the equa- tion ΔSsurr = - ΔH>T. (b) What is the value of ΔSsurr for the photosynthesis of glu- cose from CO2 at 298 K? 6 CO21g2 + 6 H2O1l2 S C6H12O61s2 + 6 O21g2 ΔG° = 2879 kJ ΔS° = - 262 J>K
Problem 146