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The First Law
Exercises
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermochemical data are for 298.15K.
2.1. Calculate the work needed for a 65 kg person to climb through 4.0 m on the surface of (a) the Earth and (b) the Moon (g= 1.60 ms-2).
Solution: on earth, 2.6 x 103 J, on the moon, 4.2 x 102 J.
2.2. A chemical reaction takes place in a container of cross-sectional area 100 cm2. As a result of the reaction, a piston is pushed out through 10 cm against an external pressure of 1.0 atm. Calculate the work done by the system.
Solution: -1.0 x 102 J
2.3. (a) A sample consisting of 1.00 mol Ar is expanded isothermally at 0°C from 22.4 dm3 to 44.8 dm3 (a) reversibly, (b) against a constant external pressure equal to the final pressure of the gas, and (c) freely (against zero external pressure). For the three processes calculate q, w, ∆U, and ∆H.
Solution: (a) ∆U = ∆H = 0, w = -1.57 kJ, q = + 1.57 kJ;
(b) ∆U = ∆H = 0, w = -1.13 kJ, q = + 1.13 kJ;
(c) ∆U = ∆H = 0, w = 0, q = 0.
2.4. A sample consisting of 1.00 mol of perfect gas atoms, for which Cv,m= R, initially at p1 = 1.00 atm and T1 = 300 K, is heated reversibly to 400 K at constant volume. Calculate the final pressure, ∆U, q, and w.
p2= 1.33 atm, ∆U = + 1.25 kJ, w =0, q = + 1.25 kJ.
2.5. A sample of 4.50 g of methane occupies 12.7 dm3 at 310 K. (a) Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by 3.3 dm3. (b) Calculate the work that would be done if the same expansion occurred reversibly.
Solution: (a) -88 J; (b) -167 J,
2.6. A sample of 1.00 mol H2O(g) is condensed isothermally and reversibly to liquid water at 100°C. The standard enthalpy of vaporization of water at 100°C is 40.656 kJ.mol-1. Find w, q, ∆U, and ∆H for this process.
Solution: ∆H= -40.656 kJ, q = -40.656 kJ, w = +3.10 kJ, ∆U= -37.55 kJ.
2.7. A strip of magnesium of mass 15 g is dropped into a beaker of dilute hydrochloric acid. Calculate the work done by the system as a result of the reaction. The atmospheric pressure is 1.0 atm and the temperature 25°C.
Solution: -1.5 kJ.
2.8. The constant-pressure heat capacity of a sample of a perfect gas was found to vary with temperature according to the expression Cp (J K-1) = 20.17 + 0.3665(T/K). Calculate q, w, ∆U, and ∆H when the temperature is raised from 25°C to 200°C (a) at constant pressure, (b) at constant volume.
Solution: (a) q=∆H=+28.3kJ,w=-1.45kJ, ∆U=+26.8kJ;
(b) ∆H=+28.3 kJ, ∆U=+26.8 kJ, w= 0, q =+26.8 kJ.
2.9. Calculate the final temperature of a sample of argon of mass 12.0 g that is expanded reversibly and adiabatically from 1.0 dm3 at 273.15 K to 3.0 dm3.
Solution: 131 K.
2.10. A sample of carbon dioxide of mass 2.45 g at 27.0°C is allowed to expand reversibly and adiabatically from 500 cm3 to 3.00 dm3. What is the work done by the gas?
Solution: -194J.
2.11. Calculate the final pressure of a sample of carbon dioxide that expands reversibly and adiabatically from 57.4 kPa and 1.0 dm3 to a final volume of 2.0 dm3, Take γ= 1.4.
Solution: 22 kPa.
2.12. When 229 J of energy is supplied as heat to 3.0 mol Ar(g), the temperature of the sample increases by 2.55 K. Calculate the molar heat capacities at constant volume and constant pressure of the gas.
Solution: Cp,m = 30 J K-1mol-1, Cv,m = 22 J K-1mol-1.
2.13. When 3.0 mol O2 is heated at a constant pressure of 3.25 atm, its temperature increases from 260 K to 285 K. Given that the molar heat capacity of O2 at constant pressure is 29.4 J K-1mol-1, calculate q, ∆H, and ∆U.
Solution: qp= +2.2 kJ, ∆H= +2.2 kJ, ∆U = + 1.6 kJ
2.14. A sample of 4.0 mol O2 is originally confined in 20 dm3 at 270 K and then undergoes adiabatic expansion against a constant pressure of 600 Torr until the volume has increased by a factor of 3.0. Calculate q, w, ∆T, ∆U, and ∆H. (The final pressure of the gas is not necessarily 600 Torr.)
Solution: q = 0, w=-3.2 kJ, ∆U=-3.2 kJ, ∆T=-38 K, ∆H= -4.5 kJ
2.15. A sample consisting of 1.0 mol of perfect gas molecules with Cv = 20.8 J K-1 is initially at 3.25 atm and 310 K. It undergoes reversible adiabatic expansion until its pressure reaches 2.50 atm. Calculate the final volume and temperature and the work done.
Solution: Vf = 0.0113 m3, Tf = 344 K, w = 7.1x102 J
2.16. A certain liquid has ∆H = 26.0 kJmol-1. Calculate q, w, ∆H, and ∆U when 0.50 mol is vaporized at 250 K and 750 Torr.
Solution: q = 13.0 kJ, w = -1.0 kJ, ∆U = 12.0 kJ
2.17. The standard enthalpy of formation of ethylbenzene is -12.5 kJmol-1. Calculate its standard enthalpy of combustion.
Solution: -4564.7 kJ mol-1
2.18. The standard enthalpy of combustion of cyclopropane is -2091 kJ.mol-1 at 25°C. From this information and enthalpy of formation data for CO2(g) and H2O(g), calculate the enthalpy of formation of cyclopropane. The enthalpy of formation of propene is +20.42 kJmol-1. Calculate the enthalpy of isomerization of cyclopropane to propene.
Solution: ∆Hf[(CH2)3,g] =+53 kJmol-1, ∆H = -33 kJmol-1
2.19. When 120 mg of naphthalene, C10H8(s), was burned in a bomb calorimeter the temperature rose by 3.05 K. Calculate the calorimeter constant. By how much will the temperature rise when 10 mg of phenol, C6H5OH(s), is burned in the calorimeter under the same conditions?
Solution: ∆U = -5152 kJ rnol-1, C = 1.58 kJ K-l, ∆T= +0.205 K
2.20. Calculate the standard enthalpy of solution of AgCl(s) in water from the enthalpies of formation of the solid and the aqueous ions.
Solution: 65.49 kJ.mol-1
2.21. The standard enthalpy of decomposition of the yellow complex H3NSO2 into NH3 and SO2 is +40 kJmol-1, Calculate the standard enthalpy of formation of H3NSO2.
Solution: -383 kJmol-1
2.22. Given the reactions (1) and (2) below, determine (a) ∆H and ∆U for reaction (3), (b) ∆H for both HCl(g) and H2O(g) all at 298 K.
(1) H2(g) + Cl2(g) → 2HCl(g) ∆H = -184.62 kJmol-1
(2) 2H2(g) + O2(g) → 2H2O(g) ∆H = -483.64 kJmol-1
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The First Law
Exercises
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermochemical data are for 298.15K.
2.1. Calculate the work needed for a 65 kg person to climb through 4.0 m on the surface of (a) the Earth and (b) the Moon (g= 1.60 ms-2).
Solution: on earth, 2.6 x 103 J, on the moon, 4.2 x 102 J.
2.2. A chemical reaction takes place in a container of cross-sectional area 100 cm2. As a result of the reaction, a piston is pushed out through 10 cm against an external pressure of 1.0 atm. Calculate the work done by the system.
Solution: -1.0 x 102 J
2.3. (a) A sample consisting of 1.00 mol Ar is expanded isothermally at 0°C from 22.4 dm3 to 44.8 dm3 (a) reversibly, (b) against a constant external pressure equal to the final pressure of the gas, and (c) freely (against zero external pressure). For the three processes calculate q, w, ∆U, and ∆H.
Solution: (a) ∆U = ∆H = 0, w = -1.57 kJ, q = + 1.57 kJ;
(b) ∆U = ∆H = 0, w = -1.13 kJ, q = + 1.13 kJ;
(c) ∆U = ∆H = 0, w = 0, q = 0.
2.4. A sample consisting of 1.00 mol of perfect gas atoms, for which Cv,m= R, initially at p1 = 1.00 atm and T1 = 300 K, is heated reversibly to 400 K at constant volume. Calculate the final pressure, ∆U, q, and w.
p2= 1.33 atm, ∆U = + 1.25 kJ, w =0, q = + 1.25 kJ.
2.5. A sample of 4.50 g of methane occupies 12.7 dm3 at 310 K. (a) Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by 3.3 dm3. (b) Calculate the work that would be done if the same expansion occurred reversibly.
Solution: (a) -88 J; (b) -167 J,
2.6. A sample of 1.00 mol H2O(g) is condensed isothermally and reversibly to liquid water at 100°C. The standard enthalpy of vaporization of water at 100°C is 40.656 kJ.mol-1. Find w, q, ∆U, and ∆H for this process.
Solution: ∆H= -40.656 kJ, q = -40.656 kJ, w = +3.10 kJ, ∆U= -37.55 kJ.
2.7. A strip of magnesium of mass 15 g is dropped into a beaker of dilute hydrochloric acid. Calculate the work done by the system as a result of the reaction. The atmospheric pressure is 1.0 atm and the temperature 25°C.
Solution: -1.5 kJ.
2.8. The constant-pressure heat capacity of a sample of a perfect gas was found to vary with temperature according to the expression Cp (J K-1) = 20.17 + 0.3665(T/K). Calculate q, w, ∆U, and ∆H when the temperature is raised from 25°C to 200°C (a) at constant pressure, (b) at constant volume.
Solution: (a) q=∆H=+28.3kJ,w=-1.45kJ, ∆U=+26.8kJ;
(b) ∆H=+28.3 kJ, ∆U=+26.8 kJ, w= 0, q =+26.8 kJ.
2.9. Calculate the final temperature of a sample of argon of mass 12.0 g that is expanded reversibly and adiabatically from 1.0 dm3 at 273.15 K to 3.0 dm3.
Solution: 131 K.
2.10. A sample of carbon dioxide of mass 2.45 g at 27.0°C is allowed to expand reversibly and adiabatically from 500 cm3 to 3.00 dm3. What is the work done by the gas?
Solution: -194J.
2.11. Calculate the final pressure of a sample of carbon dioxide that expands reversibly and adiabatically from 57.4 kPa and 1.0 dm3 to a final volume of 2.0 dm3, Take γ= 1.4.
Solution: 22 kPa.
2.12. When 229 J of energy is supplied as heat to 3.0 mol Ar(g), the temperature of the sample increases by 2.55 K. Calculate the molar heat capacities at constant volume and constant pressure of the gas.
Solution: Cp,m = 30 J K-1mol-1, Cv,m = 22 J K-1mol-1.
2.13. When 3.0 mol O2 is heated at a constant pressure of 3.25 atm, its temperature increases from 260 K to 285 K. Given that the molar heat capacity of O2 at constant pressure is 29.4 J K-1mol-1, calculate q, ∆H, and ∆U.
Solution: qp= +2.2 kJ, ∆H= +2.2 kJ, ∆U = + 1.6 kJ
2.14. A sample of 4.0 mol O2 is originally confined in 20 dm3 at 270 K and then undergoes adiabatic expansion against a constant pressure of 600 Torr until the volume has increased by a factor of 3.0. Calculate q, w, ∆T, ∆U, and ∆H. (The final pressure of the gas is not necessarily 600 Torr.)
Solution: q = 0, w=-3.2 kJ, ∆U=-3.2 kJ, ∆T=-38 K, ∆H= -4.5 kJ
2.15. A sample consisting of 1.0 mol of perfect gas molecules with Cv = 20.8 J K-1 is initially at 3.25 atm and 310 K. It undergoes reversible adiabatic expansion until its pressure reaches 2.50 atm. Calculate the final volume and temperature and the work done.
Solution: Vf = 0.0113 m3, Tf = 344 K, w = 7.1x102 J
2.16. A certain liquid has ∆H = 26.0 kJmol-1. Calculate q, w, ∆H, and ∆U when 0.50 mol is vaporized at 250 K and 750 Torr.
Solution: q = 13.0 kJ, w = -1.0 kJ, ∆U = 12.0 kJ
2.17. The standard enthalpy of formation of ethylbenzene is -12.5 kJmol-1. Calculate its standard enthalpy of combustion.
Solution: -4564.7 kJ mol-1
2.18. The standard enthalpy of combustion of cyclopropane is -2091 kJ.mol-1 at 25°C. From this information and enthalpy of formation data for CO2(g) and H2O(g), calculate the enthalpy of formation of cyclopropane. The enthalpy of formation of propene is +20.42 kJmol-1. Calculate the enthalpy of isomerization of cyclopropane to propene.
Solution: ∆Hf[(CH2)3,g] =+53 kJmol-1, ∆H = -33 kJmol-1
2.19. When 120 mg of naphthalene, C10H8(s), was burned in a bomb calorimeter the temperature rose by 3.05 K. Calculate the calorimeter constant. By how much will the temperature rise when 10 mg of phenol, C6H5OH(s), is burned in the calorimeter under the same conditions?
Solution: ∆U = -5152 kJ rnol-1, C = 1.58 kJ K-l, ∆T= +0.205 K
2.20. Calculate the standard enthalpy of solution of AgCl(s) in water from the enthalpies of formation of the solid and the aqueous ions.
Solution: 65.49 kJ.mol-1
2.21. The standard enthalpy of decomposition of the yellow complex H3NSO2 into NH3 and SO2 is +40 kJmol-1, Calculate the standard enthalpy of formation of H3NSO2.
Solution: -383 kJmol-1
2.22. Given the reactions (1) and (2) below, determine (a) ∆H and ∆U for reaction (3), (b) ∆H for both HCl(g) and H2O(g) all at 298 K.
(1) H2(g) + Cl2(g) → 2HCl(g) ∆H = -184.62 kJmol-1
(2) 2H2(g) + O2(g) → 2H2O(g) ∆H = -483.64 kJmol-1
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