DICUANGCO, Sarah Jane A.2010106946 Quiz no.3 1. One mole of a perfect gas contained in a 10-L vessel at 27°C is permitted to expand freely into an evacuated vessel of 10-L capacity so that the final volume is 20-L. What is the change in entropy (in Joules) accompanying the process? (Note that for this process q=0 because w=0 for an expansion against a vacuum and that ΔU=0 for an ideal gas.) a. 0 b. 5.76 c. 8.31 d. 12.56 2. Calculate the change in entropy (in J/K) involved in heating 2 moles of an ideal gas from a volume of 100 L at 50°C to a volume of 150 L at 150°C. Cv = 7.88 cal mol-1 K-1. a. 5.5 b. 11.0 c. 24.0 d. 24.5 3. The atomic heat capacity of solid Mo is given by the equation Cp= 5.69 + 1.88 x 10-3T – 0.503 𝑥 105 𝑇 2 Find the change in entropy (in eu) which accompanies the heating of one mole of Mo from 0°C to its melting point 2620°C. (An entropy unit, eu, is equal to 1 cal/K-1) a. 13.7 b. 18.6 c. 25.3 ANSWER: NONE OF THE CHOICES. 18.02 d. 28.9 4. Three moles of N2 (g) , originally at 1atm pressure, are mixed isothermally with 5 moles of H2(g) , also at 1 atm pressure, to yield a mixture whose total pressure is 1 atm. What is the molar entropy of mixing (in J mol-1 K-1)? a. 3.36 b. 4.98 c. 5.50 d. 6.56 5. Repeat problem 4 on the basis that the total pressure of the mixture is 10 atm. a. -65.6 b. 40.5 c. 73.7 d. -109.1 6. Stream is condensed at 100°C and the water is cooled to 0°C and frozen to ice. What is the molar entropy change of water in kJ mol-1 K-1 ? Consider that the average specific heat of liquid water is 4.2 J K-1 g-1 . The enthalpy of vaporization at the boiling point and the enthalpy of fusion at the freezing point are 2258.1 and 333.5 J g-1 , respectively. a. -57.9 b. -90.0 c. -121.7 d. -154.4 ANSWER: NONE OF THE CHOICES. -0.154.4 KJ/mol 7. The purest acetic acid is often called glacial acetic acid because it is purified by fractional freezing at its melting point of 16.6°C . A flask containing several moles of acetic acid at 16.6°C is lowered into an ice-water bath briefly. When it is removed it is found that exactly 1 mole of acetic acid has frozen. Given: ΔHfus(CH3CO2H)= 11.45 KJ mol-1 and : ΔHfus (H2O)= 5.98 KJ mol1 . What is the entropy change (in J K-1) for the combined system? a. 1.67 b. 1.98 c. 2.40 d. 2.75 and complete a cycle with the two paths plus one isothermal path. (c) ΔH.8L is allowed to expand irreversibly into and evacuated vessel such that the final volume total volume total volume is 228 L.4 B. 0. Assuming a constant molar volume. (h) ΔH.6 b. (d) ΔG.7 c. and (j) ΔS for the gas. . respectively? a.0 g cm-3? a. Calculate (k) ΔS for the system and its surroundings involved in the reversible isothermal expansion and calculate (l) ) ΔS for the system and its surroundings involved in the irreversible isothermal expansion. When a liquid is compressed its Gibbs energy is increased. Cp ln (1/2) b. Metal block 1 and block 2 at temperatures T K and 2T K . (g) q .8 9. and (e) ΔS for the gas.4 d. Prove that two adiabatic paths can never cross. 2. One mole of a perfect gas in 22. ) 10pts. -63. respectively. Calculate (f) w . Calculate (a) w . 5.3 and 38 J mol-1 K-1. what is the change in Gibbs energy (in k J mol-1) for liquid water when it is compressed from 1 bar to 1000 bar? Assume that water has a density of 1. 1. (b) q . Calculate the molar Gibbs energy of fusion (in J mol-1) when supercooled water at -3°C freezes at constant T and P. 1. (i) ΔG. were allowed to equilibrate to the same temperature. 20pts. Derive the relationship ( 𝜕𝑆 ) 𝜕𝑉 𝑈 𝜕𝑈 ) 𝜕𝑃 𝑇 = 𝑉(𝜅𝑃 − 𝛼𝑇) = 𝑃 𝑇 and confirm that it applies to a perfect gas. Assume that the energy of the system under consideration is a function of temperature only. One mole of a perfect gas expanded isothermally and reversibly at 0°C from 1 to 1/10 bar.8 d. -5. -45. If the Gibbs energy varies with temperature according to 𝐺 𝑇 = 𝑎 + + 𝑇 𝑏 𝑐 𝑇 2 How will the enthalpy and entropy vary with temperature? Check that these three equations are consistent. Cp ln (9/8) 10.8. Cp ln (9/4) d. Consider the changes accompanying each stage of the cycle and show that they conflict with the Kelvin Statement of the Second Law. The heat capacities of water and ice in the vicinity of the freezing point are 75. 2. 1. 10pts. 3. Derive the thermodynamic equation of state ( 4. 6 b. (Hint: Suppose that two such paths can intersect. What is the change in entropy associated with the process given that block 1 and block 2 are of the same sizes and are made from the same material? a. Cp ln (3/8) c. The enthalpy fusion of ice is 6000 J mol-1 at 0°C. Comment on the values obtained. -23.2 c. 5°C and the standard enthalpy of transition is 509 kJ mol-1.6.28 kJ K-1 mol-1 and can be assumed to be independent of temperature . The protein lysozyme unfolds at a transition temperature of 75. . Calculate the entropy of unfolding lysozyme at 25°C given that the difference in constant-pressure heat capacities upon unfolding is 6.