LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

M.Sc., DEGREE EXAMINATION – CHEMISTRY

 SECOND SEMESTER – NOVEMBER 2003

CH-2800/815  – THERMODYNAMICS & STATISTICAL MECHANICS

28-10-2003                                                                                                     Max:100 marks

1.00 – 4.00

 

PART – A                                           (10×2=20 marks)

Answer ALL questions.

 

1. If V = for 1mole of an ideal gas show that dV is a complete differential.
2. K_p for the reaction at 500^oC is 3.99×10^-3 atm^-1 Calculate DG^o for the reaction.
3. Show that .
4. What is chemical potential? Is it extensive or intensive?
5. How many components are present in a system in which NH₄Cl (s) undergoes thermal decomposition?
6. Calculate the number of ways of distributing 20 identical objects with the arrangement 1, 0, 3, 5, 10, 1.’
7. What is the significance of partition function?
8. What is the residual molar entropy of CO at T = O?
9. Identify the systems for which it is essential to include a factor of on going from molar partition function to molecular partition function a) a sample of CO₂ (g) b) water vapour.
10. Calculate the ratio of the translation partition functions of D₂ and H₂ at the same temperature and pressure.

 

PART – B                                           (8×5=40 marks)

Answer any EIGHT questions.

 

11. Derive expressions for isothermal reversible expansion of 1 mol of Vander Waal’s gas for a) W b) D
12. DS of a solid in cal/k/mole is given by the equation C_p = 6.2 + 1.3 x 10^-3T in the temperature range 27^oC to 600^o Calculate DS when 1 mole of this metal is heated from 300 k to 600 k.
13. Derive any two Maxwell equations.
14. The volume of an aqueous soltuon of NaCl at 25^oC was measured in series of molalities (m) and it was found that the volume fitted the expression

V (CC) = 1003 + 16.62m + 1.77 m^3/2 + 0.km² where V is the volume of a solution of molality 1.  Calculate the partial molar volume of a the components in a solution of molality 0.1.

15. 325 g of N₂O₄ when heated was found to occupy a volume of 500 ml at 45^oC and at 800 mm Hg pressure Calculate i) Kp ii) pressure at which the degree of dissociation is 50%.
16. Explain how partition functions can be separated.
17. Calculate the standard molar entropy of Xenon gas at 100 K.
18. Calculate the electronic partition function of a Tellurium atom at 500 K using the following data.

Term                Degeneracy                 Wave number (cm^-1)

 

Ground                 5                                     0

1                      1                                   4707

2                      3                                   4751

3                      5                                 10559

19. Explain how the absolute entropy of a gas at 25^oC can be determined using third law of thermodynamics.
20. Compare Maxwell – Bolltzmann, Fermi – Dirac and Bose – Einstein statistical distributions.
21. Calculate the molecular rotational partition function for N₂ (g) at 27^o

(I = 13.9 x 10^-47 kgm^-2).

22. Derive an expression for transnational partition function.

 

 

PART – C                                           (4×10=40 marks)

Answer any FOUR questions.

 

23. a) Derive Gibbs – Duhem equation.
24. b) Show that for 1 mole of a van der waal’s gas.
25. a) Explain how activity coefficient of an electrolyte be determined using EMF data.
26. b) Derive thermodynamically phase rule equation.
27. a) The virial equation of state for N₂(g) at O^oC is

PV = RT – 1.051 x10^-2 P + 8.63 x 10^-5 P² + ….

Where P is in atm; V is in litres.  Find the fugacity of N₂ at O^oC and 100 atm.

pressure.

1. b) Deduce the expression for the variation of chemical potential with i) temperature ii)

pressure.

26. State the postulates of Maxwell – Boltzmann statistics and hence derive an expression for the most probable distribution.
27. Compare Einstein’s theory of heat capacity of solids with Debye’s theory.
28. a) Explain how equilibrium constant of a reaction be obtained using statistical mechanics.
29. b) Explain transition state theory using statistical concepts.
30. a) Derive the relation

E = .

1. b) Calculate the vibrational contribution to the entropy of Cl₂ at 500K if the wave

number of the vibration is 560 cm^-1.

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

LM 34

SECOND SEMESTER – APRIL 2007

CH 2810 – THERMODYNAMICS AND STATISTICAL MECHANICS

 

Date & Time: 21/04/2007 / 1:00 – 4:00    Dept. No.                                            Max. : 100 Marks

 

 

PART A

Answer ALL the questions.                                                    (10 x 2 = 20 Marks)

1. Calculate the fugacity of H₂ at 100⁰C and 300 atm. The density of H₂ at the above conditions is 16.79 g dm^-3.
2. Show that m_i (Chemical potential) = (dH/dn_i)_P,S,,nj
3. A 4.84 molal aqueous solution of a non-volatile solute has a vapour pressure of 18.5 mm of

Hg at 25⁰C.  At the same temperature the vapour pressure of the pure water is 23.6 mm of Hg.  Assuming that the water vapour behaves ideally, calculate the activity and the activity coefficient of water (g _x) in the given solution.

4. The equilibrium constant for the reaction, C(s)+CO₂(g) Û2CO(g) is 4.28 x 10^-3 atm at 1200 K. If the partial pressure of CO₂ is 1.2 atm, calculate partial pressure of CO.
5. What is Onsager theory?
6. State Sterling’s approximation and hence evaluate ln N!, when N = 10³⁰
7. What is the significance of partition function?
8. Using equipartition principle, evaluate C_V for PH₃(g) if R=2 cal K^-1 mol^-1.
9. Calculate the number of ways of distributing three particles among four energy levels if the particles obey Pauli’s exclusion principle.
10. What is thermionic emission?

 

PART – B

Answer ANY EIGHT questions                                            (8 x 5 = 40 Marks)

11. Explain the significances of the Ellingham Diagram.

 

12. Draw and explain the phase diagram of a three component system consisting of two solids (B and C) and water with the formation of a salt hydrate (B.nH₂O)

 

13. Calculate the fugacity of H₂ at 200 atm and 300 K if the fugacity at 25 atm and 300 K is 25.2 atm. The van der Waals constants are a=0.245 l² atm mol^-2 and b = 2.67×10^-2 l mol^-1

 

14. The dissociation of N₂O₄(g) takes place according to the equation, N₂O₄(g) Û 2NO₂(g). At 300 K, 0.92 g of N₂O₄ contained in a flask of 1.64 litre capacity was found to have a total pressure of 137 mm of Hg.  (i) Calculate the degree of dissociation at this temperature and pressure (ii) Calculate the value of K_P at the above conditions.

 

15. Explain the determination of activity coefficient of using solubility product.

 

16. Write a note on entropy production and entropy flow in the open system using the principles of non-equilibrium thermodynamics.

 

 

17. Explain how partition functions are separated?

 

18. Two of the energy levels of a molecule are e₁ = 6 x 10^-21 J and e₂ = 8.4 x 10^-21 J, the corresponding degeneracies being g₁ = 3, g₂=5. What is the ratio of the distribution numbers in an assembly of molecules at 3000 K?
19. The vibrational frequency of Cl₂ molecule is 1.66 x 10¹³ s^-1. Calculate Q_vib and the vibrational partition function at 300 K
20. Compare the three statistical distributions.
21. Calculate the equilibrium constant for the reaction S₂(g) à 2S at 2000 K. The dissociation energy is 429.7 kJ mol^-1 and the free energy function at 2000 K for S(g) and S₂(g) are – 191.4 and –265.5 J K^-1 mol^-1.

 

22. Show that the rotational energy of a diatomic molecule is equal to RT.

 

PART – C

Answer ANY FOUR questions                                              (4 x 10 = 40 Marks)

23. a) How will you determine the activity coefficient of the solvent knowing the activity of the solute?                                                                                                                                (5)

 

1000. b) Consider a hypothetical solute in 1 kg of water. The volume V(ml) at 25⁰C  and 1 atm is represented as, V = 1000.38 + 20.563 m₂ + 2.024 m₂² – 0.24 m₂³ . Derive the expression for the partial molal volume of the solute and calculate its value at 1 molal solution.                                                                                                                                                                     (5)
1001. a) Explain Lever Rule                                                                                                                   (3)
1002. b) Using the principle of microscopic reversibility, prove the Onsager’s reciprocal relation.                                                                                                                                                             (7)
1003. For the reaction 2HCl(g)+1/2 O₂(g) ó   H₂O(g) + Cl₂(g),     DH⁰_{298 K} = -57.2 kJ mol^-1,

DG⁰_{298 K} = -38.07 kJ mol^-1.  Compute the value of K_P at 500 K. C_{P (HCl)} (J K^-1 mol^-1) =

28.16 + 1.8 x 10^-3 T, C_{P (O2)} (J K^-1 mol^-1) = 25.48 + 13.6 x 10^-3 T, C_{P (H2O)} (J K^-1 mol^-1) =

30.21 + 9.92 x 10^-3 T and C_{P (Cl2)} (J K^-1 mol^-1) = 31.71 + 10.12 x 10^-3 T

 

26. a) Write Sackur-Tetrode equation and explain its significance                                              (5)
27. b) Show that the translational energy is equal to 3/2 RT.                                                              (5)

 

27. Explain the salient features of Debye’s theory of heat capacity of solids. Compare it with Einstein’s theory.

 

28. Explain an two of the following:
29. a) Statistical formulation of ARRT

1. Bose-Einstein distribution law
2. Residual entropy

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

GH 32

M.Sc. DEGREE EXAMINATION – CHEMISTRY

SECOND SEMESTER – APRIL 2008

    CH 2810 – THERMODYNAMICS AND STATISTICAL MECHANICS

 

 

 

Date : 24/04/2008            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART A

Answer ALL the questions.                                                    (10 x 2 = 20 Marks)

 

1. Show that m_i (Chemical potential) = (dE/dn_i)_S,V,nj
2. Give the cause and the manifestation of Peltier effect.
3. The mean ionic activity coefficient g_±for Al₂(SO₄)₃ in 0.1 m solution at 25⁰C is 0.13. Find m_± and a_±
4. For the reaction, CuSO₄.3H₂O(s) ⇌ CuSO₄.2H₂O(s) + H₂O(g). The equilibrium pressure is 7.37 ´ 10^-3 atm at 25°  Calculate DG⁰ for the reaction at 25°C.
5. Write down the Onsager relationship between the forces and the flux, when three fluxes (J_1, J₂ and J₃) and the conjugate forces (X₁, X₂ and X₃) are coupled.
6. Calculate the ratio of number of ways of distributing particles at 25⁰C if the energy levels are separated by 10 kJ /mol
7. Evaluate ln N!, when N = 10 using Stirling’s formula and calculate the % error introduced by this formula.
8. At what temperature Q_vib = 10 for N₂? (= 2355 cm^-1)
9. Calculate C_V of PH₃ (g) using equipartition principle.(R=8.314 J K^-1 mol^-1)
10. What is meant by residual entropy?

PART – B

Answer ANY EIGHT questions                                            (8 x 5 = 40 Marks)

 

11. Explain the use of Ellingham Diagram with reference to the extraction of metals.
12. Calculate the fugacity of H₂ at 100 atm and 298 K if the fugacity at 25 atm and 298 K is 25.4 atm. The van der Waals constants are a=0.245 l² atm mol^-2 and b = 2.67 x 10^-2 l mol^-1.
13. Partial molar volume of methanol in a methanol-water solution in which the mole fraction of methanol is 0.39, is 39.2 cm³ mol^-1. If the density of the solution is 0.91 g cm^-3, calculate the partial molar volume of water in the solution
14. With the help of a phase diagram, explain fractional distillation of a non-ideal solution consisting of a minimum boiling point mixture of water and ethyl acetate.
15. How are mass and energy conserved in irreversible thermodynamics?
16. Explain the entropy production when heat is flowing into a system.
17. Explain how partition functions can be separated.
18. Calculate the translational entropy of HCl(g) at 298 K and at 1 atm pressure.
19. Derive the general relation connecting Helmholtz free energy ‘A’ and molecular partition function (Q)
20. One vibrational mode in CO₂ molecule has a frequency 672 cm^-1 and it is doubly degenerate. Calculate Q_vib for this mode at 298 K.
21. Derive an expression for rotational partition function for a diatomic molecule.
22. Compare the three statistical distributions.

PART – C

Answer ANY FOUR questions                                              (4 x 10 = 40 Marks)

 

23       a)    How will you apply the Nernst distribution law for the determination of the activity of a solute?                                                                                                  (5)

20. b) Consider a hypothetical solute A and when n₂ moles of A is dissolved in 1000 g of water, the  DH can be expessed as, DH = 20.5 m₂ + 8.4 m₂².  Calculate L₂ and L₁ for 1 molal solution.
21. a) One mole of each of N₂ and H₂ are allowed to react in a closed container at 10 atm pressure and 725 K. The formation of NH₃ is given by the equation,  ½ N₂(g)+3/2 H₂(g) ⇌  NH₃(g). The reaction is allowed to attain equilibrium. On analysis, 0.033 moles of NH₃ was found to be formed at equilibrium. Calculate the value of Kp at 725 K.
22. b) Draw and explain the phase diagram of a three component system involving two solids (B and C) and water (A) in which only pure components crystallize from aqueous solutions.
23. a) State the postulates of irreversible thermodynamics.                                           (3)
24. b) How will you verify Onsager’s reciprocal relationship experimentally using Elecrokinetic effects?
25. Explain the postulates of Maxwell-Boltzmann distribution and hence derive an expression for most probable distribution.
26. Explain the postulates of Einstein’s theory of heat capacity of solids. Compare it with Debye’s theory.
27. Give an account of any two of the following             a)  Application of Bose-Einstein statistics           b)  Equipartition principle
28. c) Significance of partition function d)  Expression for vibrational entropy

 

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WD 33

     LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

SECOND SEMESTER – April 2009

          CH 2816 / 2810 / 2800 – THERMODYNAMICS AND STATISTICAL MECHANICS

 

 

 

Date & Time: 24/04/2009 / 1:00 – 4:00  Dept. No.                                                   Max. : 100 Marks

 

 

PART A

Answer ALL the questions.                                                          (10 x 2 = 20 Marks)

1. How does chemical potential vary with pressure?
2. State any one of the formulations of Konowaloff’s rule.
3. For the reaction, NH₄HS(s) = NH₃(g) + H₂S(g), the equilibrium pressure at 298 K was found to be 0.67 atm.  Calculate K_P of the reaction at 298 K.
4. The vapour pressures of pure A and B at 25⁰C are 250 mm of Hg and 400 mm of Hg respectively. A solution in which the mole fraction of A is 0.7 has a vapour pressure of 100 mm of Hg at 25⁰ Calculate the activity coefficient (g_x) of A in the given solution.
5. Give the basic postulates of irreversible thermodynamics.
6. What is Stirling’s approximation? Evaluate ln N! when N = 10⁴⁰
7. Calculate the number of ways of distributing 5 particles among 6 energy levels if the particles are a ) electrons b) Bosons
8. What is the approximate value of ∆S^o for the reaction,  ³⁵Cl³⁵Cl(g) + ³⁷Cl³⁷Cl(g) à  2 ³⁵Cl³⁷Cl assuming that any difference in the molar masses, moments of inertia and vibrational energy levels are negligible for the isotopes?
9. A system consisting of two energy states separated by 2×10^-23 J has a ratio of particles in each state of 51/49, what is the temperature of the system?
10. “Einstein’s introduction of quantisation accounted for the heat capacity of solids at room temperatures.” Explain.

 

PART – B

Answer ANY EIGHT questions                                            (8 x 5 = 40 Marks)

11. Draw and explain the phase diagram of a three component system consisting of two solids (B and C) and water with the formation of a salt hydrate (B.nH₂O).
12. A 1:2 salt has a solubility of 1.545 x 10^-5 moles lit^-1 at 25⁰ Calculate its mean ionic activity coefficient (a) in the absence of any electrolyte and  b) in the presence of 0.01 M BaCl₂.
13. The dissociation of N₂O₄(g) takes place according to the equation, N₂O₄(g) Û 2NO₂(g). 548 g of N₂O₄ when heated was found to occupy a volume of 600 ml at 323 K and at a pressure of 850 mm of Hg.  Calculate the value of K_P at the above conditions.
14. Explain the entropy production when current is flowing through a wire.
15. Show that the phenomenological coefficients must satisfy the following conditions:

L₁₁>0, L₂₂>0 and (L₁₂ + L₂₁)² < 4 L₁₁ L₂₂

 

16. Calculate the fugacity of H₂ at 100⁰C and at 300 atm for a van der Waals gas. (a=0.2244 dm⁶ atm mol^-2,

b = 0.0266 dm³ mol^-1 and V = 0.119 dm³ mol^-1 )

17. Derive an expression for molecular translational partition function.
18. Calculate the value of molecular vibrational partition function for N₃(g) at 298 K. w₁ = 1800 cm^-1, w₂ = 500 cm^-1, g₂ = 2 and w₃ = 1200 cm^-1.
19. Calculate the rotational contribution to entropy for O₂(g) at 25⁰ C( I = 1.937 x 10^-46 kg m²)
20. Compare Debye’s theory of heat capacity of solids with Einstein’s theory.
21. Calculate the equilibrium constant for the reaction C₆H₅CH₂CH₃ ó C₆H₅CH=CH₂ + H₂ at 500 K from the following data:  G⁰-H⁰/T for         H₂ is -27.947 cal K^-1 mole^-1, for styrene    – 74.44 cal K^-1 mole^-1 and for ethyl bnzene – 79.64 cal K^-1 mole^-1.  (∆H⁰_f)₀ for Styrene and ethyl benzene are 40.34 and 13.917 k cal/ mol respectively.
22. Write Sackur-Tetrode equation and deduce the factors affecting S_transl.

PART – C

Answer ANY FOUR questions                                              (4 x 10 = 40 Marks)

23. a) Derive Gibbs-Duhem equations.                                                                     (6)
24. b) When a solute is dissolved in 1 Kg of water, the volume V(ml) at 25⁰C and 1 atm is represented as, V = 1000.3 + 20.7 m₂ + 2.5 m₂². Calculate the partial molal volume of the solute and that of the solvent in 1 molal solution.                                              (5)
25. a) A gas obeys the equation of state P(V-b)=RT. For this gas b = 0.0391 dm³ mol^-1. Calculate the fugacity coefficient at 1000 K and 100 atm pressure.                                      (3)
26. b) How is Onsager’s reciprocal relationship verified experimentally by thermoelectric method?                                                                                                                      (7)
27. For the reaction H₂S(g)+3/2 O₂(g) ó H₂O(g) + SO₂(g),     DH⁰_{298 K} = -518.62 kJ mol^-1,            DG⁰_{298 K} = -495.95 kJ mol^-1.  Compute the value of K_P at 773 K from the C_P data in J K^-1 mol^-1  C_{P (H2S)} = 26.722 + 23.87 x 10^-3 T, C_{P (O2)}= 25.51 + 13.62 x 10^-3 T, C_{P (H2O)} = 30.21 + 9.93 x 10^-3             T and C_P (SO₂) = 25.72 + 57.92 x 10^-3 T
28. a) Explain the theory of reaction rates using statistical mechanics. (5)
29. b) Derive an expression for E_vib for a harmonic oscillator and show that it reduces to RT at moderate temperatures                                                                                                            (5)
30. Derive Fermi-Dirac distribution law and show that the Maxwell-Boltzmann distribution law is the classical limit of Fermi-Dirac distribution law             (6+4)
31. a) Deduce the equation of state for 1 mole of an ideal gas using the definition of partition function and its relation to pressure of the gas                         (6)
32. b) Explain the properties of liquid helium using the appropriate statistical distribution.(4)

.

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

SECOND SEMESTER – APRIL 2012

CH 2816/2810 – THERMODYNAMICS AND STATISTICAL MECHANICS

 

 

Date : 21-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART A

Answer ALL the questions:                                                                                       (10 x 2 = 20 Marks)

1. Show that m_i (Chemical potential) = (dU/dn_i)_S,V,nj
2. What are the conditions for the uncoupled chemical reactions in terms of forces and fluxes and phenomenological coeffcients?
3. Explain Soret effect.
4. The partial molar volume of glycerol in a glycerol-water solution (the mole fraction of glycerol is 0.5), is 72.8 cm³ mol^-1 at 15.6⁰ If the total volume of the solution is 45.05 cm³, calculate the partial molar volume of water in the solution.
5. Calculate the mean activity coefficient 0.1 m CaCl₂ (aq) at 25^O
6. Calculate the number of ways of distributing 20 identical objects with the arrangement {1,0,3,5,10,1}
7. Differentiate thermodynamic probability from mathematical probability.
8. Evaluate the characteristic vibrational Einstein temperature for diamond if ν = 46.5 x 10¹²
9. What is residual entropy? Give one example.
10. Mention four phenomena that cannot be explained by Maxwell-Boltzmann statistics.

                      PART – B

Answer ANY EIGHT questions:                                                                             (8 x 5 = 40 Marks)

11. Draw and explain the isobaric fractional distillation of a non-ideal solution of water and nitric acid exhibiting maximum boiling point.
12. The apparent molal heat capacityF_C of an aqueous solution of a glucose as a function of molality is given by F_C (J K^-1 mol^-1) = 633.9 + 4.728 m – 0.195 m². Calculate the partial molar heat capacity of the glucose and that of water in 1 molal solution. The heat capacity of pure of water is 75.31  J K^-1 mol^-1.
13. State Konowaloff^’s rule and derive it thermodynamically.
14. Discuss the application of irreversible thermodynamics to biological systems.
15. Write about the entropy production in an open system.
16. How is fugacity of a gas determined?
17. Compare the three statistical distributions.
18. Calculate the vibrational contribution to the energy of Cl₂(g) at 500 K if the vibrational frequency is 560 cm^-1.
19. Show that rotational energy of diatomic rigid rotor is equal to RT per mole.
20. State and explain Nernst heat theorem.
21. A certain atom has a three fold degenerate electronic ground level, a non-degenerate excited state at 3500 cm^-1 and a three fold degenerate level at 4700 cm^-1. Calculate the electronic partition function at 1900 K.
22. Calculate the equilibrium constant (K_P) for the reaction S₂(g) ó 2 S(g) at 2000 K. The dissociation energy of S₂ found spectroscopically is 429.7 kJ/mol and the free energy functions for S(g) and S₂(g) are – 1941.4 and – 265.5 J K^-1 mol^-1 respectively? Also calculate K_C for the same reaction.

             PART – C

Answer ANY FOUR questions:                                                                                  (4 x 10 = 40 Marks)

23. a) Derive Gibbs-Duhem equations                                                                                                                              (6)
24. b) When n₂mol of a solute A is dissolved in 1 kg of water, DH can be expressed as,

DH (J mol^-1) = 20.5 m₂ + 8.4 m₂².  Calculate  when m₂ = 2                                                      (4)

24. a) Draw and explain the phase diagram of a ternary system consisting of two solids A and B and water forming a ternary compound.                                (5)
25. b) How will you determine the partial molar volumes in solutions of liquids by measuring the densities at different concentrations?                                          (5)
26. a) What is Onsager reciprocal relation?                  (2)
27. b) Prove the Onsager reciprocal relation by the principle of microscopic reversibility.                 (8)
28. Derive the following:
29. a) Sackur-Tetrode equation    (5)
30. b) Molecular translational partition function    (5)
31. Explain any two of the following:             (5+5)
32. a) Macro states and micro states
33. b) Dependence of fugacity on temperature
34. c) Application of Bose-Einstein statistics
35. d) Separation of partition functions
36. a) Explain Einstein’s theory of heat capacity of mono atomic crystals and hence derive an expression for C_V(vibration) as per this theory.                                                                             (6)
37. b) Compare Einstein’s theory with Debye’s theory of heat capacity of crystals.                              (4)

 

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