final_2004_solutions

# final_2004_solutions - MS&E 303 – Fall 2004 Final...

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Unformatted text preview: MS&E 303 – Fall 2004 Final Exam (2.5 hours) Solutions 1. (10 points) Short, quick answers. (a) What is activity? The correction necessary to move the chemical potential from a reference state to the actual conditions. G A = G o A + RT ln a A (b) What is the difference between the chemical potential and the partial molar free energy? None. (c) What is Δ g for the reaction Si+O 2 ⇔ SiO 2 ? Zero (d) What is the activity coefficient of an ideal solution? 1.0 2. (15 points) SiCl 4 is normally a liquid at room temperature. Carol, in order to potentially create a solid, applied a pressure of 100 atm. Assuming that she was unsuccessful, estimate the change in the molar enthalpy of formation [ie. Δ H f 298 ( 100 atm )- Δ H f 298 ( 1 atm ) ]. Need only to integrate how the enthalpy changes with pressure, in this case the enthalpy difference for the reaction Si( s ) + 2Cl 2 ⇒ SiCl 4 (l). We can treat Δ H f exactly the same as a normal enthalpy. Δ[Δ H f ] = Z 100 atm 1 atm ∂ Δ H f ∂P ¶ T dP ≈ ∂ Δ H f ∂P ¶ T Δ P ∂H ∂P ¶ T = ∂H ∂P ¶ S + ∂H ∂S ¶ P ∂S ∂P ¶ T = V- T ∂V ∂T ¶ P = V (1- αT ) ∂ Δ H f ∂P ¶ T = V SiCl 4 (1- α SiCl 4 T )- V Si (1- α Si T )- 2 V Cl 2 (1- α Cl 2 T ) For Cl 2 , as an ideal gas α = 1 /T and so the term is zero. The 1- αT is a minimal correction for Si and SiCl 4 , but can be included or not. ∂ Δ H f ∂P ¶ T = (114 . 6 cm 3 /mole)(1- (1 . 3 × 10- 5 )(298))- (12 . 02 cm 3 /mole)(1- (7 × 10- 6 )(298)) = 102 . 16 cm 3 /mole = 1 . 021 × 10- 4 m 3 /mole Δ[Δ H f ] ≈ ∂ Δ H f ∂P ¶ T Δ P = (1 . 021 × 10- 4 m 3 /mole)(1 . 01 × 10 7 Pa) = 1 . 03 × 10 3 J/mole 3. (15 points) A small glass vial containing 100 cm 3 of liquid SiCl 4 is held in a 10 liter secondary containment vessel under isothermal conditions at 40 o C. The secondary containment vessel is initially evacuated to near zero pressure. At time zero, the vial is broken and the system is allowed to come to equilibrium. Determine the amount of heat exchanged with the environment and the irreversible entropy created in the universe as a consequence of this process. Clearly identify any assumptions used to solve the problem....
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final_2004_solutions - MS&E 303 – Fall 2004 Final...

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