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1. Starting with the definition of the Helmholtz Energy: A U-TS , determine an expression for...
3. [10 marks] We've covered the definition of Gibbs free energy, Helmholtz free energy, entropy, and...
3. [10 marks] We've covered the definition of Gibbs free energy, Helmholtz free energy, entropy, and enthalpy. There is also something called their fundamental equations. a) [8 marks] Use online resources and your peers to determine the total differential form of each of these terms. For example, if we're looking at Gibbs free energy, defined as G = H – TS, then determine what dG would be. b) [2 marks] Why is it useful to use this form? c) [+2...
A=U-TS is Helmholtz free energy, which is commonly used in statistical thermodynamics. Starting from dU=TdS-pdV, show...
A=U-TS is Helmholtz free energy, which is commonly used in statistical thermodynamics. Starting from dU=TdS-pdV, show that dA=-SdT-pdV
2. (25 pts) Derive the (a) Maxwell relation for the Helmholtz Free Energy F=U-TS. Show ALL...
2. (25 pts) Derive the (a) Maxwell relation for the Helmholtz Free Energy F=U-TS. Show ALL steps and justifications in your derivation. Using your result in (a) comment on how (b) the entropy behaves for an isothermal expansion of an ideal gas. Finally, show the validity of the following equations (c) U = F-TOOF) -T2 and at (T) 01 (d) C =-1(
3. Derive the following relationship between the Helmholtz free energy F and the partition function Z for a system of N particles: (a) Starting with the thermodynamic definition F-U-TS, substitute th...
3. Derive the following relationship between the Helmholtz free energy F and the partition function Z for a system of N particles: (a) Starting with the thermodynamic definition F-U-TS, substitute the statistical mechanics results which give U and S in terms of occupation numbers n, state energies e and the most probable number of microstates t* to find, (b) Write out texplicitly in terms of occupation numbers using Stirling's approxima- tion (check the Lagrange multiplier derivation of the Boltzmann distribution)...
5. (25 points For credit; show every step in the derivations. (a) Starting with the Fundamental...
5. (25 points For credit; show every step in the derivations. (a) Starting with the Fundamental Equation for U determine the associated partial derivatives for T and P. Next, determine the associated Maxwell Relation. (b) Starting with the Helmholtz free energy (A = U – TS) derive the associated Fundamental Equation and identify the partial derivative relationships for P and S. Then derive the associated Maxwell Relation.
CHEM 351 Biochemistry I - Fall 2018 Study Problems for Metabolism and Glucose Catabolism For the...
CHEM 351 Biochemistry I - Fall 2018 Study Problems for Metabolism and Glucose Catabolism For the reaction: aA + bB =cC + dD Gibbs free energy: AG = AG" + RT IN THE glucose + glucose 6-phosphate + H20 1. The equilibrium constant for phosphorylation of glucose is: Ke = 3.97 x 10- a. Calculate the standard Gibbs free energy for the uncatalyzed reaction. b. Use the physiological concentrations for glucose (2.0 mm) and inorganic phosphate (20 mM) to determine...
(b) (i) Starting with the definition of enthalpy, H = U + pl, and using a...
(b) (i) Starting with the definition of enthalpy, H = U + pl, and using a Maxwell relation, derive the following general equation of state. Write your derivation clearly and logically, showing all steps. You may use the following fundamental equation for change in internal energy without further proof: dU = Tds -pdv. TUDENT NAME NSHE # or My Nevadał: ii) Using the expression derived in (i) above, prove that for an ideal gas,
4. [20pt] The equilibrium constant of the reaction 2 C3H6 = C2H4 + C4H8 has been...
4. [20pt] The equilibrium constant of the reaction 2 C3H6 = C2H4 + C4H8 has been measured over a range of temperatures. Between 300 K and 600 K, it fits to the expression (T in Kelvin), 1088 1.51 · 105 In K = -1.04 - T + 12 Use this information and the Gibbs-Helmholtz equation and calculate the standard reaction enthalpy and standard reaction entropy at 400 K. /T) / (Here, the Gibbs-Helmholtz equation can be derived by taking (/...
Which of the following statements does not apply to the definition of an ideal gas? Group...
Which of the following statements does not apply to the definition of an ideal gas? Group of answer choices a. Intermolecular interactions are negligible. b. The Gibbs free energy only depends upon the temperature. c. The enthalpy only depends upon the temperature. d. The internal energy only depends upon the temperature. e. None. The previous answers are all correct. Consider a solid substance. Which of the following expressions is wrong? Group of answer choices a. Internal energy increases when the...
1. The simplest ammonia formation is from nitrogen and hydrogen. Consider the reversible reaction N2(g) + 3H2(g) → 2NH3(g) The standard enthaply and Gibbs free energy of formation one mole NH3 is ∆H◦...
1. The simplest ammonia formation is from nitrogen and hydrogen. Consider the reversible reaction N2(g) + 3H2(g) → 2NH3(g) The standard enthaply and Gibbs free energy of formation one mole NH3 is ∆H◦ m = −46.11 kJ mol−1 and ∆G◦ m = −16.78 kJ mol−1 . (a) What is equilibrium constant at standard condition (25°C and 1 atm)? (b) What is equilibrium constant at 60°C and 1 atm? (c) What is the Gibbs free-energy change relative to that under standard...
3. [10 marks] We've covered the definition of Gibbs free energy, Helmholtz free energy, entropy, and enthalpy. There is also something called their fundamental equations. a) [8 marks] Use online resources and your peers to determine the total differential form of each of these terms. For example, if we're looking at Gibbs free energy, defined as G = H – TS, then determine what dG would be. b) [2 marks] Why is it useful to use this form? c) [+2...
2. (25 pts) Derive the (a) Maxwell relation for the Helmholtz Free Energy F=U-TS. Show ALL steps and justifications in your derivation. Using your result in (a) comment on how (b) the entropy behaves for an isothermal expansion of an ideal gas. Finally, show the validity of the following equations (c) U = F-TOOF) -T2 and at (T) 01 (d) C =-1(
3. Derive the following relationship between the Helmholtz free energy F and the partition function Z for a system of N particles: (a) Starting with the thermodynamic definition F-U-TS, substitute the statistical mechanics results which give U and S in terms of occupation numbers n, state energies e and the most probable number of microstates t* to find, (b) Write out texplicitly in terms of occupation numbers using Stirling's approxima- tion (check the Lagrange multiplier derivation of the Boltzmann distribution)...
5. (25 points For credit; show every step in the derivations. (a) Starting with the Fundamental Equation for U determine the associated partial derivatives for T and P. Next, determine the associated Maxwell Relation. (b) Starting with the Helmholtz free energy (A = U – TS) derive the associated Fundamental Equation and identify the partial derivative relationships for P and S. Then derive the associated Maxwell Relation.
CHEM 351 Biochemistry I - Fall 2018 Study Problems for Metabolism and Glucose Catabolism For the reaction: aA + bB =cC + dD Gibbs free energy: AG = AG" + RT IN THE glucose + glucose 6-phosphate + H20 1. The equilibrium constant for phosphorylation of glucose is: Ke = 3.97 x 10- a. Calculate the standard Gibbs free energy for the uncatalyzed reaction. b. Use the physiological concentrations for glucose (2.0 mm) and inorganic phosphate (20 mM) to determine...
(b) (i) Starting with the definition of enthalpy, H = U + pl, and using a Maxwell relation, derive the following general equation of state. Write your derivation clearly and logically, showing all steps. You may use the following fundamental equation for change in internal energy without further proof: dU = Tds -pdv. TUDENT NAME NSHE # or My Nevadał: ii) Using the expression derived in (i) above, prove that for an ideal gas,
4. [20pt] The equilibrium constant of the reaction 2 C3H6 = C2H4 + C4H8 has been measured over a range of temperatures. Between 300 K and 600 K, it fits to the expression (T in Kelvin), 1088 1.51 · 105 In K = -1.04 - T + 12 Use this information and the Gibbs-Helmholtz equation and calculate the standard reaction enthalpy and standard reaction entropy at 400 K. /T) / (Here, the Gibbs-Helmholtz equation can be derived by taking (/...
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