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- 3. Consider a 2 × 2 square lattice of spins interacting via the Ising Hamiltonian in the absence of a magnetic field: H = - ΣSi Sj, (ij) we have set J = 1. (a) Write down all the possible configurations and calculate the energy for each one of them. (b) Calculate the partition function Z, as a function of temperature, by summing over all configurations. (c) Repeat question (3a) and (3b), using periodic boundary condi- tions.Elaborate four (4) components of spontaneous potential.Prove that statement mathematically?
- ) Given the following data on Phosphorus and its allotropeso ∆Hf kJ mol-1 ∆Gfo kJmol-1 So J mol-1 K-1 White phosphorus, P(s, white) 0 0 0 Gaseous Phosphorus, P(g) 315 278 163 Gaseous Phosphorus, P4(g) 59 24 280 b) For the transformation P(g) -> ¼ P4(g), is work done by the system or on the system? How much work is involved? Explainwith solutions. c) Calculate the ∆E in kJ for the process P(g) ¼ P4(g) in (b). d) Calculate the sublimation temperature for white Phosphorus (in oC) assuming constant values of enthalpy and entropyover the temperature range involved.2) Calculate ∆S (for the system) when the state of 2.00 mol diatomic perfect gas molecules, for which Cp,m = (7/2)R, is changed from 25°C and 1.50 atm to 135°C and 7.00 atm.Hydrogen is one of only seven elements which exist as stable diatomic molecules at (or close to) room temperature and atmospheric pressure. Let’s investigate just how much more thermodynamically favorable diatomic hydrogen is compared to atomic hydrogen. Given the following reaction and associated data at T = 298.15 K. 2 H(g) ⇌ H"(g) or equivalently H(g) + H(g) ⇌ H2(g) Δf?° (kJ mol-1) ?° (kJ K-1 mol-1) H(g) 218.0 0.115 H2(g) 0 0.131 Calculate ΔH, ΔS, and ΔG for the formation of H2(g) from H(g) at 298.15 K. Calculate KP for the reaction. Calculate the temperature at which the reverse reaction becomes favorable. Assume ΔH and ΔS do not change with temperature.
- 3. A particular protein heat denatures with a melting temperature Tm = 332 K with an enthalpy of unfolding, AHm = 372 kJmol-¹. (a) What is the entropy of unfolding in kJ mol-1 K-1 at Tm? (b) If ACp is 6.6 kJ mol-1 K-1, at what temperature does the free energy of unfolding (AG unfolding) have the greatest value (i.e. the native state is most stable)? (c) Calculate the value of AG and K at this temperature.Combustion of glucose (C6H12O6) is the main source of energy for animal cells: CHO) +60, (e) 600, (e) 6H,O) + (1) rxn AG (37 °C)=-2872. kJ One of the most important uses to which this energy is put is the assembly of proteins out of amino acid building blocks. The Gibbs free energy of formation of one peptide bond, joining one amino acid to another, is 21 kJ/mol. Suppose some cells are assembling a certain protein made of 27 amino acids. (Note that the number of peptide bonds in the protein will be one less than the number of amino acids.) Calculate the minimum mass of glucose that must be burned to assemble 250. umol of this protein. Round your answer to 2 significant digits. g 0 EThe second law of thermodynamics states that for a process to be spontaneous: (A) The entropy of the system must increase; (B) The energy of the system must decrease; (C) The energy of the universe must decrease. (D) The entropy of the universe must increase;
- Gibbs free energy (G�) is a measure of the spontaneity of a chemical reaction. It is the chemical potential for a reaction, and is minimized at equilibrium. It is defined as G=H−TS�=�−�� where H� is enthalpy, T� is temperature, and S� is entropy. The chemical reaction that causes magnesium to corrode in air is given by 2Mg+O2→2MgO2Mg+O2→2MgO in which at 298 K, ΔH∘rxn = −1204 kJΔ�rxn∘ = −1204 kJ and ΔS∘rxn = −217.1 J/KΔ�rxn∘ = −217.1 J/K. Part A Part complete What is the standard Gibbs free energy for this reaction? Assume the commonly used standard reference temperature of 298 K. Part B What is the Gibbs free energy for this reaction at 5958 KK ? Assume that ΔHΔ� and ΔSΔ� do not change with temperature. Express your answer to two decimal places and include the appropriate units. Part C At what temperature Teq�eq do the forward and reverse corrosion reactions occur in equilibrium? Express your answer as an integer and include the appropriate units.P2C.4 From the following data, determine A,H° for diborane, B,H,(g), at 298 K: (1) B,H,(g) + 30,(g) → B,O,(s) +3 H,O(g) A̟H° =-1941kJ mol -> %3D (2) 2B(s) + 를0,(g) → B,O, (s) A̟H® =-2368 kJ mol (3) H,(g)+±O,(g) → H,O(g) A,H° =-241.8kJ mol %3D2. In a non-ideal binary mixture of A and B, the chemical potential of A is (a) The partial derivative of the total Gibbs free energy, with respect to the number of moles of A. (b) The partial derivative of the Gibbs free energy of A, with respect to the number of moles of A. (c) The partial derivative of the Gibbs free energy of B, with respect to the number of moles of A. (d) The total Gibbs free energy, divided by the number of moles of A. (e) The Gibbs free energy of A, divided by the number of moles of A.