Reference no: EM131475055

Assignment

1) Assuming the inter-electronic (electron 1 - electron2) repulsion in Helium is zero, determine the ground state energy and wave function for He.

2) Given the following thermodynamic data for the hydrogenation of benzene, determine the relative concentrations at 298K of the equilibrium mixture, at a hydrogen pressure of 101.3 kPa.

Substance           ΔH^oY (kJ/mol)       S^o 298 (J/molK)
Benzene                82.93                     269.0
Cyclohexadiene      107.1                     288.3
Cyclohexene          -7.20                     310.5

3) Explain how the classical physics concepts of momentum and mean free path are fundamental to the discussion of chemical kinetics.

4) Calculate the population ratio of the first two energy states of a hydrogen atom at 25C in a field of 1.41 Tesla parallel to the z-axis, given that the Hamiltonian operator is given by: H^= H^₀ + (β_BB_z/h) L_z, where H^₀ = Hamiltonian of a hydrogen atom in the absence of an external field, β_B is the Bohr magneton, B_z is the magnitude of the external magnetic field in the z direction, and L_z is the Z-angular momentum operator.

5) The adiabatic flame temperature (AFT) is the temperature that would be attained if a compound were burned completely under adiabatic conditions so that all the heat evolved would go into heating the product gases. Calculate the AFT for the burning of ethane to CO₂(g) and H₂0(0, at constant pressure, in an air mixture initially containing twice as much oxygen as needed for complete combustion. Assume air is 20% oxygen and 80% nitrogen. For any heat capacity equations, neglect terms containing T² or higher.

6) The following story appears in Reynolds, Thermodynamics, 2nd ed., McGraw Hill, N.Y. 1968, p43:

One Friday afternoon in December of 1843, Prof. J. Yule left his Laboratory in charge of his assistant Dr. B. T. Ewe. On returning the following Monday, Yule found that a half-full beaker that on Friday had been at 25C, was now at 40C. Yule's student Cal Oric said Ewe must have heated the water. Ewe denied this, saying that the only heat transfer involved was cooling the beaker by placing it on a block of ice for a time. Shortly thereafter Cal Oric went mad, and J. Yule was invited to become a member of the Royal Society.

Explain how B. T. Ewe increased the beaker's temperature by a process with q < 0.

7) Consider a reversible Carnot cycle that includes 2 phases - liquid and vapor water. The cycle consists of 4 steps:

a. First, 1 mole of liquid water is vaporized at 400K with an isothermal absorption of 39.3 kJ.
b. Second, the system is expanded adiabatically with a temperature change to 300K.
c. Third, an isothermal compression is carried out
d. This is followed by an adiabatic compression to return the system to its starting point. Assuming this 2-phase system obeys the first and second laws of thermodynamics, and given the heat of vaporization of water at 300K is 43.5 kJ/mol, how many grams of water must condense in the isothermal compression step?

8) Phenol (C₆H₅-OH) is partially dimerized to diphenol, (C₆₁-H₅-OH)₂, when dissolved in the solvent bromoform (Br₃CH). When 2.58 g. phenol is dissolved in 100 g. bromoform, the bromoform freezing point is depresses by 2.37 C. Pure bromoform freezes at 8.3 C and has a k_f = 14.1C kg/mol. Calculate the equilibrium constant, K_eq, for the dimerization reaction of phenol in bromoform at 6C assuming an ideally dilute solution.

9) A system consists of 1.00 mole supercooled liquid water at -10C in an adiabatic container. The pressure is held constant at 1.00 atm. The system spontaneously crystallizes.

a. Calculate ΔS for the transformation.

b. Determine the equilibrium amounts of ice and liquid water in the system at equilibrium.

10) The nucleophilic substitution reaction of bis phenylsulfone ether (ΦSO₂-O₂SΦ) with hydrazine (N₂H₄) was found to be first order in the ether at 300K. For an initial concentration of the ether of 3.15 * 10^-5 mol/L, the following rate data were observed. Determine the rate law and rate constant for this reaction.

Hydrazine Initial Concentration, (mol/L)     0.5 mmol/L       1.0 mmol/L         2.4 mmol/L        5.6 mmol/L
Rate, (mol/L)/s                                          0.085               0.17                    0.41                 0.95