1(a) Draw the Lewis structure with resonance structures for azide anion, N₃^- Indicate the value for the formal charge on each atom. 

(b) Draw the stereo-structure for the compound IF₄⁺

2(a) Draw the molecular orbital energy level diagram of N2 molecule. (b) Draw Lewis structures of the following ions, PtCI62-，NO3-，and CIO4-. Name the type of hybrid valence orbital and draw an orbital diagram for the hybrid orbital for the center atom.

3(a) Describe the first law, second law, and third law of thermodynamics in words of q, w, △S, △G, △E, and △H. (b) Write the rate law for a first order and a second order reaction. What is the unit of first order reaction rate constant?

4(a) Using the acetic acid(x g), sodium acetate(y g), and water(z mL) to prepare a buffer solution of pH 4.8. The acidity of acetic acid, Ka, is 1.8 x 10-5 (b) Write the equilibrium chemical reaction of methanol with K2Cr2O7 in acidic solution.

5(a) Draw the condensed structural formulas for the following compounds: methyl te-butyl ether, isopropyl alcohol, acetaldehyde, polyester, nylon. (b) Draw and name all the possible structural isomers of organic compounds. 

(c) (5%) What is the Gibbs free energy of freezing water at -10°C? (Molar melting enthalpy of ice: △mH° = 5619 J mol -1at–10°C, △mH° = 6008 J mol-¹ at 0°C; molar heat capacity: ice Cp,m=37.66 J mol-¹K-¹, water Cp,m-75.38 J mol¹K¹)

(b) (5%) The entropy of change for the isolated system upon freezing includes the entropy change of the surrounding as the entropy change of the water. Since the heat capacity of surrounding is large, the heat evolved by the water on freezing us absorbed by the surrounding with only an infinitesimal change in temperature. Calculate the entropy change of the surrounding! What is the change in the entropy of the universe?

(a) (5%) Calculate the change in the entropy when 1 mol of liquid water at -10°C changes to ice at -10°C. Explain your result!

(d) (4%) Sketch the graph ofthe lineweaver-Nurk equation. Use a coordinate system in which (1/[S]0) is on the horizontal axis and (1/V0) is on the vertical axis. Show the resulting graph is a line that intersects the horizontal axis at (-1/Km) and the vertical axis at (1/Vmax)

(c) (4%) Show that the Michaelis-Menten equation can be written in the form (1/V0)=(Km/Vmax)(1/[S]0) + (1/Vmax) (This formula is know as the Lineweaver-Burk equation and shows that there is a linear relationship between (1/V0) and (1/[S]0).)

(b) (4%) Applying the steady-state approximation to ES, show that the initial rate V0 at which P is formed can be described by the Michaelis-Menten equation Vo=(Vmax*[S]0)/ ([S]0 +Km), where [S]0 is the concentration of the substrate and Vmax=kcat [E]0 is the maximum rate at which the product may be formed and Km = (kf+kcat)/kf is the MichaelisMenten constant.

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