2. (a) Please derive the integrated rate law of the first-order reaction. (4%)

二、非選擇題1. (a) Justify: at constant pressure, qp = △H. (3%)

(b) Justify: at constant temperature and pressure, △G = maximum of Wuseful (4%)

(b) Briefly describe how to get the activation energy of a chemical reaction. (3%)

3. Use the molecular orbital model to draw MO energy-level diagrams for predicting the magnetism and bond order of B2 molecule. (6%)

(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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