27. The formation of stalactite is closely related to the concentration of carbon- containing species formed by the dissolution of CaCO₃ in the rocks and CO₂ in the air in natural water bodies. Given that (CaCO₃) = , pM = -log[M] where M = , the variation of pM with pH  in a cave water body at room temperature is shown on the right.  Which of the following is   incorrect  ? 

(A) represents .
(B)
(C) m = 2.75 and n = 4.35
(D) When pH is 10.3,
(E) When pH is increased from 4 to 8, increases faster than .

23. Which pair of the following compounds that measured under the same conditions have the same amplitude of specific rotation but with opposite direction? (A) cis-1,2-dichlorocyclopentane and trans-1,2-dichlorocyclopentane (B) (2S, 3R)-butane-2,3-diol and (2R, 3S)-butane-2,3-diol (C) cis-2-butene and trans-2-butene (D) (2S, 3R)-butane-2,3-diol and (2R, 3R)-butane-2,3-diol (E) D-glucose and L-glucose

24. (i) The number of the following species which exhibit resonance is a. O3, SeO2, NF3, N2O, CCl4, SCN⁻, OF2 (ii) The number of the following diatomic species which are paramagnetic is b.  What is (a + b)? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9

25. 2-Methoxy-2-methylbutane (TAME) is commonly used as a gasoline additive. With the presence of appropriate catalysts, TAME can be produced by the liquid- liquid reaction between methanol and olefins, in which the following reactions occur simultaneously. The equilibrium constants Kx, expressed in terms of the amount fraction of the substance, for reactions I, II, and III are shown above. What is the range of values of ?  (A) ＜-1 (B)-1~0 (C) 0~1 (D) ＞ 1  (E)

26. Consider the reaction 2 X(g) + Y(g) ⇌2Z(g) in a rigid container at 27 °C. The initial concentrations of X and Y are 2.0 mol/L and 3.0 mol/L, and 1.0 mol/L of Z will be produced at equilibrium. If you want to prepare 0.40 atm of Z from an initial pressure of 1.0 atm of X, what would be the approximate initial pressure of Y? (gas constant R = 0.082 atm·L·K⁻¹·mol⁻¹) (A) 1.3 atm (B) 3.3 atm (C) 10.2 atm (D) 21.3 atm (E) 28.0 atm

28. At a certain temperature, cis-1,2-dimethylcyclopropane (M) and trans-1,2- dimethylcyclopropane (N) undergo the following transformation. The rate laws for the reactions can be expressed as , with ky and k, being constants at a given temperature, called the forward and reverse rate constants, respectively, and the equilibrium constant of the reaction, K = 3. Which of the following statements is correct? (A) At this temperature, the conversion of M is 66.7%. (B) As the temperature increases, both , increase. (C) At room temperature, N is a gas under 1 atm. (D) M is more stable than N. (E) Heating this reaction increases the equilibrium constant K.

29. When the following monosaccharide form furanose, a new bond is formed between which two atoms (use underlined numbers)? (A) (B)(C)(D)(E)

30. Consider the complex ions . The wavelengths of absorbed electromagnetic radiation for these ions in solution are (in no specific order) 293 nm, 442 nm, and 768 nm. Which of the following statements is correct? (A) absorbs 293-nm electromagnetic radiation. (B) absorbs 442-nm electromagnetic radiation. (C) absorbs 768-nm electromagnetic radiation. (D) The solution of is blue. (E) The solution of is red.

31. The capacitor in the figure (right) is initially uncharged. w The emf of the battery is 8 = 10 volts. The values of the resistors are: R1 = R2 = R3 = 1 Ω. The capacitor C is 10 μF. Τ The switch is initially open and is closed at t = 0. What is R R R switch C the final charge on the capacitor if one waits long enough? (A)10 μC (B) 50 μC (C) 100 μC (D) 200 μC (E) 0

32. A particle collides with an identical particle at rest relative to an inertial frame S. These two (noninteracting) particles has speed 0.6c moving toward each other along the x direction in their center-of-momentum frame (namely, in the inertial frame in which the total momentum of the system vanishes), denoted by S'. What is the speed of frame S'relative to frame S? (A) 1.2c (B)(C) (D) 0.6c (E) (2 - √3)c 

33. The wave function of a transverse wave propagating on a rope is y(x, t) = 5sin(πχ 4πt), where x and y are measured in meters and t is in seconds. What is the velocity (m/s) of a particle on the rope at x = 2 m and t = 0.5s? (A) 0 (B) -4 (C) 5π (D) 10π (E) 20π