25. The correct mathematical expression for finding the molar solubility(s) of Al(OH)3 is .
(A) 9 s² = K_sp
(B) 3 s³ = K_sp
(C) 27 s⁴ = K_sp
(D) s⁴ = K_sp
(E) 9 s³ = K_sp

26. Consider the following octahedral complex structures, each involving ethylene diamine and two different, unidentate ligands X and Y. Which, if any, of the following pairs are optical isomers? (A) 1 and 4 (B) 1 and 2 (C) 3 and 4 (D) 1 and 3 (E) None of the above.

27. For which of the following processes would ∆S° be expected to be most positive? (A) NH3(g) + HCl(g) → NH4Cl(g) (B) 2NH4NO3(s) → 2N2(g) + O2(g) + 4H2O(g) (C) H2O(l) → H2O(s) (D) N2O4(g) → 2NO2(g) (E) O2(g) + 2H2(g) → 2H2O(g)

28. Why is this reaction considered to be exothermic? (A) Because energy difference A and energy difference C are about equal. (B) Because energy difference B is greater than energy difference C plus energy difference A. (C) Because energy difference A is greater than energy difference C. (D) Because energy difference B is greater than energy difference A. (E) Because energy difference B is greater than energy difference C.

29. The structure of pentose is shown on the down figure. How many carbon atoms with chirality are there in this molecule? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

30. Which one is Bragg equation? (A) F = ma (B) Hɸ = Eɸ (C) nλ = 2dsinθ (D) Δx ∙ Δp = h (E) E = mc2

31. A uniform solid ball with mass M is supported by a massless rod. Derive the period of the pendulum with a small displacement. (A) T = 2π(1.1L/g)1/2 (B) T = 2π(1.8L/g)1/2 (C) T = 2π(1.5L/g)1/2 (D) T = 2π(0.9L/g)1/2 (E) T = 2π(0.7L/g)1/2

32. A rocket moving in space, far from all other objects, has a speed of vi relative to the Earth. Its engines are turned on, and fuel is ejected in a direction opposite to the rocket’s motion at a speed of vrel relative to the rocket. What is the speed of the rocket, vf relative to the earth once the rocket’s mass is reduced to half its mass before ignition? (A) vi+ vrel ln2 (B) vi+ vrel ln(1/2) (C) vi+ 2vrel (D) (vi+ vrel) / 2 (E) vi+ vrel / 2

33. A satellite is in a circular orbit and has a total mechanical energy of U. If the satellite lost half of its weight and doubled its radius of the circular orbit, what will be its total mechanical energy? (A) 1/4 U (B) 1/2 U (C) U (D) 2 U (E) 4 U

34. A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision? (A) 2.0 (B) 4.2 (C) 6.1 (D) 8.1 (E) 10

35. A set of pulleys is used for supporting the calf (100 N). Please determine the weight of the subject in the right hand side. (A) 50 N (B) 73 N (C) 100 N (D) 141 N (E) 173 N

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