51. For a particle in a three-dimensional cubic box with infinite potential walls, its energy level dependd on three quantum numbers. Let us denote these three quantum numbers by (n, I, m). Which of the following statements is true?
(A) The energy of the particle only increases with the quantum number n.
(B) The ground state energy is zero.
(C) These quantum numbers have specified allowed ranges: n≥ 1, 0 ≤1≤n-1, -I ≤m ≤1.
(D) The probability density function is uniform throughout the box.
(E) None of the above is true.

1. A mixture of C2H6(g) and C3H8(g) in a closed rigid container has a total pressure of 1.0 atm. Just enough O2(g) is added to the mixture to bring about its complete combustion to CO2(g) and H2O(g). After the combustion, the total pressure in the container is 6.3 atm. Assuming constant temperature and volume, find the mole fraction of C3H8(g) in the original mixture. (A) 0.25(B) 0.35(C) 0.50 (E) 0.75 (D) 0.65

2. Stretch a rubber band while holding it gently to your lips. Then, let it relax while still in contact with your lips. Which of the following statements about the above process are correct?(I) The temperature of the rubber band increases on stretching.(II) The stretching is an endothermic process.(III) The intermolecular forces within the rubber band increase on stretching.(IV) △G is negative for stretching the rubber band. (V) △S is negative for stretching the rubber band. (B) I, IV (D) I, III, V (E) I, IV, V  (A) I, II (C) III, IV

3. When the compound with a molecular formula of C6H14O is oxidized, a ketone is produced. How many possible structures are forC6H14O in this reaction? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8

4. At 25 ℃, what is the approximate pH of a 0.5 M ammonium nitrite(NH4NO2) solution? (Ka = 5.6 x 10-10 for NH4+, 4.0 x 10-4 for HNO2; log2 = 0.301, log7 = 0.845) (A) 4.70 (B)5.40 (C)6.30 (D)7.50 (E) 8.60

5.Which of the following show the more stable chair conformers (from two possible chair conformers) of the cyclohexane scaffolds?(A)(B)(C)(D)

6. Given the following standard reduction potentials at 25 ℃: In a galvanic cell, the copper compartment contains a copper electrode and [Cu2+] = 1.00 M. The zinc compartment contains a zinc electrode and Zn2+at an unknown concentration. The compartment containing the zinc (1.00 L of solution) was titrated with 0.600 M H2EDTA2-, resulting in the reaction: The potential of the cell was monitored to determine the stoichiometric point for the process, which occurred when 400.0 mL of H2EDTA2- solution was added. What is Ecell at the halfway point of titration? (A)1.04V (B) 1.07V (C) 1.10V (D)1.13 V (E) 1.16 V

7. Which of the following statements is incorrect? (A) 2 NO(g) + 2 CO(g) → N2(g) + 2 COz(g) is spontaneous at room temperature, then the reaction has △H >0. (B) The reaction NH3(g) + HCI(g)→  NH4CI(s) can proceed spontaneously at room temperature, so the AH of the reaction is < 0. (C) For the reaction MgCl2(1)→ Mg(I) + Cl2(g) to proceed at a certain temperature, it has △H > 0 and △S > 0. (D) The reaction C(s) + CO2(g)→2CO(g) cannot proceed spontaneously at room temperature, then the reaction has △H > 0. (E) After the coating of copper-plated iron products is broken, the iron products are more likely to corrode than before the damage.

8. It is known that 3.6 g of simple carbon is burned in 6.4 g of O2 until the reactants are exhausted, giving off XkJ of heat. The heat of complete combustion of simple carbon is Y kJ•mol-1 . What is the heat of reaction △H for the reaction of 1 mole of simple carbon with O2 to form CO? (A) -YkJ•mol-1(B) -(10X -Y) kJ•mol-1 (C) -(5.X- 0.5Y) kJ•mol-1(D) +(10X-Y)kJ•mol-1(E) +(5X -0.5Y) kJ•mol-1

9. If 100 mL of 0.4 M Ba(OH)2 solution is added to a sufficient amount of H2SO4 solution, the amount of heat released is 5.12 kJ. If 100 mL of 0.4 M HCl solution is added to a sufficient amount of Ba(OH)2 solution, the amount of heat released is 2.2 kJ. Which of the following is the thermochemical equation for the reaction between an Na2SO4 solution and a BaCl2 solution? (A)(B) (C) (D)(E)

10. Concentrated sulfuric acid and 2 M of dilute sulfuric acid are placed open in the experiment. The relationship between their masses and the number of days in which they are placed is shown in the figure on the right. Which of the following process pairs is responsible for the change in the curves of a and b? (A)(B)(C)(D)(E)

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