課程名稱︰普通化學甲下 課程性質：必修 課程教師︰鄭原忠 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2018/5/4 考試時限（分鐘）：120 試題 : 1 (10pt) Assuming energy in-flow and out-flow of Earth are steady and balanced. The surface temperature of the sun in approximately 6000K. The Earth's surface temperature depends on sunlight conditions; however, generally speaking the Earth absorbs sunlight energy at a higher temperature and radiates energy at a lower temperature. Let's assume on Earth the energy is absorbed at approximately 300K and radiated at approximately 290K. If 6000kJ of energy flows from sun to Earth and then out of Earth. Answer the following questions: (a) Calculate ΔS_{sun} and ΔS_{Earth} (b) What is the sign of ΔS_{sun}+ΔS_{Earth}? Explain why this process is actually spontaneous. 2 (15pt) Consider state transition of n mole of ideal gas in a reversible adiabatic process. (a) Explain "reversible" and "adiabatic". How to achieve such a process experimentally? (b)Show that nc_v dT = -PdV for this process. Provide full justification for your derivation. (c) Show that during this process, PV^γ=constant, where γ=c_p/c_v. What is the value of γfor an ideal gas? 3 (10pt) For an one-component system, show that: (a) (∂A/∂V)_S - S(∂p/∂S)_V = -p (b) ΔH=-T^2 (∂(ΔG/T)/∂T)_{P_i,P_f;n_i,n_f} （為了方便此另外附上這兩題的LaTex碼） (a) \left(\frac{\partial A}{\partial V}\right)_S-S\left(\frac{\partial p}{\partial S}\right)_V = -p (b) \Delta H = -T^2\left(\frac{\partial (\Delta G/T)}{\partial T}\right)_{P_i,P_f;n_i,n_f} 4 (10pt) The equilibrium constant for a hypothetical process was determined as a function of temperature(Kelvin) with the results plotted on the right. （圖是一條直線，y軸：ln(K)、x軸：1000/T、線過(0,40)、(3,0)） (a) From ΔG°=-RTlnK, give the equation that explains the plot. (b) From the plot. determine the values of ΔH°and ΔS°. Is this process endothermic or exothermic? 5 (10pt) As O2(l) is colled at 1 atm, it freezes at 54.5K to form solid I. At a lower temperature, solid I rearranges to solid II, which has a different structure. Thermal measurements show that ΔH for the I→II phase transition is -743.1J/mol, and ΔS for this transition is -17.0J/K‧mol. (a) Calculate ΔS_{surr} for the O2 solid I→II phase transition at 50K. (b) Give the second law of thermodynamics (you need to present its mathematical form). Use the second law to predict whether the O2 solid I→II phase transition is spontaneous at 50K. (c) At what temperature do you expext solid I and II would be in equilibrium? 6 (10pt) The boiling point of hexane is 342K and its enthalpy of vaporization ΔH_{vap}=28.9kJ/mol. (a) Assuming that the intermolecular interactions are negligible, estimate the molar volume of hexane at 342K. (b) Estimate the vapor pressure of hexane at 300K. 7 (10pt) What is the pH if a 0.125 solution of the weak base B if ΔH°=-25.0kJ/mol and ΔS°=-175J/K for the following equilibrium reaction at 25°C? B(aq)+H2O(l)←→BH+(aq)+OH-(aq) 8 (15pt) Lactic acid is a common by-product of cellular respiration. A 25.0mL sample of 0.100M lactic acid (HC3H5O3, pKa=3.86) is titrated with 0.100M NaOH solution. (a) Calculate the pH after the addition of 0.0mL, 12.5mL, 25.0mL, 25.1mL, and 30.0mL of the NaOH. (b) Sketch the titration curve. You must properly label the titration curve and be as quantitative as you can. 9 (15pt) Consider a single quantum harmonic oscillator with vibrational angular frequency ω. The energy levels of the system are E_n=(n+1/2)(h-bar)ω, where n=0,1,2,... is the quantum number. (a) Calculate the canonical partition function of the system as a function of temperature T. (b) Calculate the internal energy of the system. Plot the internal energy as a function of T. What happens when the temperature is high,i.e. kT>>(h-bar)ω? (c) Calculate the constant volume heat capacity(Cv) of the system. 10 (15pt) Consider the galvanic cell based on the following half-reactions. MnO4- + 8H+ + 5e- → Mn(2+) + 4H2O IO4- + 2H+ + 2e- → IO3- + H2O (a) Sketch the galvanic cell. Show the direction of electron flow, direction of ion migration through the salt bridge, and identify the cathode and anode. Which materials/chemicals would you use for the electrodes and the salt bridge solution? (b) Give the overall balanced equation, and determine the standard cell potential for this galvanic cell. (c) Derive a relation between the pH of the solution and the cell potential at 25°C. Assume that all other concentrations are 1.0M and that all partial pressures are 1.0atm. 11 (10pt) The following standard reduction potential have been determined for the aqueous chemistry of indium: In(3+)(aq) + 2e- → In+(aq), E°=-0.444V In+(aq) + e- → In(s), E°=-0.126V (a) What is the equilibrium constant for the disproportionation reaction, where a species is both oxidized and reduced, shown below? 3In+(aq) → 2In(s) + In(3+)(aq) (b) What is ΔG_f°for In+(aq) if ΔG_f°=-97.9kJ/mol for In(3+)(aq)? ────12,13號稱加分題──── 12 (10pt) See the photo of a pattern certification on the right. （就是一張印得很模糊不需要看的專利證書） This pattern describes a "water-injecting device" for can engines, and this device is used to increase the performance of the engine. A short paragraph found on the Internet regarding this pattern is as follow:「本創作之主要目的，乃在於提供一種兼具輔助引擎室燃燒及提升引擎功效之裝置，藉由適量水蒸氣自引擎進氣管導入引擎室，並利用引擎室內之高溫，使氫氧分子鍵結而成的水分子，能分離形成獨立的氫氧分子，藉其產生助燃效果，提升引擎的燃燒效率，讓燃油燃燒更為完全。」 You have learned thermodynamics in General Chemistry. Do you believe the device descirbed in the pattern can functino as it claims? (Y/N) Explain your answer and try to be quantitatively. Please use full sentences (either Chinese or English is fine) and equations when necessary. 13 (10pt) The engine powering the BMW Concept M4 GTS is equipped with a "water injection system" that has endowed the BMW M4 MotoGP Safety Car with a noticeable increase in output of the engine cycle. In this system, water is precisely timed to inject at the last compression stage of the engine cycle. Apply your thermodynamics knowledge to come up with a mechanism to explain how it works. Please use full sentences (either Chinese or english is fine) and equations when necessary. ─────────────── Thermodynamic functions: H=U+PV, A=U-TS, G=H-TS ΔG = ΔG°+RTlnQ A=-kTlnQ Physical constants: c=3.0E8m/s, m_e=9.1E-31kg, h=6.626E-34Js, 1eV=1.60E-19J, R=0.082L*atm/K/mol=8.3J/mol/K --

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