[試題] 96上 蘇志明 普通化學甲 期末考

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課程名稱︰普通化學甲上
課程性質︰
課程教師︰蘇志明
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰2008.1.18
考試時限（分鐘）：180
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :

1.Consider a one-dollar coin lying on a table at 25℃. The table could be regarded as a heat reservoir with respect to the dime. Assume that the mass of the dime is 1.00g.

(a) What would be the change of the entropy of the whole system(i. e. dime plus table) if the dime should jump up from the table top to a height of 0.10 cm.(Note: It's a good approximation to assume that the potential energy of the dime comes from the heat of the table . The gravitation acceleration is 9.8 m/s^2. )

(b) With the information obtained in part(a), one could calculate the probability of this jumping event from the Boltzmann's entropy relation. Calculate this probability, i.e. the ratio of the microstate numbers between these two states.

(c) If a benzene molecule (C6H6) instead of a coin is lying on the table, what would be the probability for the benzene molecule to do the same jumping?

2.Consider the combustion reaction of the methane gas:

        CH4(g) + 2 O2(g) -----> CO2(g) + 2 H2O(g)
With the help of the related thermodynamic data as listed below, answer the following questions:

(a) Calculate ΔS, ΔH, and ΔG of this reaction at 298K and a constant pressure of 1.00 atm.

(b) Calculate ΔS, ΔH, and ΔG of this reaction at 1000K and a constant pressure of 1.00atm.

(c) What would be the theoretical equilibrium constants of the above reaction at 298K and 1000K?

(d) Calculate the theoretical maximum temperature that could be reached by igniting a mixture of methane and the air (O2/N2 mole ratio is 1/3) under 1 atm constant pressure (i.e. your kitchen stove condition). The initial system temperature is assumed to be 298K.

(e) From the above calculations, propose the ways or methods that could increase your stove theoretical maximum attainable temperature?

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Related thermodynamic data:

(i) Molar heat capacities at constant pressure (J/mol):

        H2 = 28.9       O2 = 29.5       N2 = 29.0

        H2O(g)=24.8     CO2 = 37.3      CH4 = 35.0

(ii) Enthalpies of formation (KJ/mol):

        CO2(g) = -394   CH4(g) = -75    H2O(l) = -286

        H2O(g) = -242

(iii) Entropies (J/K mol)

        H2 = 131        O2 = 205        N2 = 192

        CO2(g) = 214    CH4(g) = 186    H2O(l) = 70

        H2O(g) = 189

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3.Consider the same system as described in problem 2. One could theoretically construct a fuel cell with the following reation:

        CH4(g) + 2 O2(g) ------> CO2(g) + 2 H2O(l)

Note that now the water is in liquid state.

For 1 mole of methane being consumed, calculate the theoretical maximum useful work and also at the same time the heat that the fuel cell could generate.

4.The solubility of a salt and its solubility product are not necessary directly related.

Several factors would affect the solubility of a salt. They include the pH value of the solution, the possibility of the formation of the solvated ion pairs, and the possibility of complex formation. Explain how these factors affect the solubility of a salt by some concrete examples.

5.Calculatate q, w, ΔE, and ΔH, and ΔS for the process in which 88.0g of N2O(g) is cooled from 165℃ to 55℃ at a constant pressure of 5.00 atm. The C_v and C_p of N2O is 38.7 and 30.4 J/K/mol, respectively, and are assumed to be temperature independent.

6.Calculate the difference in free energy between 1.00M HCl(aq) and 0.100M HCL(aq) at 25℃.

7.A chunk of iron weighing 111 g is taken from a beaker of boiling water (at 1.00 atm) and placed in 3000 liters of water at 0℃. Calculate ΔS for the iron(molar heat capacity, 25.1 J/K mol) and for water (molar heat capacity, 75.3 J/K mol), respectively.

8.Consider the autoionization reaction of water:

        H2O(l) ----------> H+(aq) + OH-(aq)

(a) The equilibrium constants measured at 0℃ and 40℃ are found to be 1.14 x 10^(-15) and 2.92 x 10^(-14), respectively . Determine ΔS and ΔH of this reaction.

(b) Estimate the value of ΔG for the autoionization of water at its critical temperature, 374℃.

9.In a coffee cup calorimeter 50.0mL Of 0.100M AgNO3(aq) and 50.0mL of 0.100M HCl(aq) are mixed. The following reaction occurs:

        Ag+(aq) + Cl-(aq) ---------> AgCl(s)

If the two solutions are initially at 22.60℃,  and if the final temperature is 23.40℃, calculate ΔH for the above reaction in KJ/mol of AgCl formed. Assume a mass of 100.0g for the combined solution and a specific heat capacity of 4.18 J/℃ g.


Some constants and equations:

R = 1.987 cal/mol-deg = 8.314 J/mol-deg

k_B = 1.38 * 10^(-23) J/K

dE = dq + dw

dS = dq_rev / T

S = k_B ln Ω

H = E + PV

G = H - TS

ΔG = ΔG° + RT*ln(Q)

For ideal gas: Cp = Cv + R

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