[試題] 100下 蘇志明 普通化學丙 期末考
課程名稱︰普通化學丙
課程性質︰群組必修
課程教師︰蘇志明
開課學院：工學院 生物資源暨農學院
開課系所︰工科系 機械系 生工生
考試日期（年月日）︰2012/06/21
考試時限（分鐘）：130分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. (a) The following figure indicates three possible types of electrostatic
interactions between molecules and/or ions. Assuming that the
intermolecular distance R is much larger than the intra-molecular
charge seperation d, derive the functional forms of the intermolecular
potentials for each for the three electric charge distributions.
(Note: the final forms should be expressed in terms of the dipole
moment and R for the charge-dipole and dipole-dipole interactions, and
each + or - sign indicates a positive or negative charge. You should
denote the related constant in the Coulumb potiential as k.) (12%)
|─────────| charge-charge
○ R ○
q+ q-
|─────────| charge dipole
○ ○---○
q- δ+ δ-
|──|
d
|─────────| dipole-dipole
○---○ ○---○
δ+ δ- δ+ δ-
|──| |──|
d d
(b) Among all sorts of the intra-molecular interactions, why do we
specifically pick out the so-called hydrogen bonding as a unique and
important interaction form between moleculars? Explain the origin of
the hydrogen bond. (6%)
2. Construct the molecular orbitals of the hetero-nuclear diatomic molecule HF
Explain the nature of chemical bonding in HF, and the origin of the
electric dipole moment of HF in terms of the approximate molecular wave
functions obtained. Note that the first ionization energy of the F atom is
much higher than that of the H atom. (10%)
3. The vapor pressure of a substance follows the Clausius-Clapeyron equation
-ΔH vap
ln P = ──── + C
RT
(a) Derive the following relationship between the vapor pressure P1 and P2
and the absolute temperatures at which they were measured, T1 and T2:
(3%)
P1 -ΔH vap 1 1
ln ── = ──── (─ - ─)
P2 R T1 T2
(b) Gasoline is a mixture of hydrocarbons, a major component of which is
octane C8H18. Octane has a vapor pressure of 13.95 torr at 25℃ and
a vapor pressure of 144.78 torr at 75℃. Calculate the heat of
vaporization of octane. (3%)
(c) Calculate the normal boiling point of octane. (3%)
(d) Calculate the vapor pressure of octane at -30℃. (3%)
4. Consider the gas-phase reaction of nitric oxide with bromine:
2 NO(g) + Br2 (g) → 2 NOBr(g)
The experimentally determined rate law is
d[NO] d[Br2]
-─── = -─── = k obs [NO]^2[Br2]
2dt dt
The proposed reaction mechanism is:
k1
step 1 : NO(g) + Br2(g) ←→ NOBr2(g) (fast)
k-1
k2
step 2 : NOBr2(g) + NO(g) → 2 NOBr(f) (slow)
(a) Using the steady-state approximation, derive the rate law for the above
proposed mechanism. (10%)
(b) By assuming the Step 1 is in quasi-equilibrium state, one could further
simplify the rate law derived in (a). Obtain this final simplified
form. Express K obs in terms of the rate constants of the elementary
reactions in Step 1 and Step 2. (5%)
(c) According to the result obtained in (b), what would be the activation
energy of k obs? Express the observed activation energy in terms of the
activation energies of the above elementary steps. (5%)
5. Consider a first-order reaction A → B + C with the following differential
rate law: d[A]
-── = k [A]
dt
(a) Assuming that initially the concentration of A is [A]o, solve the above
differential quation. (5%)
(b) What are the half-life and life-time of this reaction? (5%)
6. The reaction between ethyl iodide and hydroxide ion in ethanol (C2H5OH)
solution, C2H5I(alc) + OH-(alc) → C2H5OH(l) + I-(alc), has an activation
energy of 86.8 kJ/mol and a frequency factor of 2.10 x 10^11 M^-1 s^-1.
(a) Predict the rate constant for the reaction at 35℃. (3%)
(b) A solution of KOH in ethanol is made up by dissolving 0.335g KOH in
ethanol for form 250.0 mL of solutions. Similarly, 1.453g of C2H5I is
dissolved in ethanol for form 250.0 mL of solution. Equal volumes of
the two solutions are mixed. Assuming the reaction is first order in
each reactants, what is the initial rate at 35℃? (3%)
(c) Which reagent in the reactions is limiting, assuming the reaction
proceeds to completion? (3%)
(d) Assuming the frequency factor and activation energy do not change as a
function of temperature, calculate the rate constant for the reaction
at 50℃. (3%)
7. The equilibrium constant Kc for the following reaction is 1.9 at 1000K and
0.1333 at 298K:
→
C(s) + CO2()g equil. 2CO(g)
←
(a) If excess C is allowed to react with 25.0g of CO2 in a 3.00L vessel at
1000K, how many grams of CO are produced? (3%)
(b) How many grams of C are consumed? (3%)
(c) If a smaller vessel is used for the reaction, will the yield of CO be
greater or smaller? (3%)
(d) Is the reaction endothermic or exothermic? (3%)
8. Consider the following equibrium reaction in the gas phase:
→
2 H2(g) + O2(g) Keq 2 H2O(g)
←
(a) Calculate the standard enthalpy, entropy, and Gibbs free energy of the
reaction at 298K. (9%)
(b) Calculate the equilibrium constant Kp at 298K. (3%)
(c) The vapor pressure of water at 298K is 24.0 torr. Calculate the
equilibrium pressure of H2 under this condition. (3%)
(d) Calculate the standard enthalpy, entropy, and Gibbs free energy of the
reaction at 1500K. (9%)
(e) Calculate the equilibrium constant Kp at 1500K. (3%)
(f) At 1500K, the equilibrium water vapor is measured to be 24.0 torr, What
would be the pressure of H2? (3%)
Related thermodynamic date:
(i) Molar heat capacities at constant pressure (J/mol), and assume to be
constant over the temperature range considered in this problem:
O2(g) = 29.5 H2(g) = 28.9 H2O(l) = 75.2 H2O(g) = 24.8
(ii) Standard enthalpies of formation (kJ/mol) at 298K:
H2O(l) = -286 H2O(g) = -242
(iii) Standard molar entropies (J/mol-K) at 298K:
H2(g) = 130.6 O2(g) = 205.0 H2O(g) = 188.8 H2O(l) = 69.9
Additional information:
(a) The gas constant R = 0.0821 L atm K^-1 = 8.31 J K^-1 mol^-1
(b) 1 L atm = 101.3 J
(c) 1 atm = 760 torr
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