課程名稱︰物理化學一
課程性質︰必修
課程教師︰金必耀
開課系所︰化學系
考試時間︰06/06/27
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試題 :
1.Show that the equilibrium mole fractions of n-butane and isobutane are given
by
Yn = e^(-△fG*n/RT) / (e^(-△fG*n/RT)+e(-△fG*iso/RT))
Yiso= e^(-△fG*iso/RT) / (e^(-△fG*n/RT)+e(-△fG*iso/RT))
(△fG*表標準生成自由能)
2.Starting with the fundamental equation for G in the form
dG = -SdT + VdP + △rGdζ
derive equation for calculation △rS , △rV and △rH from experimental data
on △rG for a chemical reaction as a function of T and P.
3.The following molecular species are in equilibrium in the gas phase : CH4,
C2H6 , C2H4 , and C3H6. How many independent chemical reactions are required
to represent all possible changes in this system? Derive a set of independent
reactions.
4.What is the maximum number of phase that can be in equilibrium in one- , two-
, and three-component systems?
5.A binary liquid mixture of A and B is in equilibrium with its vapor constant
temperature and pressure.Prove that μA(g)=μA(l) and μB(g)=μB(l) by
starting with
G = G(g) + G(l)
and the fact that dG = 0 when infinitesmal amounts of A and B are
simultaneously transferred from the liquid to the vapor.
6.Give the expressions for the mean ionic activity coefficients of LiCl ,AlCl3
and MgSO4 in terms of the activity of the electrolyte and its molality.
7.An investigator , who is interested in the copper disproportionation reaction
, studies the cell Cu(s)|Cu2+︴︴Cu+ |Cu(s).
(a)What are the half-cell reaction ?
(b)What is the cell reaction and the standard electromotive force of the cell
at 298.15K?
(c)Whats is the equilibrium constant for the cell reaction ?
8.Fumarase catalyzrs the reaction
fumatate + H2O = L-malate
At 25'C and pH 7
K'=4.4= [L-malate]/[fumarate]
What is the value of K' at pH 4? Given:For fumaric acid K1=10^-4.18.For
L-malic acid K1=10^-4.73.
9.A protein molecule has two different and independent sites ; one binds A and
the other binds B . What are the probabilities of P , PA , PB , and PAB ?
10.Consider the following system of reaction,
K1
AH + B ←→ CH
↑↓ ↑↓
A+B ←→ C
K2
Where the K's represent equilibrium constants.(a)Calculate the dependence on
hydrogen ion concentration of apparent equilibrium constant
K'=([C]+[CH])/([A]+[AH])[B]
(b)What is the relationship between the four equilibrium constant?
11.van der Waals Equation of state
(a)Plot the isothermal lines of the van der Waals equation with Maxwell
construction schematically in the p-V plane(including T >Tc , T =Tc , T >Tc)
and also the curve for |@p/@V| = 0 on the T =Tc curve (@是偏微分)
_ _ | |T
[p + a/(V)](V - b) = RT
(b)Indicate the regions of unstable , metastable , and phases on the figure in
(a)
(c)Plot schematically the Gibbs energy as a function of the pressure for a
system obeying van der Waals equation of state below critical point.Explain
what change the system under consideration makes in this process below the
critical temperature .Hint:the pressure dependence of G is determined by
p
|@G/@p| = V , and G(p , T) = ∫ V(p,T)dp + ψ(T)
| |T 0
where ψ(T) is a function of T
12.Efficiencies of Heat Engines
Discuss the advantage of using fuel cells rather than the corresponding
combustion reactions to produce electricity based on the difference in
energy conversion efficiencise for the eletrochemical cell and the heat
engine.(The following thermodynamical data of water at 25'C can be used
to facilitate your discussion :
H2(g) + 1/2 O2(g) -> H2O(l)
△H*f = -286 kJ/mol , △G*f = -237 kT/mol , S*=70 J/K*mol , C*p(H20(l))=75.3
J/K*mol , C*p(H2O(g))=33.6 J/K*mol. For simplicity , you can also assume
that the heat engine consists of a steam engine operating between a
condenser at 300K and a boiler at 600K.)
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