a) For the spreading of the oil C16H34 over water, at constant temperature and pressure, a small change in the surface free energy of the system is given by the total differential: ƏG ƏG ƏG dAB dG =) dA₂+ -) dAAB+ JAAB JAB Knowing that the values of the surface tensions are: Ywater = 72.8 mN m-¹ Y C16H34 = 30.0 mN m-¹ Y C16H34/water = 52.1 mN m-¹ Derive from the above equation an expression for the spreading coefficient and calculate the spreading coefficient for C₁6H34 on water. b) Consider the Gibbs energy of the total system made of two perfect gases (A and B) in two separate containers, at constant temperature and pressure: Gi = μANA + μBnB = NA (μA + RT Inp) + nB (uB +RT Inp) After mixing the two gases, the partial pressures of the gases are PA and P.B. Prove mathematically that the (isothermal and isobaric) enthalpy of mixing AH mix = 0. c) Suggest a mechanism for cis/trans exchange and equilibration of bridging and terminal carbonyl groups in the compound [Cp₂Fe(CO)2] 2. Calculate the free energy of activation for the cis/trans exchange process given that the slow exchange peak separation for the Cp protons is 0.120 ppm at 100 MHz and coalescence is 224 K. AG 19.1T. [10.32-log (k/Tc)]
a) For the spreading of the oil C16H34 over water, at constant temperature and pressure, a small change in the surface free energy of the system is given by the total differential: ƏG ƏG ƏG dAB dG =) dA₂+ -) dAAB+ JAAB JAB Knowing that the values of the surface tensions are: Ywater = 72.8 mN m-¹ Y C16H34 = 30.0 mN m-¹ Y C16H34/water = 52.1 mN m-¹ Derive from the above equation an expression for the spreading coefficient and calculate the spreading coefficient for C₁6H34 on water. b) Consider the Gibbs energy of the total system made of two perfect gases (A and B) in two separate containers, at constant temperature and pressure: Gi = μANA + μBnB = NA (μA + RT Inp) + nB (uB +RT Inp) After mixing the two gases, the partial pressures of the gases are PA and P.B. Prove mathematically that the (isothermal and isobaric) enthalpy of mixing AH mix = 0. c) Suggest a mechanism for cis/trans exchange and equilibration of bridging and terminal carbonyl groups in the compound [Cp₂Fe(CO)2] 2. Calculate the free energy of activation for the cis/trans exchange process given that the slow exchange peak separation for the Cp protons is 0.120 ppm at 100 MHz and coalescence is 224 K. AG 19.1T. [10.32-log (k/Tc)]
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
PLEASE ANSWER ALL THE QUESTIONS WITH PROPER REASONINGS. WHY ARE YOU USING THE EQUATIONS AND HOW ARE YOU DERIVING IT. THANK YOU.
![a)
For the spreading of the oil C16H34 over water, at constant temperature and
pressure, a
small change in the surface free energy of the system is given by the total differential:
ƏG
ƏG
ƏG
dG = ( -) dA₂ + (- -) dAAB+ ( ) dAB
OAB
ОAA
AAB
Knowing that the values of the surface tensions are:
Ywater = 72.8 mN m-¹
Y C16H34 = 30.0 mN m-¹
Y C16H34/water = 52.1 mN m-¹
Derive from the above equation an expression for the spreading coefficient and calculate
the spreading coefficient for C₁6H34 on water.
b) Consider the Gibbs energy of the total system made of two perfect gases (A and B) in
two separate containers, at constant temperature and pressure:
G₁ = μANA + μBnB = ṇa (µAⒸ + RT Inp) + nB (µB© + RT Inp)
After mixing the two gases, the partial pressures of the gases are på and P.B. Prove
mathematically that the (isothermal and isobaric) enthalpy of mixing AHmix = 0.
c) Suggest a mechanism for cis/trans exchange and equilibration of bridging and
terminal carbonyl groups in the compound [Cp₂Fe(CO)2]2. Calculate the free energy
of activation for the cis/trans exchange process given that the slow exchange peak
separation for the Cp protons is 0.120 ppm at 100 MHz and coalescence is 224 K.
AG‡ 19.1Tc [10.32 – log (k/Tc)]
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Transcribed Image Text:a)
For the spreading of the oil C16H34 over water, at constant temperature and
pressure, a
small change in the surface free energy of the system is given by the total differential:
ƏG
ƏG
ƏG
dG = ( -) dA₂ + (- -) dAAB+ ( ) dAB
OAB
ОAA
AAB
Knowing that the values of the surface tensions are:
Ywater = 72.8 mN m-¹
Y C16H34 = 30.0 mN m-¹
Y C16H34/water = 52.1 mN m-¹
Derive from the above equation an expression for the spreading coefficient and calculate
the spreading coefficient for C₁6H34 on water.
b) Consider the Gibbs energy of the total system made of two perfect gases (A and B) in
two separate containers, at constant temperature and pressure:
G₁ = μANA + μBnB = ṇa (µAⒸ + RT Inp) + nB (µB© + RT Inp)
After mixing the two gases, the partial pressures of the gases are på and P.B. Prove
mathematically that the (isothermal and isobaric) enthalpy of mixing AHmix = 0.
c) Suggest a mechanism for cis/trans exchange and equilibration of bridging and
terminal carbonyl groups in the compound [Cp₂Fe(CO)2]2. Calculate the free energy
of activation for the cis/trans exchange process given that the slow exchange peak
separation for the Cp protons is 0.120 ppm at 100 MHz and coalescence is 224 K.
AG‡ 19.1Tc [10.32 – log (k/Tc)]
=
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