CH273 Properties of Solutions and Foundations of Electrochemistry and Statistical Mechanics
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CH273_A
Properties of Solutions and Foundations of Electrochemistry and Statistical Mechanics
PROPERTIES OF SOLUTIONS AND FOUNDATIONS OF ELECTROCHEMISTRY
AND STATISTICAL MECHANICS (CH273)
1. Answer ALL parts
(a) Describe the purpose of the 2nd Debye-Hückel approximation.
[10%]
(b) Consider the Br2 molecule, which is characterised by a symmetric electronic
ground state. The Br nucleus has spin number I = 3/2. In the case of para-Br2 , is the rotational wave function symmetric or anti-symmetric? Explain your reasoning. Assume that the symmetry of the nuclear wavefunction of para-Br2 is the same of para-H2 .
[30%]
(c) Consider the following gas phase reaction, taking place at the temperature T = 1565 K:
H2 + CO2 ⇋ H2O + CO,
(i) Write down the expression for the equilibrium constant in terms of partial pressures, Kp(T), in terms of molecular partition functions.
[10%]
(ii) Calculate the translational contribution to Kp(T).
[10%]
(iii) Calculate the vibrational contribution to Kp(T). Assume that the zero of the
energy corresponds to the vibrational ground state. Note that CO2 and H2O have N=4 and N=3 different vibrational modes. Each i-th mode is characterised by a different vibrational temperature (vib,i, given in Table1), and the vibrational partition function for a molecule with N vibrational modes can be written as:
Table 1
|
CO2 |
H2O |
H2 |
CO |
|||||
vib,i [K] |
3381 |
1899 |
961.1 |
961.1 |
5404 |
5254 |
2295 |
6332 |
3122 |
[30%]
(iv) Calculate Kp(T), knowing that the rotational and electronic contributions at the temperature of interest are equal to 23.56 and 0.0445, respectively.
[10%]
2. Answer ALL parts
(a) Explain why the virial expansion cannot be used to describe dense liquids. [10%]
(b) Consider the two molecules K2 and CO, which are characterised by a
vibrational temperature of 133 K and 3103 K, respectively. Sketch, qualitatively, on the same graph, the population of the vibrational levels, fn(n,T), as a function of the vibrational quantum number n, at temperature T = 10 K. On a different graph, sketch the same populations, this time at T = 300 K. Comment on any differences between the two graphs, providing justifications.
[30%]
(c) Consider a homonuclear diatomic molecule characterised by a symmetry number, G = 2.
(i) Write an expression for the rotational partition function of this molecule in the high-temperature limit.
[10%]
(ii) Derive the expression for the rotational contribution to the thermodynamic
energy, Erot, which can be written as:
[20%]
(iii) Derive the expression for the rotational contribution to the heat capacity,
CV,rot(T), which can be written as:
[10%]
(iv) Sketch the rotational contribution to CV,rot(T) as a function of temperature. [10%]
(v) Do you expect the result in (iv) to hold if we start with the low-temperature expression of the rotational partition function? Justify your answer.
[10 %]
3. Answer ALL parts (a)
(i) Explain what is meant by a partial molar entropy measurement and how it can be used to determine whether a hydrated ion is structure making or structure breaking. Use the following partial molar entropy data to illustrate your answer, explaining the differences between the three values:
Ca2+ = -101 J K-1 mol-1 ; H+ = -23 J K-1 mol-1 ; and I- = +135 J K-1 mol-1 .
(ii) What partial molar entropy value would be expected if an ion was behaving
ideally?
[30%]
(b) Electrochemical methods can be used to determine equilibrium constants, K,
for reactions.
Using the table of standard electrode potentials, Eo , provided:
(i) Outline an electrochemical cell that could be used to calculate K for equation 1, under standard conditions.
(ii) Provide the cell notation and individual half-cell equations which when
combined give equation 1.
(iii) Sketch the cell set-up including solution conditions.
(iv) Calculate K.
(1) 2[Ru(CN)6]4- + Cl2 一 2[Ru(CN)6]3- + 2Cl-
(i) Calculate the cell potential, E, and the new K, if the activities of all the potential determining ions were 1 x 10-5 .
[30%]
(c) Milk can be described as an electrolyte containing suspended immiscible non- aqueous droplets. Explain why the liquid droplets do not coalesce in milk.
[15%]
(d) Discuss the differences in the molar conductivity values in -1 cm2 mol-1 for the four ions below at 298 K in pure sulfuric acid. Predict what would happen to these values if the measurements were made in water, which is less viscous
than sulfuric acid.
Na+ = 3; K+ = 6; H+ = 151; HSO4- = 152
[25%]
4. Answer ALL parts
(a) Electrolyte solutions are non-ideal. Deviation from ideal behaviour can be
described in terms of an activity coefficient, γ± .
(i) Calculate γ± for an aqueous solution of 0.0002 M KNO3 .
(ii) What concentration of CuSO4 would give the same γ± as in (i)? (iii) Provide a physical explanation, in terms of the Debye-Huckel theory, as
to why the concentrations of the two electrolytes in (i) and (ii) are different.
[25%] (b)
(i) Why is a 3-electrode set up used for voltammetric studies with macroscopic electrodes and what are the roles of each of the 3 electrodes?
(ii) Why can a simpler 2-electrode set up be used for voltammetric studies
with ultramicroelectrodes and what are the 2 electrodes?
(iii) Write an equation for the limiting current density (current divided by
electrode area) at a disc shaped ultramicroelectrode (UME), consult Appendix 2 for a starting equation.
(iv) What does the diffusion field look like at an UME and why is there an
interest in fabricating increasingly smaller electrodes?
[30%] (c)
(i) Sketch the shape of a plot of conductivity versus concentration for a strong (1:1) electrolyte from 0 to 1 mM and explain the characteristic features.
(ii) How would you expect the plot to differ if the electrolyte was replaced
with a (2:2) electrolyte? Explain your reasoning.
[25%]
(d) Calculate rGo and the equilibrium constant, K, under standard conditions (use
the Table of standard potentials supplied):
acetaldehyde + NADH + H+--> ethanol + NAD+
[20%]
2022-08-23