MODULE CODE : CHEM0019
ASSESSMENT PATTERN: CHEM0019A5UD 001
CHEM0019A5UE 001
MODULE NAME : Physical Chemistry
Candidates should attempt ALL questions. Each question is marked out of 20 and the numbers in square brackets in the right-hand margin indicate the provisional allocation of marks to the subsections ofa question. To obtain full marks you must show all steps of your working. You must write down all equations and all the numerical values that you use in your calculations.
1. Answer ALL parts.
(a) Consider the following elementary reactions, with rate coefficients indicated:
A2 + M → 2A + M k1
A + B → C + D k2
C → A k3
(v) Explain BRIEFLY what is meant by the steady state approximation and use it to obtain an expression for the concentration of species A in terms of rate coefficients and other species concentrations in the reactions above. [2]
(b) (i) Write down the mechanism proposed by Lindemann to account for the kinetics of the unimolecular decomposition reaction
E = products (P). [3]
(ii) Using your mechanism, derive an expression for the rate of product (P) formation in terms of rate coefficients and stable molecule concentrations only. [2]
(b) (iii) The experimentally observed rate coefficient kobs for the decomposition of species E, defined by
was found to be k bs = 57.1 s–1 when the total concentration of all species present [M] = 5 × 10–3 mol dm–3
, and k bs = 64.0 s–1 when [M] = 8 × 10–3 mol dm–3
. Use these data to determine a rate coefficient and a ratio of rate coefficients from elementary reactions in your mechanism.
(iv) Explain BRIEFLY and QUALITATIVELY the principal deficiency of the Lindemann mechanism and how the mechanism could be improved. Kinetic derivations are not required here. [2]
2. Answer ALL parts.
(a) 2 H127 I has a rotational constant B0 = 3.223 cm-1 and harmonic wavenumber we = 1639.65 cm-1.
(i) Calculate the reduced mass of 2H127I in kg. [3]
(ii) Calculate the equilibrium bond length r0 of 2H127I in pm. [3]
(iii) Calculate the force constant k of 2H127I in N m–1
. [3]
(iv) Explain how the rotational constant would vary with increasing vibrational quantum number. [1]
(b) In the vibrational absorption spectrum of 1H81Br, the fundamental and first overtone lie at 2558.54 cm-1 and 5026.645 cm-1 respectively.
(i) Label these transitions on an energy level diagram and determine we and wexe. [5]
(ii) Calculate the well depth De and dissociation energy D0 of 1 H81Br in cm-1. [3]
(iii) Explain how D0 and De would differ for 2 H81Br compared to 1 H81Br. [3]
USEFUL INFORMATION
Relative isotopic masses: 2 H 2.014; 127 I 126.904
3. Answer ALL parts.
The π molecular orbitals (MOs) of 1,3-butadiene may be expressed using a linear combination of atomic orbitals, , where is the carbon 2p orbital perpendicular to the molecular plane at atom k with the atomic labelling
H2C1=C2H-C3H=C4H2. A Hückel calculation gives normalised π MOs (Ψiπ with i = 1, 2, 3, 4) with the following coefficients:
(a) Using circles of different size and shading to represent the magnitude and
phase of the atomic orbital coefficients, sketch the π MOs, indicating any nodal planes. [4]
(b) Write down the Hückel secular equations in matrix form in terms of
(f) A Hückel calculation on C2 H4 (ethene) yields a total π electron energy of
2α + 2β and a π bond order of 1. Compare these values to those
calculated in parts (c) and (e), and hence describe the π bonding in 1,3-
butadiene. How realistic are the assumptions in the Hückel calculations for 1,3-butadiene? [6]
4. Answer ALL parts.
(a) 14N16O has a doubly degenerate ground electronic state and a low-lying doubly degenerate first excited state of the same multiplicity at a relative energy corresponding to a wavenumber of 121 cm-1.
(i) Assuming that no other electronic states contribute, write the
expression for the electronic partition function qE and calculate its value at 298 K. [4]
(ii) State how you would expect the expression for qE to change if both
the ground and the first excited electronic states were non-
degenerate and separated by a much larger energy. [1]
(iii) Explain why a maximum is observed at approximately 75 K in the
calculated excess heat capacity CV for 14N16O. [4]
(b) The rotational temperature of a molecule is given by , where B is the rotational constant. This expression is used to justify the validity of the continuum approximation. For 14N16O:
(i) calculate the rotational temperature given that its moment of inertia
5. Answer ALL parts.
(a) Define the term azeotrope. Sketch and label the temperature-composition
phase diagram for a positive azeotrope. Indicate the azeotropic composition on the diagram. [3]
(b) 2.5 kg of benzene (molar mass Mb = 78.11 g mol-1) is mixed with 1.5 kg of
toluene (molar mass Mt = 92.14 g mol-1) at 303.15 K. Assuming ideal
behaviour, calculate the Gibbs energy of mixing, the entropy of mixing and the enthalpy of mixing. [8]
(c) Two components, A (vapour pressure of pure A, pA(*) = 26.3 kPa) and
B ( pB(*) = 23.4 kPa) are mixed at 298.15 K. At equilibrium after mixing, the mole fractions of A in the liquid phase and in the vapour phase are
xA = 0.7 and yA = 0.81 respectively. The total vapour pressure of the
mixture is p = 20.3 kPa. Calculate the excess molar Gibbs free energy of
the mixture. Is mixing of A and B more or less favourable than that in an ideal mixture? [5]
(d) Molecules composed of a hydrophilic head and a hydrophobic chain can
form. structures in water, where the solvated heads are on the surface protecting the chains at the centre from the solvent. These structures form. in response to a chemical potential μ = Ya + Ka , where a is a variable describing the solvated surface of each molecule exposed to water, γ is a constant describing the attraction between the chains, and K is a constant describing the repulsion between the heads. Draw and label a plot of μ as a function of a. Comment on the nature of this equilibrium in terms of the dynamics described above. [4]