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Physical Chemistry

-f z=m\left(\frac{d^{2} z}{d t^{2}}\right)

O What is the mathematical operator in this equation?

(10%) Under what conditions is the function z(t) = B sin (wt) a solution of Eq. 6.2? Justify your answer by showing a detailed proof.

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Physical Chemistry

Q2 (40%) Consider a system at 400 K which has an infinite ladder of evenlyspaced quantum states with an energy spacing of o.15 kJ/mol. You may assumethat the ground state has an energy of ɛo= o and that all the states are non-degenerate (g = 1).

1. (10%) What is the minimum possible value of the partition function for this system? Justify

O What is the value of BAɛ for this system?

3. (10%) Estimate the number of quantum states which are populated.thermally

4. (10%) If the temperature is doubled, estimate the number of thermally populated states.

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Physical Chemistry

Q1 (40%) Given that translational and rotational degrees of freedom typically behave classically, but vibrations behave quantum mechanically, the total(average) energy of a diatomic is predicted to be, U = (5/2)RT + <e>, where <e> is obtained from Eq. 1.24 in the textbook.

1. (10%) Calculate the contribution from translation and rotation to the molar heat capacity of the Cl2 gas at 400 K.

2. (10 %) Calculate the contribution from vibration to the molar heat capacity of the Cl2 gas at 400 K, given that diatomic molecule Cl, has a vibrational wavenumber of 565 cm¬1.

3. (10%) Predict the molar heat capacity of Cl2 gas at 400 K and compare your result with the experimental molar heat capacity of Cl2 , Cy × 29 J/(K mol) at400 K.

6) Calculate the average internal energy <U> for the Cl2 gas at 400 K.

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Physical Chemistry

- (a) Explain why quantisation of energy occurs. What experimental evidence is [5]there to indicate that energy is quantised?

The Boltzmann equation for the difference in population between two energylevels is:

\frac{n_{\text {uper }}}{n_{\text {lower }}}=\exp \left(\frac{-\Delta E}{k T}\right)

where h is Planck's constant, yis the gyromagnetic ratio (which equals 42.58×10Hz Tesla for 'H), and B is the applied magnetic field (in Tesla).

O Describe qualitatively the effects on the populations of the energy states of a six [4]level system, where the gap between each subsequent level is approximately2x102 J, on decreasing the temperature from 300 K to 100 K.

In NMR spectroscopy, the energy gap between the ground and excited states is given by:

\Delta E=\frac{h \gamma B}{2 \pi}

where AE is the energy gap between the states (in J), k is the Boltzmann constant,and Tis the temperature.

Calculate the population difference between the ground and excited states for 'H atB = 7 Tesla and 300 K, and hence comment on the sensitivity of NMR as a spectroscopic technique.

Calculate the wavelength of the electromagnetic radiation that would be absorbed in the transition in part (c). In what part of the electromagnetic spectrum does this radiation lie?

For electronic spectroscopy, deltaE =1.97 x 10 J. Comment on the consequences of this value for the spectroscopic technique.

• Peaks observed in electronic spectroscopy are broad (Av = 1.6 MHz), where as those observed in NMR spectroscopy are very narrow (Av= 1.6 Hz). Explain this difference, and also explain how it affects the uses of the two spectroscopic methods.

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Physical Chemistry

(a) Explain the physical principles of absorbance of light by a chromophore.Why is light of specific wavelengths absorbed? Give two examples of biological chromophores.[S]

(b) Explain using the appropriate equations what is meant by (i) the Transmittance (T) and (ii) the Absorbance (A) of a solution. What is the relationship between A and T?

3 ml of a solution of the oxidized copper (Cu²) protein pseudoazurin was prepared. The solution had an absorbance of 0.25 at 590 nm in a cuvette of path length 1 cm.

(c) Calculate the mass of pseudoazurin required to make up this solution if the molar absorptivity of oxidized pseudoazurin is 1390 M' cm' at 590 nm and the molecular weight is 12,000.

(d) Explain what would happen to the absorbance of the material in (c) if the spectrum was recorded on a spectrophotometer with a lamp of 10 times the intensity of that used in (c).

If pseudoazurin is reduced so that the copper ion is in the Cu* oxidation state,the protein no longer has any absorbance in the visible region of the electromagnetic spectrum. Physiologically, the copper of reduced pseudoazurindonates one electron to the enzyme nitrite reductase (NiR), which catalyses the one-clectron reduction of nitrite to nitric oxide.

(e) 5 µl of a 10 mg ml" solution of NİR was added to a 1 cm path length cuvette containing 2.5 ml of a solution of 10 mg ml" reduced pseudoazurin and nitrite. The absorbance at 590 nm increased by 0.3 unit sin 2 minutes. Calculate ket (in units of s'; i.e. mol NO produced per mol of NiR per sec) for NiR if its molecular mass is 120,000 and the enzyme reduces nitrite to nitric oxide at a constant rate in this experiment.

(f) Explain why pseudoazurin containing Cu* absorbs in the visible region of the electromagnetic spectrum whereas the protein containing Cu' does not.

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Physical Chemistry

(a) Explain how the spatial localisation of waves leads to the quantisation ofencrgy.

(b) Starting from the de Broglie relationship and the equation for kinetic energy,show that the allowed energy levels for a wave on a circle are:

E=\frac{n^{2} h^{2}}{2 m C^{2}}

where C is the circumference of the circle and n is an integer.

The R-clectrons of benzene (CHg) can be treated as waves localised on a “circle"with a circumference that equals six times the carbon-carbon bond length. In thissimplified model, the lowest energy level (n=0) is singly degenerate, and all theother levels are doubly degenerate.

Assuming a carbon-carbon bond length of 140 pm, usc the equation derived(c)in (b) to calculate the energies of the first four allowed levels for the T-clectrons of benzenc.

(d) Calculate the wavelength of the lowest energy transition in the UVabsorption spectrum of the x-clectrons of benzene.

(c) Compare the results from (c) and (d) with:

O the measured value of 180 nm for the lowest energy transition in theUV spectrum of benzene;

(i) the measured values of 9.4 eV and 12.3 eV for the ionisation potentialsfrom the occupied benzene R-orbitals.

What is the most likely explanation for any discrepancies?

\left[\text { Mass of an electron }=9.1 \times 10^{-31} \mathrm{~kg} ; 1 \mathrm{pm}=1 \times 10^{-12} \mathrm{~m} ; 1 \mathrm{~J}=6.24 \times 10^{18} \mathrm{eV}\right]

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Physical Chemistry

(a) Explain the concept of the steady-state approximation with reference to thereaction scheme:

Where k, and k,are first order rate constants.

(b) Use the steady-state approximation to derive the Michaelis-Mentonequation for the rate of an enzyme-catalyzed reaction and explain themeaning of the parameters Km and Vmax.

The activity of triose phosphate isomerase (TPI) was studied as a function of theconcentration of its substrate, glyceraldehyde 3-phosphate (GAP) with thefollowing results.

The velocity is expressed in the units mM GAP consumed min'.

appropriate graphical procedure to determine the values of Km and Use an Vmax.

O TPI is a dimer with a molecular weight of 52000 Daltons. The assay mixture contained 1 ug enzyme per dm, and only 3.8% of the substrate was in the reactive hydrated form. Use this information, and your values ofK and Kto calculate k

Comment on the significance of the keat/Km value.

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Physical Chemistry

(a) Starting from the definition of an acid dissociation constant, derive an equation that relates the pH of an equilibrium mixture of an acid and its conjugate base to the composition of the solution.

(b) Which ionisable groups are likely to contribute to the buffering capacity of the intracellular medium at normal intracellular pH values? What other mechanisms are available for maintaining intracellular pH values at appropriate values?

(c) The pKa of methanoic acid is 3.8. What ratio of methanoic acid to sodium methanoate would be necessary to give a solution of pH 4.5?

(d) Methanoic acid/methanoate is going to be used as a buffer for a reaction. The unbuffered reaction at pH 4.5 results in a decrease in the pH of 2.5 units. What is the minimum concentration of the buffer needed to prevent the pH falling below 4.25?

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Physical Chemistry

State the Arrhenius equation, and use it to calculate the effect on the rate constant of an increase in temperature from 10°C to 35°C for a reaction with an activation energy of 80 kJ mol·'.

b) Describe the main features of the transition state theory of reaction rates, including a full explanation of the terms in the Eyring equation for a bimolecular rate constant (k2):

\mathrm{k}_{2}=\mathrm{K} \times \frac{\mathrm{kT}}{\mathrm{h}} \times \mathrm{K}^{\dagger}

c) Describe the underlying thermodynamic parameters that determine the reaction profile, and explain the relationship between the Eyring equation and the Arrhenius equation.

) The temperature-dependence of the activity of a Ca2+-ATPase was measured with the following results. The activity is expressed in arbitrary units.

(e) Comment on the implications of the data for the reaction mechanism.

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Physical Chemistry

6. One material normally has multiple types of bonding. Some are dominant (major) bonding and some are non-dominant (minor) bonding. What type(s) of bonding would be expected for each of the following materials: solid xenon, calcium fluoride (CaF2), bronze (a copper-tin alloy), cadmiumtelluride (CdTe), rubber, and tungsten? Please identify the major and the minor types of bonding.

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