CHM2304(S1)

CHM2304(S1)

CHM2304(S1) 1 CONTINUED

Data Provided: Chemistry Ancillary Booklet THE UNIVERSITY OF SHEFFIELD DEPARTMENT OF CHEMISTRY Autumn Semester 2013/2014 2 hours duration PHYSICAL CHEMISTRY 4 Questions – Answer ALL Questions You MUST answer each QUESTION in a SEPARATE Answer Booklet

CHM2304(S1)


1. Answer all parts of this question.

The Clapeyron equation, shown below, gives the rate of change of pressure with temperature for a first-order phase transition, in terms of entropy and volume changes.

(a) Provide a simple derivation of this equation.

[6 marks]

(b) The Clausius-Clapeyron equation for the variation of vapour pressure with temperature can be written as

€

d ln pdT

⎛

⎝ ⎜

⎞

⎠ ⎟ =

ΔvapHRT 2

where the symbols have their usual meaning. Derive this equation from the Clapeyron equation, stating any approximations that you make.

[6 marks]

(c) The vapour pressure of ethene as a function of temperature is given by the expression

€

log(p /Pa) =−843.13T /K

+1.75xlog(T /K) − 8.375x10−3(T /K) + 5.3240

Calculate the enthalpy of vaporisation of ethene at its normal boiling point (169.3 K)

[6 marks]

(d) State Trouton’s rule. Does your answer to part (c) agree with this rule? If not, why not?

[2 marks]

CHM2304(S1)



(a) The time-independent Schrödinger equation for a single particle with one degree of freedom and potential energy function V(x) can be written in general form as

€

ˆ H ψ = Eψ

(i) Give the detailed mathematical form of the Hamiltonian operator in this one-dimensional Schrödinger equation, defining all symbols that you introduce.

[2 marks]

(ii) What conditions must be obeyed by the functions ψ(x) if they are to represent physically acceptable solutions for this problem?

[4 marks]

(iii) What does it mean to say that two wavefunctions are orthogonal?

[1 mark]

(iv) What does it mean to say that two wavefunctions are orthonormal?

[1 mark]

(v) What does it mean to say that two wavefunctions are degenerate?

[1 mark]

(b) A particular case of the one-dimensional Schrödinger equation applies to the ‘particle on a ring’, where a particle is confined to a circular path defined by an angle ϕ.

(i) Describe and sketch the potential function V(ϕ) for this case.

[1 mark]

(ii) State the boundary condition on the wavefunction, and explain why this leads to the introduction of a quantum number for the particle on a ring.

[2 marks]

(iii) Give a formula for the energy levels of the particle on a ring, defining all symbols that you introduce. Illustrate the formula with an energy level diagram, showing any degeneracies that may be present.

[4 marks]

(iv) What is the analogue of the usual Heisenberg Uncertainty Principle for the case of the particle on a ring?

[1 mark]

(v) Given that the particle is a proton, and the circle is of radius 0.1 nm, calculate the frequency of radiation needed to raise the system from its ground state to its first excited state.

[3 marks]

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(a)

(i) Define the terms molecularity and order of a chemical reaction.

[2 marks]

(ii) Describe the concept of the pre-equilibrium and of the rate-limiting step.

[2 marks]

(b) Consider a process, which has the following experimental rate law:

v = kr[CH3CO]3/2

Assume that the mechanism consists of the following elementary steps:

CH3CHO → •CH3 +•CHO •CH3 + CH3CHO → CH4 + •CH3CO •CH3CO → •CH3 + CO •CH3 + •CH3 → C2H6

(i) What is the role of CH3 and CH3CO? [1 mark]

(ii) Assign names to each elementary step in this reaction.

[1 mark]

(iii) What is the stoichiometric equation for this reaction?

[2 marks]

(iv) Define the steady-state approximation.

[2 marks]

(v) Write down a rate equation for each of the intermediates in this reaction, CH3 and CH3CO.

[2 marks]

(vi) Apply steady-state approximation to the intermediates from (v).

[2 marks]

(vii) Derive the equation for the concentration of the CH3 radical.

[2 marks]

(viii) Use the equation for the concentration of CH3 radical to derive the reaction rate law with respect to CH4.

[2 marks]

(ix) Does the rate law you derived under (viii) correspond to the experimental rate law? Justify your answer.

[2 marks]

CHM2304(S1)


4. Answer all parts of the following question.

(a)

(i) Define the distribution ratio D for a base B, and explain the difference between D and the distribution (or partition) coefficient KD.

(ii) Calculate the percentage of base B left in the aqueous phase at pH 10, when 100 mL of a solution of base B in water is extracted with 50 mL of dichloromethane (assume KD = 5 and Ka = 10-9 M).

(iii) Will base B be more soluble or less soluble in the dichloromethane phase at pH 2? Explain your reasoning.

[5 marks]

(b)

(i) Explain the thermodynamic basis of a chromatographic separation.

(ii) Define the height equivalent to a theoretical plate (HETP). Explain how this parameter is used for the selection of a chromatographic column, assuming that the columns have the same number of theoretical plates.

(iii) In ion-exchange chromatography, how would you increase the ionic strength of the mobile phase during elution?

[5 marks]

(c) An HPLC analysis was conducted for caffeine on a sports drink. A 10.1 ppm methanol internal standard was introduced, both into the unknown sample and into a solution of 304 ppm caffeine standard. The absorbances for methanol and for caffeine are summarised in the table below. Calculate the concentration of caffeine in the sports drink.

methanol internal standard

(arbitrary units)

caffeine

(arbitrary units)

unknown sample 23141 52777

304 ppm caffeine standard 28441 77313

[6 marks]

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(d)

(i) Briefly explain the basis of separation in gas chromatography (GC).

(ii) State the type of stationary phase you would choose to separate a mixture of hydrocarbons with a wide range of molecular weights.

(iii) How would you elute high molecular weight hydrocarbons showing peaks with high retention times in GC?

[4 marks]

END OF QUESTION PAPER

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