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Lectures in Classical Thermodynamics with an Introduction to Statistical Mechanics

99 SOLVED PROBLEMS

Question: 25.3

(a) Use the Grand-Canonical ensemble to calculate the standard-state chemical potential, μ0(T), of Ar (g) at 298 K. It is known that (i) the standard-state pressure, P0, equals 1 bar, (ii) the mass of argon is 0.03995 kg/mol, and (iii) the first electronic state of argon is nondegenerate.How does ...

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(a) We are asked to calculate the chemical potenti...
Question: 25.2

Statistical mechanics can be used to predict the dependence of protein folding on temperature. Consider a polypeptide chain consisting of six beads having the energy ladder shown below, where the energy increment of the unfolded states, ε0, is positive. You are asked to answer the following ...

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(a) The degeneracy corresponds to the number of mi...
Question: 25.1

(a) The energies and degeneracies of the two lowest electronic levels of atomic iodine are listed below: Calculate the temperature at which 2% of the iodine atoms will be in the excited electronic state. NOTE: 1 cm^-1 = 1.986 × 10^-23 J, kB = 0.69509 cm^-1 K^-1. (b) Two monoatomic ideal gases ...

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(a) The probability that the iodine atoms will be ...
Question: 24.3

Adapted from Molecular Driving Forces – Statistical Thermodynamics in Chemistry and Biology by Ken A. Dill and Sarina Bromberg, Garland Science, Taylor & Francis Group, New York and London (2003). Hereafter, we will abbreviate the names of the authors as D&B.(a) Given the intermolecular potential, ...

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(a) By inspection of the figure in the Problem Sta...
Question: 24.2

Adapted from Molecular Driving Forces – Statistical Thermodynamics in Chemistry and Biology by Ken A. Dill and Sarina Bromberg, Garland Science, Taylor & Francis Group, New York and London (2003). Hereafter, we will abbreviate the names of the authors as D&B.(a) The protein below has four ...

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(a1) N_{L}=0 \quad \Rightarrow \quad W=\fra...
Question: 24.1

Adapted from Molecular Driving Forces – Statistical Thermodynamics in Chemistry and Biology by Ken A. Dill and Sarina Bromberg, Garland Science, Taylor & Francis Group, New York and London (2003). Hereafter, we will abbreviate the names of the authors as D&B.(a) One mole of a molecular system can ...

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(a1) Because the number of moles, the temperature,...
Question: 23.3

(a) Calculate the vibrational partition function of a diatomic molecule treating the vibrational mode classically. (b) Calculate the average vibrational energy of a diatomic molecule treating the vibrational mode classically.(c) Compare your results in Parts (a) and (b) with the corresponding ...

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In this problem, the main goal is to compare the c...
Question: 23.2

Consider a vessel containing a gas consisting of N independent and indistinguishable atoms at pressure, P, and temperature, T. The walls of the vessel have n adsorbing sites, each of which can only adsorb one atom. Let – ε be the energy of an adsorbed atom. (a) Use the Grand-Canonical ensemble to ...

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This problem asks us to use the Grand-Canonical en...
Question: 23.1

Consider a system of N identical, but distinguishable, particles, each having two energy levels with energies 0 and ε > 0, respectively. The upper level is g-fold degenerate and the lower level is nondegenerate. The total energy of the system is E.(a) Use the Micro-Canonical ensemble to calculate the entropy of the system. ...

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In this problem, we are asked to find the entropy,...
Question: 22.3

For O2(g), the following spectroscopic data is available: Mass = 53.15 × 10^-27 kg Bond Length = 1.21 × 10^-10 m v = 1567 cm^-1 D0 = 118 kcal mol^-1 (a) What is the fraction of O2(g) in the ground translational state when T = 298 K and V = 1000 cm^3? (b) What is the fraction of O2(g) in the ...

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The fraction of O _{2}( g ) in a sp...
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