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Thermodynamics (Classical) for Biological Systems
Additional Problems for Practice
The students have worked out many problems (tutorials), based on the principles discussed,
during the class time itself, to improve understanding through active learning. The following
problems are additional problems that the student can work out, to further strengthen the
understanding of the course material, and to develop skills of application of the fundamentals. In
addition, the students can work out the problems at the back of the relevant chapters in the text-
book by Smith, VanNess and Abbott, given in the next Table.
Topic Corresponding chapter in SVA
Module 2: Additional useful thermodynamic functions The thermodynamic functions H, A and G Concept of chemical potential Equations for a closed system, Maxwell’s relations Gibbs-Duhem equation Thermodynamic analysis of processes – lost work, irreversibility
6 10 6 10 16
Module 3: Thermodynamic properties of pure fluids Review of ideal gas, non-ideal gas, fugacity, fugacity coefficient PVT behaviour, virial and cubic equations of state, generalized correlations Residual properties Estimation of thermodynamic properties using equations of state Estimation of the fugacity coefficient.
10 3 6 13 10
Module 4: Thermodynamic properties of solutions Ideal and non-ideal solutions, partial molar properties, excess properties of mixtures, activity coefficient and its estimation.
Module 5: Phase Equilibria Criteria for phase equilibria Phase rule Clausius-Clayperon equation VLE for pure component, VLE for multi-component system
10 2 6 11
Module 6: Reaction Equilibria Equilibrium criteria for homogenous reactions, evaluation of equilibrium constant, effect of temperature and pressure on equilibrium constant Ionic equilibria
1. At high tempearture, 1 mole of a non-ideal gas in a system undergoes changes
isothermally. A PV versus P curve is drawn for that. Using the Van der Waals EOS
(i) Find RT at minima of the curve
(ii) Find T given that at minima P = 0 (approx)
(problem formulated by Pallavi Singh)
2. Show that
3. Show that (derive) the constants in the Redlich-Kwong equation of state can be expressed in
terms of the critical properties as
4. For a pure bio-substance, the compressibility factor was given by the first three terms of the
virial expansion in terms of the pressure, i.e. . Express the following
quantities for such a bio-substance in terms of P, T, B1 and B2 alone: (a) fugacity coefficient (b)
fugacity (c) GR (d) VR (e) HR
(problem formulated by Akhil Sai Valluri)
5. A solution mixture is made up of methanol and ethanol. The difference in volume of the
solutions upon mixing is given by Δ V = 4 x2 + 24, where x2 is the mole fraction of ethanol. If
the initial volume of ethanol taken was 10 L, then estimate the partial molar volume of ethanol
solution in the given mixture.
(problem formulated by Pallavi Chakraborthy and V. Sowmya)
6. A solution of an imaginary liquid and water is prepared.0.2 moles of the liquid is again added
to the solution prepared, and mixed thoroughly, to retain the same temperature T = 300 K, and
pressure P = 0.5 bar. For this liquid, γ, i.e., the activity co-efficient, is found to be a function of
pressure, and is known to be . The calculated molar volume (ideal) of the
imaginary liquid is 1260 m3 mol-1
(problem formulated by Chetan Shenoy and Kanishka Waghmare)
. Find the change in the volume of the solution on addition of
the excess liquid.
7. Ampicillin is a β-lactam antibiotic that has been extensively used to treat bacterial infections.
It is able to penetrate gram +ve and some gram –ve bacterial cell envelopes. An ampicillin
solution in distilled water has a molar volume (in m3 mol-1
) given by the following equation, in
terms of the relevant mole fractions; the subscript 1 refers to ampicillin:
Find the expressions for the partial molar volumes of ampicillin and water. Also find the
expressions for the partial molar volumes at infinite dilution.
(problem formulated by Shikha Jain)
8. Consider the reaction of splitting water into oxygen and hydrogen (where does splitting water
occur in nature?). Find the number of degrees of freedom for this system.
(problem formulated by Akhil Sai Valluri and Aman Kumar)
9. Starting with Eq. 6.27 (discussed in the class), and by following a similar procedure to arrive
at the Van’t Hoff’s equation, derive Eq. 6.41.
10. Starting with Eq. 6.47 (discussed in the class), derive Eq. 6.48