# Search in the document preview

1

**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.

Docsity.com

2

**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.

10

**
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

15 None

Docsity.com

3

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

Docsity.com

4

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

Docsity.com