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Calculating Entropy Changes

1. Total Entropy Change
2. Entropy change for the System
3. Entropy change for the Surroundings
4. External Links
5. References
6. Contributors

Entropy (S) of the universe is always increasing, and is denoted by S.

1. Total Entropy Change
2. Entropy change for the System
3. Entropy change for the Surroundings
4. External Links
5. References
6. Contributors

Total Entropy Change

A system and surrounding are both components of the universe (total), which can be seen in this equation:

ΔS_total=ΔS_univ= ΔS_sys + ΔS_surr>0

the system and surroundings collective represent the change in entropy. The entropy change of the surroundings is driven by heat flow and the heat flow determines the sign of ΔS_surr. Therefore if we had an exothermic reactions with a constant temperature the system would cause heat to flow into the surroundings, which causes ΔS_surr to become positive. The opposite can be see in an endothermic reaction.

Entropy change for the System

We begin by first calculating the difference between the standard entropy values of the products and standard entropy values of the reactants:

ΔS_reaction=Δn_pS_products - ΔnpS_reactants

where S represents entropy, and n_p and n_r represent moles of products and reactions. Once the you have calculated the entropy of the system, you can calculate the entropy change for the surroundings.

Entropy change for the Surroundings

And from the Second Law of Thermodynamics, we know that the sign of ΔS_total determines whether the reaction under investigation happens spontaneously. For calculating the entropy for the surrounding, we can use the general definition of S:

ΔS_surroundings = ? dS _surroundings = ? (Δq _surroundings / T _surroundings)

In which ?q is the element of heat and T is temperature (in K). From the conservation of energy, q _surroundings and q _system are related:

q _surroundings = - q _system

In general, to do the integration, one needs to know T along the path. As a common specific case, if the surrounding is big enough (e.g. the lab or the universe, with respect to the beaker in which the experiment is being done is too big), one can assume that temperature (T) does not change during the course of the reaction, in which case the integral is simplified:

ΔS_surroundings = q _surroundings / T _surroundings = - q _system / T _surroundings

in which the value for q _system is the same as enthalpy change and internal energy (internal energy change) of the system at constant pressure and constant volume, respectively.

Example

For example, if one has a generic reaction

Reactants --> Products q_rxn = 75 kJ at 300K

Then, for the surrounding, one has,

ΔS_surroundings = - (75 × 103 ) / 300 = 250 J/K

One should appreciate the fact that the aim of defining new state functions like Gibbs free energy and Helmholtz free energy is partly to bypass the calculation of the change in the entropy of the surrounding. Calculating the entropy change for the system in such thermodynamic potentials can substitute the calculation of the total entropy in determining the spontaneity of the reaction (under particular conditions (e.g., G, Gibbs free energy is useful at constant pressure (isobar) and constant temperature (isotherm) conditions).

External Links

http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node40.html
For more information about entropy and how it relates to the second law of thermodynamics, click here: www.entropysite.com_students_approach.html">http://www.entropysite.com/students_approach.html
To see some entropy calculation examples, click here: http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node40.html
For more information on entropy, click here: web.chemistry.gatech.edu_~williams_bCourse_Information_6521_dgdsdh_text_1.html">http://web.chemistry.gatech.edu/~williams/bCourse_Information/6521/dgdsdh/text_1.html
To see how the entropy change of the surroundings relates to entropy and the entropy change of the system, click here: http://www.dartmouth.edu/~chemlab/chem3-5/calor2/full_text/chemistry.html
To see how entropy relates to Gibbs free energy, click here: http://www.2ndlaw.com/gibbs.html
http://www.2ndlaw.com/
http://id.mind.net/~zona/mstm/physics/mechanics/energy/heatAndTemperature/heatAndTemperature.html

References

Zumdahl, Steven S. Chemistry. New York: Houghton Mifflin, 1997.
Kotz, John C., Paul M. Treichel and Grabriela C. Weaver. Chemistry and Chemical Reactivity. Belmont: Brooks Cole, 2005.
Greiner, Neise, Stocker - Thermodynamics and Statistical Mechanics (Springer, 1997)
Petrucci, Harwood, Herring, Madura. General Chemistry: Principles & Modern Applications, Ninth Ed. Upper Saddle River, NJ: Pearson Education, Inc., 2007.
McMurray, Fay. Chemistry, Third Ed. Upper Sadle River, NJ: Prentice-Hall, Inc., 2001.

Contributors

Cindy Ramirez (UCD), Zafir Javeed (UCD)

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