Calculating Entropy Changes
Entropy (S) of the universe is always increasing, and is denoted by S.
Total Entropy Change
A system and surrounding are both components of the universe (total), which can be seen in this equation:
ΔStotal=ΔSuniv= ΔSsys + ΔSsurr>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 ΔSsurr. Therefore if we had an exothermic reactions with a constant temperature the system would cause heat to flow into the surroundings, which causes ΔSsurr 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:
ΔSreaction=ΔnpSproducts - ΔnpSreactants
where S represents entropy, and np and nr 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 ΔStotal determines whether the reaction under investigation happens spontaneously. For calculating the entropy for the surrounding, we can use the general definition of S:
ΔSsurroundings = ? 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:
ΔSsurroundings = q surroundings / T surroundings = - q system / T surroundings
For example, if one has a generic reaction
Reactants --> Products qrxn = 75 kJ at 300K
Then, for the surrounding, one has,
ΔSsurroundings = - (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).
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