The entropy change can be calculated using this equation as long as the temperature remains constant.įor example, Chloroform, CHCl 3, is a common organic solvent once used as an anesthetic. Δ S is the entropy change of the system measured in J/K, and T – the temperature in Kelvin Rearranging the equation, we get an expression for Δ S: Remember, also that when the system is at equilibrium the Gibbs free energy is equal to zero: To derive an equation for the entropy change associated with phase transitions, we need to remember that these changes occur when the system is at equilibrium. Remember this pattern, and the corresponding terms for each pair of opposite processes: melting/fusion vs freezing, evaporation/vaporization vs condensation.Ĭalculating the Entropy Change of State Changes These are the points of phase transitions where, for example, the liquid turns into a gas even at the same temperature. Notice how the entropy is still increasing in the regions where the temperature is not changing. The phase transition graph showing the entropy vs temperature is very useful to visualize this concept: This behavior is explained by the increasing freedom of motion when molecules go from the most ordered solid state to liquid, and then a gas state where the degree of randomness is the highest. The results show that the present method is robust even for a complex system with some metastable states.On the basis of determining the entropy change associated with phase transitions is the third law of thermodynamics: the entropy of a perfect crystalline substance is zero at the absolute zero temperature.Īn implication of this is that the entropy is the lowest in solids, and it keeps increasing in the order of going to liquid and gas states: solid < liquid < gas. Moreover, the error bars are approximately one-half of those obtained using QHA. In contrast, the error of DFT/HNC is very small from low to high temperature. 4) cannot completely deal with such a mode. 26 The Gaussian distribution employed in QHA (dashed line in Fig. 4, which is usually observed in proteins. However, the principal mode with the lowest frequency has a double-well character, as shown in Fig. By evaluating the principal modes in QHA, metastable states are partially described. Although the QHA approach somewhat corrects the errors of HA, the deviation at high temperature is still large. At 280 K, however, the distribution has two peaks and the contribution from another metastable state is underestimated in HA qm. In HA qm, entropy is computed by harmonic oscillators around the most stable geometry ( ϕ = − 73.3 ° and ψ = 65.8 °). The reason for this may be understood from a Ramachandran plot at 280 K (Fig. Although this error is considerably improved using HA qm, the calculated entropy change is small compared to the reference value. At high temperature, the error obtained by HA cl is large compared to the other methods because in the classical scheme the contribution from high-frequency oscillators is overstated. 2 with the reference value of multistep LTI. The entropy changes computed using DFT/HNC, the harmonic approximation (HA) under the quantum mechanical scheme ( HA qm ), HA under the classical scheme ( HA cl ), and the quasiharmonic approximation (QHA) with Schlitter’s formula 6 are shown in Fig.
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