Entropy of Mixing
Entropy of mixing refers to the measure of disorder or randomness that occurs when different substances are mixed together. It is a concept in thermodynamics that quantifies the extent of mixing in a system. When substances are mixed, the entropy of the system increases, reflecting the increase in disorder and the tendency of the system to move towards a more disordered state.
4 Key excerpts on "Entropy of Mixing"
eBook - ePubBiomolecular Thermodynamics
From Theory to Application
- Douglas Barrick(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...For example, even though the two pairs of chemical potentials in Figure 7.7A and B cross at very different mole fractions, the same mixing energy and entropy is obtained in both cases, with a symmetric minimum at a mole fraction of 0.5. It is only when the mixed components can interconvert via chemical reaction that the standard state chemical potential values influences the process. By taking the temperature derivative of Equation 7.22, we can obtain the molar entropy of. mixing: Δ S ¯ m i x i n g = − (∂ Δ G ¯ m i x i n g ∂ T) p = − (∂ R T { x A ln x A + x B ln x B } ∂ T) p, n A , n B = − R { x A ln x A + x B ln x B } (7.23) As can be seen in Figure 7.8, the Entropy of Mixing (red curve) has the same shape as the free energy of mixing, though it is inverted. about the x -axis due to the negative sign in the thermodynamic identity relating S and G. Finally, the enthalpy of mixing can be calculated from the entropy and free energy of mixing from the relationship Δ G ¯ = Δ H ¯ − T Δ S ¯. Inserting Equations 7.22 and 7.23 and rearranging leads to the result that Δ H ¯ m i x i n g = 0. Thus, for mixing of ideal solutions the driving force is entirely entropic. This makes sense, because there is no preferential bonding between ideal components (by assertion). Thus, any enthalpic interactions that maintain the solution in its condensed (liquid) phase should be the same for both self and nonself interactions, rendering enthalpy independent of composition. That the same result was obtained for lattice mixing (Chapter 4, and see Problem 7.10) when we analyzed a model lacking any specific interactions supports the concept of an entropic driving force. Though the ideal solution approach is quite useful, most solvent mixtures display preferential interactions, and as a result, show some degree of nonideal behavior. The water–ethanol mixture in Figure 7.6B is one example, where partial pressures show significant deviations from Raoult’s law...
eBook - ePubFundamentals of Polymer Science
An Introductory Text, Second Edition
- Michael M. Coleman, Paul C. Painter(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
...Its entropy will therefore be larger than the sum of the entropics of the initially separate liquids (recall equation 8.4). However, we also know that oil and water do not mix. (Actually they do just a little bit, but what we are really saying is that they are phase separated; we’ll explain this in chapter 9 !) So, where have we gone wrong? The problem is that we have only considered a part of the entropy change that would occur if the liquids were to mix. Mixing involves a heat exchange with the surroundings, the direction of energy transfer depending upon whether the process is exothermic or endothermic. As a result of this energy change there is also a change in the entropy of the surroundings (ΔS surr). For a spontaneous process to occur, (i.e., for the liquids to mix) the second law tells us that ΔS > 0, but this inequality refers to the total entropy change (ΔS tot > 0), not just the entropy change in the system (Δ sys). We must therefore write: Δ S tot = Δ S sys + Δ S surr (8.18) and impose the condition that ΔS tot > 0 for mixing to occur, but how do we calculate ΔS surr ? (We will assume that we can construct a model to calculate ΔS rys and our aim is to calculate whether or not ΔS tot > 0 to predict if two liquids will or will not mix.) What we would really like is to be able to confine our attention to the properties of the system alone, because we can usually construct models that at least allow us to estimate the quantities that we are trying to determine. Fortunately, if the process we are considering is reversible we can write: Δ S surr = − Δ Q T = − Δ H T (8.19) at constant pressure (where ΔQ = ΔH): we have put in a minus sign to indicate that we are discussing heat transferred from the system to the surroundings, the heat being the heat of mixing, a property of the system (resulting from interactions between the molecules)...
eBook - ePub- Dov M. Gabbay, Paul Thagard, John Woods(Authors)
- 2011(Publication Date)
- North Holland(Publisher)
...Entropy in Chemistry Robert J. Deltete 1. Introduction Contemporary textbooks in physical chemistry and chemical thermodynamics regularly refer to the importance of the concept of entropy in describing the course of chemical reactions and the conditions for chemical equilibrium (e.g., [ Winn, 1995, p. 63]). This was not always the case. In fact, for the most part, it was quite the opposite for a long time, enough so that two recent authors could subtitle a paper “the tortuous entry of entropy into chemistry” [ Kragh and Weininger, 1996 ]. In this essay, I begin in Section II with a brief description of the entry of entropy into physics through the work of Rudolf Clausius. I then sketch, in Sections III and IV, the productive use to which the concept was put in the work of Josiah Willard Gibbs and Max Planck, before turning in Section V to the reasons that most chemists did not follow Gibbs and Planck. Section VI offers some speculations on how resistance to entropy on the part of chemists was gradually overcome. 2. Clausius on Entropy The essential step leading to the concept of entropy was taken by Clausius in 1850, when he argued that two laws are needed to reconcile Carnot's principle about the motive power of heat with the law of energy transformation and conservation. Efforts to understand the second of the two laws finally led him in 1865 to his most concise and ultimately most fruitful analytical formulation. In effect, two basic quantities, internal energy and entropy, are defined by the two laws of thermodynamics. The internal energy U is that function of the state of the system whose differential is given by the equation expressing the first law, (1) where đ Q and đ W are, respectively, the heat added to the system and the external work done on the system in an infinitesimal process. 1 For a simple fluid, the work is given by the equation 1 I have altered Clausius' notation, and also Gibbs's in what follows, to conform to contemporary usage...
- Michael M. Coleman, Paul C. Painter, John F. Graf(Authors)
- 2017(Publication Date)
- CRC Press(Publisher)
...CHAPTER 1 The Thermodynamics of Mixing An Incomplete and Biased Overview A. INTRODUCTION TO THEORIES OF MIXING Guggenheim 1 classified mixtures primarily into two types, “those in which molecular orientation is unimportant and those in which is it all important.” In this latter class are, of course, molecules that interact through the formation of strong specific interactions, particularly hydrogen bonds, but the majority of both theoretical and experimental studies of mixing have been aimed at obtaining an understanding of the behavior of mixtures of the first type and it is these simpler systems we will consider first. For binary mixtures of small (i.e., non-polymeric) molecules a particularly simple expression for the Gibbs free energy of mixing is obtained if the energy of interaction between the unlike components is the same as the energy of interaction between like molecules (i.e., the interchange energy is zero): Δ G m RT = n A ln x A + n B ln x B (1.1) where n A and n B are the number of moles of components A and B and x A, x B are the corresponding mole fractions...
