Spontaneous process mixing

The process opposite to vesicle division is that of fusion, when two or more vesicles come together and merge with each other, yielding a larger vesicle. As outlined in the previous chapter, vesicle fusion is generally not a spontaneous process. If two populations of POPC liposomes with different average dimensions are mixed with each other, they do not fuse to produce a most stable intermediate structure - they stay in the same solution as stable, distinct species. This is connected to the notion of kinetic traps, as discussed previously, and is supported by theoretical and experimental data from the literature (for example, Hubbard etal, 1998 Olsson and Wennerstrom, 2002 Silin et al, 2002). 

Note that Gm< 0 because Nt < 0. Therefore mixing is a spontaneous process. 

If one suddenly opens the tap (valve) on a cylinder containing a gas confined under a pressure Pi (much greater than atmospheric pressure, Patm (i.e. P, 3> Patm)) and allows it to escape by into the atmosphere this process will continue until the pressures are equalised and the final pressure Pf = Patm. The expansion (leaving aside all discussion of throttle effects at the valve, gas/air mixing, friction effects etc.) takes place rapidly - and under non-equilibrium conditions - usually at constant temperature, T (= ambient) and is a spontaneous process. Since this process is not at equilibrium and hence is not reversible, we refer to it as being an irreversible process. 

The basic prirrciples of a separation are depicted in Figure 30-1. As shown, separations can be complete or partial. The separation process involves transport of material and spatial redistribution of the components. We should note that a separation always requires energy, because the reverse process, mixing at constant volume, is spontaneous, being accompanied by an increase in entropy. Separations can be preparative or analytical. We focus here on analytical separations, although many of the same principles are involved in preparative separations. 

Figure 3.28 Nucleophilic participation by carboxylate in the departure of various leaving groups from mixed acetals of phthalic hemialdehyde Rate enhancements of these spontaneous processes of 100 for 3,5-dichloro-phenolate departure, 22 for thiophenolate departure " and 20 for catechol monoanion departure were estimated from the rates of the p-phthalic derivatives intermolecular general acid catalysis of the catechol was also accelerated.

SO that mixing of liquids is a spontaneous process. Since we know that equation (18.14), Frame 18 ... 

At very high temperatures (Ti), has for any arbitrary composition a smaller value than which means the melting process mixed phase smixed phase l always proceeds spontaneously. For this reason, the system is liquid independent of the composition. When the system is cooled, it will eventually reach the point where the two ji x) curves touch for the first time. This means that they exhibit the same value In our example, this is at Xb = 0 and therefore at the melting... 

This is always a positive quantity because the logarithm of all mole fractions is negative (x, < i) and the minus sign makes the right-hand side positive. According to this result, the mixing of components in the ideal-gas state is a spontaneous process and leads to entropy generation. The reverse process, separation, is not spontaneous and requires work. 

Comments Mixing is a spontaneous process and generates entropy. Accordingly, the separation of the mixture to its constituents is not a spontaneous process but requires work. The minimum amount of work to separate air into its... 

The use of fermentation to preserve and improve the properties of food has a long history. For example, milk has been preserved by fermentation for at least seven millennia (Dunne et al 2012). Initially, fermentation was a spontaneous process, probably with mixed results, and it was quickly learned that inoculation of the material to be fermented with a suitable inoculum would increase the likelihood of success. Traditionally, this was done by using part of a previous fermentation as an inoculum, but as microbiological knowledge increased, inoculation with specifically prepared fermentation starter cnltnres developed (H0ier et al 2010). This in turn gave a better control of the fermentation process and allowed for the development of new products with novel properties. This is well illustrated in the dairy industry, where a diversity of bacterial species is used to manufacture a large variety of fermented dairy products (Table 10.1). 

It s worth pointing out again, though, that this does not mean that the reaction will occur readily if we mix the reactants. Simply because a reaction has a negative value for AG° does not mean we will observe a spontaneous conversion. In some cases, the rate of the reaction is so slow that, despite the thermodynamic indication of spontaneity, the reaction is not observed. Thermodynamics does not tell us how rapidly a spontaneous process will take place. 

Athletic trainers use instant ice packs that can be cooled quickly on demand. Squeezing the pack breaks an inner container, allowing two components to mix and react. This reaction makes the pack become cold. Describe the heat flow for this spontaneous process. 

Because the mixing of A and B takes place at a constant T and P and is a spontaneous process, A G must be negative. The curve shown is an expression of Equation (7.20). No experimental data are required just mole fraction numbers from 0 to 1. 

---