Abstract
Some ingredients will dissolve in one another while others do not, or at least not completely. For example, ethanol and water can be blended at all proportions, as can olive oil and canola oil. On the other hand, while oil and water can be combined to make a salad dressing, they do not actually dissolve in one another. Often the tendency to dissolve depends on the conditions; if you add sugar to iced tea, the first few crystals will dissolve, sweetening the drink, but sugar added beyond a certain limit will sink to the bottom of the pitcher and not be tasted. It is possible to make much sweeter hot tea as the solubility limit of sucrose in water increases with temperature.
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Notes
- 1.
Remember that in Sect. 1.9, water activity, a measure of the chemical potential of water in the food, was lowered by the presence of a solute.
- 2.
Because the lattice has a fixed number of spaces, i.e., fixed volume, we will calculate a Helmholtz free energy in terms of entropy and internal energy rather than the more familiar Gibbs free energy used at constant pressure and calculated in terms of entropy and enthalpy. The differences are relatively minor and need not concern us here.
- 3.
It may be reassuring to some readers that we could have calculated the free energy in this case directly from Eq. 1.18,\(\mu_A=\mu_A^{\circ}+RT\ln{x_A}\)As chemical potential is additive on a molar basis (Eq. 1.13) the free energy of one mole of mixture isx B μ B + x W μ Wor
$$\it{F}_{mixed}=\left[x_B(\mu_B^{\circ}+\it{RT}\ln{x_B})+x_W(\mu_W^{\circ}+\it{RT}\ln{x_W})\right]$$The free energy of the same ingredients if they were not mixed is\(x_B\mu_B^{\circ}+x_W\mu_B^{\circ}\)(taking the standard state as the pure substance). Subtracting gives the free energy change of preparing one mole of an ideal mixture from the pure components:
- 4.
More formally, we should be looking for two points on the curve with similar slopes. Fig. 4.16 is a plot of free energy against molar composition and the slope of the curve is the chemical potential. By finding compositions with similar slopes, we are finding phases with equal chemical potential that can be at equilibrium with one another. However, this curve is symmetrical and so these points are coincident with the minima and we will not pursue the point further.
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Coupland, J. (2014). Phase Behavior. In: An Introduction to the Physical Chemistry of Food. Food Science Text Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0761-8_4
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DOI: https://doi.org/10.1007/978-1-4939-0761-8_4
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