Boyle-Van’t Hoff relation

In this chapter we will derive the Boyle-Van t Hoff relation using the chemical potential of water, and in Chapter 3 (Section 3.6B) we will extend the treatment to penetrating solutes by using irreversible thermodynamics. Although the Boyle-Van t Hoff expression will be used to interpret the osmotic responses only of chloroplasts, the equations that will be developed are general and can be applied equally well to mitochondria, whole cells, or other membrane-surrounded bodies. 

The Boyle-Van t Hoff relation applies to the equilibrium situation for which the water potential is the same on either side of the two membranes surrounding a chloroplast. When T1 equals T°, net water movement across the membranes ceases, and the volume of a chloroplast is constant. (The superscript i refers to the inside of the cell or organelle and the superscript o to the outside.) If we were to measure the chloroplast volume under such conditions, the external solution would generally be at atmospheric pressure (P° =0). By Equation 2.13a (T = P — H, when the gravitational term is ignored), the water potential in the external solution is then... 

To appreciate the refinements that this thermodynamic treatment introduces into the customary expression describing the osmotic responses of cells and organelles, we compare Equation 2.18 with Equation 2.15, the conventional Boyle-Van t Hoff relation. The volume of water inside the chloroplast is VM,n because n v is the number of moles of internal water and Vw is the volume per mole of water. This factor in Equation 2.18 can be identified with V — b in Equation 2.15. Instead of being designated the nonosmotic volume, b is more appropriately called the nonwater volume, as it includes the volume of the internal solutes, colloids, and membranes. In other words, the total volume (V) minus the nonwater volume (b) equals the volume of internal water (Ew ). We also note that the possible hydrostatic and matric contributions included in Equation 2.18 are neglected in the usual Boyle-Van t Hoff relation. In summary, although certain approximations and assumptions are incorporated into Equation 2.18 (e.g., that solutes do not cross the limiting membranes and that the... 

The intercept on the ordinate in Figure 2-11 is the chloroplast volume theoretically attained in an external solution of infinite osmotic pressure —a l/n° of zero is the same as a n° of infinity. For such an infinite 11°, all of the internal water would be removed = 0), and the volume, which is obtained by extrapolation, is that of the nonaqueous components of the chloroplasts. (Some water is tightly bound to proteins and other substances and presumably remains bound even at the hypothetical infinite osmotic pressure such water is not part of the internal water, Vwn v). Thus the intercept on the ordinate of a F-versus-l/n° plot corresponds to b in the conventional Boyle-Van t Hoff relation (Eq. 2.15). This intercept (indicated by an arrow in Fig. 2-11) equals 17 pm3 for chloroplasts both in the light and in the... 

In Chapter 2 (Section 2.3B) we derived the Boyle-Van t Hoff relation assuming that the water potential was the same on both sides of the cellular or organelle membrane under consideration. Not only were... 

When molecules cross the membranes bounding cells or organelles, the reflection coefficients of both internal and external solutes should be included in the Boyle-Van t Hoff relation. Because less than 1 when the external solutes can penetrate, the effect of the external osmotic pressure on Jv is then reduced. Likewise, the reflection coefficients for solutes within the cell or organelle can lessen the contribution of the internal osmotic pressure of each solute. Replacing nj by RTn j / (VM ji v ) (Eq. 2.10) in Equation 3.41 and dividing by a° leads to the following Boyle-Van t Hoff relation for the stationary state condition (Jv = 0 in Eq. 3.40) ... 

As indicated in Chapter 2 (Section 2.3B), V — b in the conventional Boyle-Van t Hoff relation [H°(V — b) = RTY ffinj (Eq. 2.15)] can be identified with Vwn v, the volume of internal water. Comparing Equation 2.15 with Equation 3.44, the osmotic coefficient of species /, permeation properties of solutes, both internal and external. Indeed, failure to recognize the effect of reflection coefficients on

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