Solute particles

The solute molecular weight enters the van t Hoff equation as the factor of proportionality between the number of solute particles that the osmotic pressure counts and the mass of solute which is known from the preparation of the solution. The molecular weight that is obtained from measurements on poly disperse systems is a number average quantity. 

We shall see in Sec. 9.9 that D is a measurable quantity hence Eq. (9.79) provides a method for the determination of an experimental friction factor as well. Note that no assumptions are made regarding the shape of the solute particles in deriving Eq. (9.79), and the assumption of ideality can be satisfied by extrapolating experimental results to c = 0, where 7=1. 

This simple model illustrates how the fraction K and, through it, Vj are influenced by the dimensions of both the solute molecules and the pores. For solute particles of other shapes in pores of different geometry, theoretical expressions for K are quantitatively different, but typically involve the ratio of solute to pore dimensions. 

We assume that the Rayleigh theory can be corrected by subdividing the actual solute particle into an array of scattering sites which, considered individually, obey the Rayleigh theory. It can be shown that this approach is a valid approximation so long as (47rR/X)(n2/fii - 1) 1, where R is... 

On the other hand, if Fig. 24b is compared with Fig. 23a, it will be seen that here each solute particle occupies a position that in the pure solvent would be occupied by a solvent particle. Such a solution, which can be formed by one-for-one substitution, is called a substitutional solution."1 This kind of solution will not be formed if the forces of attraction between adjacent solute and solvent particles are weak, while the forces of attraction between adjacent solvent particles are strong. For, if we look at Fig. 24b, we see that each solute particle prevents three solvent particles from coming together under their mutual attraction—that is to say, it prevents them from falling to a state of much lower potential energy. We can be certain that, when neon or argon is dissolved in water, the solute particles will not tend to take up such positions, which are suitable only for a solute particle which attracts an adjacent solvent particle with a force at least as great as the force of attraction between two adjacent solvent particles. 

The theory of the structure of ice and water, proposed by Bernal and Fowler, has already been mentioned. They also discussed the solvation of atomic ions, comparing theoretical values of the heats of solvation with the observed values. As a result of these studies they came to the conclusion that at room temperature the situation of any alkali ion or any halide ion in water was very similar to that of a water molecule itself— namely, that the number of water molecules in contact with such an ion was usually four. At any rate the observed energies were consistent with this conclusion. This would mean that each atomic ion in solution occupies a position which, in pure water, would be occupied by a water moldfcule. In other words, each solute particle occupies a position normally occupied by a solvent particle as already mentioned, a solution of this kind is said to be formed by the process of one-for-one substitution (see also Sec. 39). 

The Contact between Solvent and Solute Particles Molecules and Molecular Ions in Solution. Incomplete Dissociation into Free Ions. Proton Transfers in Solution. Stokes s Law. The Variation of Electrical Conductivity with Temperature. Correlation between Mobility and Its Temperature Coefficient. Electrical Conductivity in Non-aqueous Solvents. Electrical Conduction by Proton Jumps. Mobility of Ions in D20. 

In the nineteenth century a liquid was thought to be like a gas. In a gas a molecule makes a collision, travels freely, makes another collision, again travels freely, and so on. It was thought that a liquid should be described in the same way—only with much shorter free paths. In a solution each solute particle would moke frequent collisions with solvent molecules. But in an aqueous solution containing atomic ions the question was asked between collisions is the atomic ion traveling alone, or does it travel with water molecules attached to it Electrochemists unanimously came to the conclusion that to each species of atomic ion several water molecules were attached, to form a hydrate when they spoke of the mobility of the ion, they meant the mobility of this large rigid hydrated ion. 

The internal structure of a liquid at a temperature near its freezing point has been discussed in Sec. 24. Each molecule vibrates in a little cage or cell, whose boundaries are provided by the adjacent molecules, as in Fig. 20, and likewise for each solute particle in solution in a solvent near its freezing point. It is clear that the question of the hydration of ions no longer arises in its original form. In aqueous solution an atomic ion will never be in contact with less than three or four water molecules, which in turn will be in contact with other water molecules, and so on. There is an electrostatic attraction, not only between the ion and the molecular dipoles in immediate contact with it, but also between the ion and molecular dipoles that are not in contact with it. For solvent dipoles that are in contact with a small doubly charged ion, such as Ca++,... 

With rise of temperature any solvent becomes less viscous. For visible particles the Brownian motion is observed to become more lively and in the same way we should expect a solute particle to execute a more lively random motion. As a result, the mobility of each species of ion should increase with rise of temperature. 

Ideal and Nonrideal Solutions. Treatment of Solutions by Statistical Mechanics. A Solution Containing Diatomic Solute Particles. A Solution Containing Polyatomic Solute Particles. An Interstitial Solution. Review of Solutions in General. Quantities De-pendent on, and Quantities Independent of, the Composition of the Solution. Unitary Quantities and Cratic Quantities. Molality and Activities on the Molality Scale. 

A Solution Containing Diatomic Solute Particles. We have begun in Sec. 39 to sketch the application of statistical mechanics to solutions this is a rather new branch of physics, and relatively few problems have been solved. Since the author has elsewhere1 devoted 40 pages to a... 

In studying the most familiar electrolytes, we have to deal with various molecular ions as well as atomic ions. The simplest molecular solute particle is a diatomic molecule that has roughly the same size and shape as two solvent particles in contact, and which goes into solution by occupying any two adjacent places that, in the pure solvent, are occupied by two adjacent solvent particles. This solution is formed by a process of substitution, but not by simple one-for-one substitution. There are two cases to discuss either the solute molecule is homonuclear, of-the type Bi, or it is heteronuclear, of the type BC. In either case let the number of solute molecules be denoted by nB, the number of solvent particles being nt. In the substitution process, each position occupied by a solvent particle is a possible position for one half of a solute molecule, and it is convenient to speak of each such position as a site, although in a liquid this site is, of course, not located at a fixed point in space. 

In the pure solvent let each particle have z nearest neighbors in contact with it. Let us ask how, removing two adjacent solvent particles from the interior, we may insert a solvent molecule. When a particular site is to be occupied by the B-half of the molecule BC, there are clearly z choices for the position of its C-half. This is true for each of the nB solute particles, provided that the solution is so dilute that they do not compete for the available sites to an appreciable extent. From the independent oiientations of nB solute particles, the quantity Wc/ receives the factor z if the molecules are heteronuclear and receives the factor (z/2)n if the molecules are homonuclear. 

Since an ionic solution contains two species of solute particles, the positive and negative ions, it is often useful to mention the molality of each species. If barium chloride, for example, dissolved in a solvent, is completely dissociated into Ba++ ions and Cl- ions, the molality of the Ba++ will be equal to the molality of the solute BaCb, while the molality of the Cl- will be twice as great. 

The term +kT In 55.5 is characteristic of a reaction in aqueous solution in which the number of solute particles is increased by unity. 

In general, when the equation for any reaction or process has been written down, let there be q solute particles on the left-hand side, and let there be (q + Aq) solute particles on the right-hand side. In any solvent let M denote the number of moles of solvent that are contained in the mass that has been adopted as the b.q.s. then for each solute species m = My. At extreme dilution the ratio of K to Kx takes the value1... 

In discussing the proton transfer (66), we saw that one of the neutral species could be a solvent molecule. We shall discuss that case below. Here we may notice that, when all four species are solute particles, the number of solute particles is unchanged by the reaction, or Aq = 0. In such a case AF° happens to be equal to the characteristic unit U multiplied by Avogadro s constant. 

In any pure liquid, the transfer of a proton from one molecule to another (distant) molecule has been named autoprololysis. I11 any solvent this process creates a positive and a negative ion and must clearly belong to class II it will not differ from other proton transfers of class II except for the fact that the relation between Kx and K will be different. On the left-hand side of (127) and (128) there is no solute particle hence the increase in the cratic term is greater than in (119) or (121). In (128) we have Aq — +2, and... 

In Fig. 37 two areas have been shaded. The area in the upper left corner, where protons in occupied levels are unstable, we have already discussed. In the lower right-hand corner the shaded area is one where vacant proton levels cannot remain vacant to any great extent. In aqueous solution any solute particle that has a vacant proton level lower than that of the hydroxyl ion will capture a proton from the solvent molecule, since the occupied level of the latter has the same energy as the vacant level of a hydroxyl ion. Consequently any proton level that would lie in this shaded area will be vacant only on the rare occasions when the thermal agitation has raised the proton to the vacant level of a hydroxyl ion. On the other hand, there are plenty of occupied proton levels that lie below the occupied level of the H2O molecule. For example, the occupied level of the NH3 molecule in aqueous solution lies a long way below that of H20. 

In a solution containing such particles, the conditions for equilibrium in all possible proton transfers must be satisfied simultaneously, In terms of these proton energy levels, we may say that this is made possible by the additivity of the J values. In Fig. 38 the values of J for the three proton transfers have been labeled J1, J2, and J3. From the relation J3 = Ji + Ji) we may obtain at once a relation between the values of Kx, and hence between the equilibrium constants K. In the proton transfer labeled Jt the number of solute particles remains unchanged, whereas in J4 and Jt the number of solute particles is increased by unity. 

The Dissociation Constant of Nitric Add. Alodcrately Weak Acids. The Variation of J with Temperature. Proton Transfers between Solute Particles. A Proton Transfer in Methanol Solution. Proton Transfers with a Negative Value for. / . The Hydrolysis of Salts. Molecules with Symmetry. Substituted Ammonium Ions. Deuteron Transfers in D2(). The Dissociation of Molecular Ions. 

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