EXPRESSING SOLUTION CONCENTRATION

In Chapter 3, you used molarity to convert liters of solution into moles of dissolved solute. Expressing concentration in terms of molarity may have drawbacks, however. Because volume is affected by temperature, so is molarity. A solution expands when heated, so a unit volume of hot solution contains slightly less solute than a unit volume of cold solution. This can be a source of error in very precise... 

Because of the instability of pure and concentrated aqueous solutions of hydrogen peroxide, it is usually used in dilute solution. The concentration of such solutions is often expressed in terms of the volume of oxygen evolved when the solution decomposes ... 

Both molarity and formality express concentration as moles of solute per liter of solution. There is, however, a subtle difference between molarity and formality. Molarity is the concentration of a particular chemical species in solution. Formality, on the other hand, is a substance s total concentration in solution without regard to its specific chemical form. There is no difference between a substance s molarity and formality if it dissolves without dissociating into ions. The molar concentration of a solution of glucose, for example, is the same as its formality. 

A standard solution of Mn + was prepared by dissolving 0.250 g of Mn in 10 ml of concentrated HNO3 (measured with a graduated cylinder). The resulting solution was quantitatively transferred to a 100-mL volumetric flask and diluted to volume with distilled water. A 10-mL aliquot of the solution was pipeted into a 500-mL volumetric flask and diluted to volume, (a) Express the concentration of Mn in parts per million, and estimate uncertainty by a propagation of uncertainty calculation, (b) Would the uncertainty in the solution s concentration be improved... 

Thus we have finally established how light scattering can be used to measure the molecular weight of a solute. The concentration dependence of r enters Eq. (10.54) through an expression for osmotic pressure, and this surprising connection deserves some additional comments ... 

Whereas there is sometimes confusion in how concentrations of aqueous solutions of hydrazine ate expressed, concentrations of wt % N2H4 ate used herein. In many parts of the wodd, however, concentrations ate often expressed in terms of wt % hydrazine hydrate, N2H4 -H2 O. Hydrazine hydrate is 64 wt % N2H, 36% H2O. The correlation between the two systems is therefore ... 

Reliable pH data and activities of ions in strong electrolytes are not readily available. For this reason calculation of corrosion rate has been made using weight-loss data (of which a great deal is available in the literature) and concentration of the chemical in solution, expressed as a percentage on a weight of chemical/volume of solution basis. Because the concentration instead of the activity has been used, the equations are empirical nevertheless useful predictions of corrosion rate may be made using the equations. 

To indicate the composition of a particular solution we must show the relative amounts as well as the kind of components. These relative amounts chemists call concentrations. Chemists use different ways of expressing concentration... 

Expression (2) applies to a solubility equilibrium, provided we write the chemical reaction to show the important molecular species present. In Section 10-1 we considered the solubility of iodine in alcohol. Since iodine dissolves to give a solution containing molecules of iodine, the concentration of iodine itself fixed the solubility. The situation is quite different for substances that dissolve to form ions. When silver chloride dissolves in water, no molecules of silver chloride, AgCl, seem to be present. Instead, silver ions, Ag+, and chloride ions, Cl-, are found in the solution. The concentrations of these species, Ag+ and Cl-, are the ones which fix the equilibrium solubility. The counterpart of equation (7) will be... 

For expressing concentrations of reagents, the molar system is universally applicable, i.e. the number of moles of solute present in 1 L of solution. Concentrations may also be expressed in terms of normality if no ambiguity is likely to arise (see Appendix 17). 

The composition of a solution can vaiy, so we must specify the concentrations of solutes as well as their identities. There are several ways to express concentration, each having advantages as well as limitations. Any concentration value is a ratio of amounts. The amount of one component, usually a solute, appears in the numerator, and some other amount, describing either the solvent or the total solution, appears in the denominator. 

Experiments show that at low solute concentration, the changes in freezing point and boiling point of a solution, A Zf and A T, depend on the concentration of the solution, expressed as molality (c j) ... 

Chemical equilibria often involve pure liquids and solids in addition to gases and solutes. The concentration of a pure liquid or solid does not vary significantly. Figure 16-4 shows that although the amount of a solid or liquid can vary, the number of moles per unit volume remains fixed. In other words, the concentrations of pure liquids or solids are always equal to their standard concentrations. Thus, division by standard concentration results in a value of 1 for any pure liquid or solid. This allows us to omit pure liquids and solids from equilibrium constant expressions. For a general reaction (2A + iBt= C D-l-. S where S is a pure solid or liquid ... 

The equilibrium concentration of Pb ions is stated to be 1.35 X 10 M, but the equilibrium concentration of iodide ions is not stated [Pb2- ],q = 1.35 X iO M[r]g(j — The equilibrium concentration of I is determined by stoichiometric analysis. Initially, the system contains only pure water and solid lead(II) iodide. Enough Pbl2 dissolves to make [Pb ]gq = 1.35 X 10 M. One formula unit of Pbl2 contains one Pb cation and two I" anions. Thus, twice as many iodide ions as lead ions enter the solution. The concentration of I at equilibrium is double that of Pb cations [r],q-2[Pb ],q-2.70 X lO M Substitute the values of the concentrations at equilibrium into the equilibrium expression and calculate the result ... 

In the preceding solvent extraction models, it was assumed that the phase flow rates L and G remained constant, which is consistent with a low degree of solute transfer relative to the total phase flow rate. For the case of gas absorption, normally the liquid flow is fairly constant and Lq is approximately equal to Li but often the gas flow can change quite substantially, such that Gq no longer equals Gj. For highly concentrated gas phase systems, it is therefore often preferable to define flow rates, L and G, on a solute-free mass basis and to express concentrations X and Y as mass ratio concentrations. This system of concentration units is used in the simulation example AMMONAB. 

The second approach is to use a specified concenfration of solution. This concentration is normally expressed as a hectolitre concentration and is the grams or milliliters of formulated product per 100 L of water. Here the trees are sprayed until run-off (the point at which the droplets coalesce and start to drip from the leaves). Once this point has been reached, the trees cannot be overdosed, since any additional solution will fall from the trees. This method, therefore, gives the advantages of (a) not overdosing, (b) tree size is irrelevant, and (c) no calculation of tree numbers is required. 

In this chapter we concentrate on dynamic, distributed systems described by partial differential equations. Under certain conditions, some of these systems, particularly those described by linear PDEs, have analytical solutions. If such a solution does exist and the unknown parameters appear in the solution expression, the estimation problem can often be reduced to that for systems described by algebraic equations. However, most of the time, an analytical solution cannot be found and the PDEs have to be solved numerically. This case is of interest here. Our general approach is to convert the partial differential equations (PDEs) to a set of ordinary differential equations (ODEs) and then employ the techniques presented in Chapter 6 taking into consideration the high dimensionality of the problem. 

It must be realized that the acidity of an acidic solution, expressed by its pH, is a physico-chemical property, which in fact (see calculations on pp. 83-85) represents a resultant of the identity and concentration of the acid even the overall pH height of the titration curve is still influenced by the concentrations of a strong acid, but for a weak acid that curve height, especially its h.n.pH value, forms a fairly reliable identity indication. 

The reaction takes place in aqueous solution. Equimolal concentrations of the ester and the phenolate are used. These concentrations are equal to 30 moles/m3. By the time the samples are brought to thermal equilibrium in the reactor and efforts made to obtain data on ester concentrations as a function of time, some saponification has occurred. At this time the concentration of ester remaining is 26.29 moles/m3, and the concentration of phenol present in the reactant mixture is 7.42 moles/m3. The rate expression for the reaction is believed to be of the form... 

The term p[H] represents the pH value of the solution expressed on a concentration scale [5], where [H] represents the concentration of hydrogen ions H+. P° represents the partition coefficient of the unprotonated species, P1 is the mono-protonated species, and so on. P may also be expressed as... 

An analyst is preparing a standard solution of concentration C by weighing out a specified amount of a material of known purity and dissolving it in a specified volume of solvent. The following information is available mass of material used (M) = 100.5mg, u(M) = 0.208mg purity of material (P) = 0.999 (expressed as a ratio), u(P) = 0.00058 volume of solvent (V) = 100ml, u(V) = 0.16ml... 

Here, Rj is reaction rate (mol cm-3 s-1), the net rate at which chemical reactions add component i to solution, expressed per unit volume of water. As before, Q is the component s dissolved concentration (Eqns. 20.14—20.17), Dxx and so on are the entries in the dispersion tensor, and (vx, vy) is the groundwater velocity vector. For transport in a single direction, v, the equation simplifies to,... 

The changes in a colligative property of a polymer solution with concentration can be expressed by a virial expansional given below ... 

Under this connection let mark that the position about an independence of the osmotic pressure of polymeric solutions into concentrated field of the strongly intertwined chains used in the scaling method is successful upon the result (8) in the presented concrete case, but can not be by general principle spreading on the all thermodynamic visualizations of polymeric solutions. For instance, free energy of the macromolecules conformation accordingly to (22) is function not only on the concentration, but also on the length of a chain at any choice of the method for the concentration expression. 

Equation (88) is the expression used commonly for solutions of synthetic polymers, but, where the nature of adsorption and binding is of critical interest, alternative forms exist. These differ mainly in the modes of expressing concentration (e.g. activity, molality, molarity, mass/unit volume). Interrelations among the units and expressions have been presented very clearly by Timasheff and Townend15. ... 

There are many ways of expressing the relative amounts of solute(s) and solvent in a solution. The terms saturated, unsaturated, and supersaturated give a qualitative measure, as do the terms dilute and concentrated. The term dilute refers to a solution that has a relatively small amount of solute in comparison to the amount of solvent. Concentrated, on the other hand, refers to a solution that has a relatively large amount of solute in comparison to the solvent. However, these terms are very subjective. If you dissolve 0.1 g of sucrose per liter of water, that solution would probably be considered dilute 100 g of sucrose per liter would probably be considered concentrated. But what about 25 g per liter—dilute or concentrated In order to communicate effectively, chemists use quantitative ways of expressing the concentration of solutions. Several concentration units are useful, including percentage, molarity, and molality. 

If the equilibrium curve can be represented by the relation ye = mi, then the number of plates required for a given degree of absorption can conveniently be found by a method due to Kremser(56) and Souders and Brown(57). The same treatment is applicable for concentrated solutions provided concentrations are expressed as mole ratios, and if the equilibrium curve can be represented approximately by Ye = mX. 

In dilute solutions, the concentration of water is almost constant. Multiplying both sides of the equilibrium expression by [H2O] gives the product of two constants on the left side. This new constant is called the acid dissociation constant, K. (Some chemists refer to the acid dissociation constant as the acid ionization constant. With either name, the symbol is Xg.)... 

As the redox reactions proceed, the availability of the active species at the electrode/electrolyte interface changes. Concentration polarization arises from limited mass transport capabilities, for example, limited diffusion of active species to and from the electrode surface to replace the reacted material to sustain the reaction. Diffusion limitations are relatively slow, and the buildup and decay take >10 s to appear. For limited diffusion the electrolyte solution, the concentration polarization, can be expressed as... 

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