Quantity-volume relationship

Because we know we are dealing with a buffer solution made from a specific conjugate acid-base pair, we can work directly with the buffer equation. We need to calculate the ratio of concentrations of conjugate base and acid that will produce a buffer solution of the desired pH. Then we use mole-mass-volume relationships to translate the ratio into actual quantities. 

A good way to remember these relationships is to use the diagram shown below. Use your finger to cover the quantity you want to know, and that quantity s relationship to the other quantities is revealed. For example, covering the At shows that mass is equal to density times volume, DxV. 

Figure 3.10 Summary of mass-mole-number-volume relationships in solution. The amount (in moles) of a compound in solution is related to the volume of solution in liters through the molarity (M) in moles per liter. The other relationships shown are identical to those in Figure 3.4, except that here they refer to the quantities in solution. As in previous cases, to find the quantity of substance expressed in one form or another, convert the given information to moles first.

CBM is adsorbed to the surface of the coal and the adsorption sites can store commercial quantities of gas as part of the coal matrix. This must not be confused with conventional pore-volume storage. Gas within petroleum reservoir rock as a gas and the traditional pressure/temperature/volume relationships hold. Adsorbed gas molecules do not behave as a gas (1) they do not conform to the shape of the container, (2) they do not conform to the modified ideal gas laws (i.e., PV ZnRT), and (3) they take up substantially less volume than the same mass of gas would require within a pore volume. 

All experimental techniques lead to heat capacities at constant pressure, Cp. In terms of microscopic quantities, however, heat capacity at constant volume, C, is the more accessible quantity. The relationship between Cp and is listed as Eq. (4) in Fig. 2.31 in continuation of Fig. 2.22. It involves several correlations, easily (but tediously) derivable from the first and second law expressions as will be shown next. To simplify the derivation, one starts assuming constant composition for the to be derived equation (no latent heats, dn = 0). From the first law, as given by Eq. (3) of Fig. 2.10, one differentiates dQ at constant pressure. Since (5Q/3T)p = Cp and (8U/8T)v = C, this differentiation gives Eq. (12) of Fig. 2.10 ... 

Pressure is an especially important variable with gases, because the volume of a quantity of gas at a fixed temperature is inversely proportional to pressure. The temperature/pressure/volume relationships of gases (Boyle s law, Charles law, and the general gas law) are discussed in Chapter 2. 

Robert Boyle (1627-1691) investigated pressure-volume relationships of air by pouring successive quantities of mercury into the open arm of a J-shaped tube as shown in Fig. 2.1. After each addition. 

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

To use GPC for molecular weight determination, we must measure the volume of solvent that passes through the column before a polymer of particular molecular weight is eluted. This quantity is called the retention volume Vj. Figure 9.14 shows schematically the relationship between M and Vj it is an... 

In developing these ideas quantitatively, we shall derive expressions for the light scattered by a volume element in the scattering medium. The symbol i is used to represent this quantity its physical significance is also shown in Fig. 10.1. [Our problem with notation in this chapter is too many i s ] Before actually deriving this, let us examine the relationship between i and 1 or, more exactly, between I /Iq and IJIq. 

The quantities VC and VC., represent the mass of biomass and substrate respeetively in the reaetor. Dividing these masses by the volume V gives the eoneentrations and as a funetion of time, whieh are required in the kinetie relationships to determine r, and r,. 

Apart from finding structures that give energy minima, most molecular mechanics packages will calculate structural features such as the surface area or the molecular volume. Quantities such as these are often used to investigate relationships between molecular structure and pharmacological activity. This field of human endeavour is called QSAR (quantitative structure and activity relations). 

Chemistry is a quantitative science. This means that a chemist wishes to know more than the qualitative fact that a reaction occurs. He must answer questions beginning How much. . . The quantities may be expressed in grams, volumes, concentrations, percentage composition, or a host of other practical units. Ultimately, however, the understanding of chemistry requires that amounts be related quantitatively to balanced chemical reactions. The study of the quantitative relationships implied by a chemical reaction is called stoichiometry. 

P the total pressure, aHj the mole fraction of hydrogen in the gas phase, and vHj the stoichiometric coefficient of hydrogen. It is assumed that the hydrogen concentration at the catalyst surface is in equilibrium with the hydrogen concentration in the liquid and is related to this through a Freundlich isotherm with the exponent a. The quantity Hj is related to co by stoichiometry, and Eg and Ag are related to - co because the reaction is accompanied by reduction of the gas-phase volume. The corresponding relationships are introduced into Eqs. (7)-(9), and these equations are solved by analog computation. 

Considerably better agreement with the observed stress-strain relationships has been obtained through the use of empirical equations first proposed by Mooney and subsequently generalized by Rivlin. The latter showed, solely on the basis of required symmetry conditions and independently of any hypothesis as to the nature of the elastic body, that the stored energy associated with a deformation described by ax ay, az at constant volume (i.e., with axayaz l) must be a function of two quantities (q +q +q ) and (l/a +l/ay+l/ag). The simplest acceptable function of these two quantities can be written... 

The graphical plot of pressure versus volume shows an inverse variation. In an inverse relationship, as the magnitude of one quantity increases, the magnitude of the second quantity decreases. This relationship may be expressed as... 

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