Concentration Terms

The acid dissociation constant has the same form m Brpnsted-Lowry as m the Arrhenius approach but is expressed m the concentration of H30" rather than The concentration terms [H30" ] and [H" ] are considered equivalent quantities m equilibrium constant expressions... 

Even though water is a reactant (a Brpnsted base) its concentration does not appear m the expression for because it is the solvent The convention for equilibrium constant expressions is to omit concentration terms for pure solids liquids and solvents... 

Fixed-time integral methods are advantageous for systems in which the signal is a linear function of concentration. In this case it is not necessary to determine the concentration of the analyte or product at times ti or f2, because the relevant concentration terms can be replaced by the appropriate signal. For example, when a pseudo-first-order reaction is followed spectrophotometrically, when Beer s law... 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

Ca " concentration, termed hypocalcemia, excitabihty increases. If this condition is not corrected, the symptoms of tetany, ie, muscular spasm, tremor, and even convulsions, can appear. Too great an increase in Ca " concentration, hypercalcemia, may impair muscle function to such an extent that respiratory or cardiac failure may occur. 

Although equation 35 is a simple expression, it tends to be confusing. In this equation the enthalpy difference appears as driving force in a mass-transfer expression. Enthalpy is not a potential, but rather an extensive thermodynamic function. In equation 35, it is used as enthalpy pet mole and is a kind of shorthand for a combination of temperature and mass concentration terms. 

The relationship between a kinetic expression and a reaction mechanism can be appreciated by considering the several individual steps that constitute the overall reaction mechanism. The expression for the rate of any single step in a reaction mechanism will contain a concentration term for each reacting species. Thus, for the reaction sequence... 

This relationship permits the measurement of the ratio k /ky. The initial concentrations [B—X]o and [B—Y]o are known from the conditions of the experiment The reaction can be stopped at some point when some of both B—X and B—Y remain unreacted, or an excess of B—X and B—Y can be used so that neither is completely consumed when A—A has completely reacted. Determination of [B—X], and [B—Y], then provides the information needed to calculate k /ky. It is clear that the reactions being compared must be of the same order. If they were not, division of the two rate expressions would leave uncanceled concentration terms. 

Here, we shall examine a series of processes from the viewpoint of their kinetics and develop model reactions for the appropriate rate equations. The equations are used to andve at an expression that relates measurable parameters of the reactions to constants and to concentration terms. The rate constant or other parameters can then be determined by graphical or numerical solutions from this relationship. If the kinetics of a process are found to fit closely with the model equation that is derived, then the model can be used as a basis for the description of the process. Kinetics is concerned about the quantities of the reactants and the products and their rates of change. Since reactants disappear in reactions, their rate expressions are given a... 

The rate is proportional to the concentrations of both A and B. Because it is proportional to the product of two concentration terms, the reaction is second-order overall, first-order with respect to A and first-order with respect to B. (Were the elementary reaction 2A P + Q, the rate law would be = A[A] second-order overall and second-order with respect to A.) Second-order rate constants have the units of (concentration) time) as in M sec. ... 

At higher concentrations, Henry s law no longer applies and activities must be substituted for the concentration terms. This statement implies that in the region of solution where Henry s law is valid, the activity coefficient 7 of /4, defined by... 

The value of the equilibrium constant tells which side of the reaction arrow is energetically favored. If Keq is much larger than 1, then the product concentration term [C 4 [Dlrf is much larger than the reactant concentration term A " B, and the reaction proceeds as written from left to right. If Keq is near 1, appreciable amounts of both reactant and product are present at equilibrium. And if Koq is much smaller than l, the reaction does not take place as written but instead goes in the reverse direction, from right to left. 

This way, the concentration terms cancel for that reactant. 

Concentricity Term to describe two circles or cylindrical shapes having a common center and common axis, such as the inside or outside diameters of a barrel or outside diameters of the surface and bearing surfaces of a screw. Deviation from concentricity is referred to as runout. Also refers to the relationship of all inside dimensions to all outside dimensions usually expressed in thousands of inch or millimeter FIM (full indicator movement). Deviation from concentricity is usually referred to as a runout. The concentricity should allow for the maximum part tolerance. The geometry of the part should help indicate the tolerance applied. 

Given the postulated reaction scheme, the net rate of reaction often takes a simple form when it is expressed in terms of the concentration of the intermediate. Such an expression is algebraically correct, and is the form one needs so as to propose and interpret the mechanism. This form is, however, usually not useful for the analysis of the concentration-time curves. In such an expression the reaction rate is given in terms of the concentration of the intermediate, which is generally unknown at the outset. To eliminate the concentration term for the intermediate, one may enlist certain approximations, such as the steady-state approximation. This particular method is applicable when the intermediate remains at trace levels. 

If the concentration term C is transferred to the right-hand side of equation 5.22 (taking account of the fact that (i — iw) is not necessarily linearly related to C), it may be written as ... 

Setting An established analytical method consisting of the extraction of a drag and its major metabolite from blood plasma and the subsequent HPLC quantitation was precisely described in a R D report, and was to be transferred to three new labs across international boundaries. (Cf. Section 4.32.) The originator supplied a small amount of drug standard and a number of vials containing frozen blood plasma with the two components in a fixed ratio, at concentrations termed lo, mid, and hi. The report provided for evaluations both in the untransformed (linear/linear depiction)... 

Recall that from the perspective of thermodynamics, every concentration is measured relative to a defined standard concentration. For any gas, the defined standard is 1 bar pressure for any solute in aqueous solution, the defined standard is 1 M. We treat the concentration terms in equilibrium constant expressions in this same way. 

The first four steps of the seven-step strategy are identical to the ones in Example. In this example, addition of a strong acid or base modifies the concentrations that go into the buffer equation. We need to determine the new concentrations (Step 5) and then apply the buffer equation (Step 6). In dealing with changes in amounts of acid and base, it is often convenient to work with moles rather than molarities. The units cancel in the concentration term of the buffer equation, so the ratio of concentrations can be... 

Yield and other mass-related metrics such as atom economy, reaction mass efficiency and mass intensity have been examined by Constable et al with regard to their significance concerning greenness and costs. The importance of using a (product) concentration term, which can be mass intensity or mass index, is additionally emphasized by Laird et al This is in compliance with Winterton, who in his twelve more green chemistry principles demands the establishment of full mass balances. 

On the other hand, the ratio of total concentrations of ionized and nonionized species between both phases is named distribution coefficient (symbolized as D). It is often referred to as an effective or apparent partition coefficient and, in concentration terms, it is mathematically defined as ... 

In kinetics, reactions are classified as being first, second, third, etc. order depending on the way the rate of the reaction is related to the concentration terms in the rate equation. If the rate of reaction is apparently independent of concentration, the reaction is said to be of zero order. 

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