Other units of concentration

Very low concentrations of substances are usually expressed in terms of parts per million (ppm) or even parts per billion (ppb) by mass, where  

If we are dealing with gaseous mixtures, it is often more convenient to express ppm and ppb by volume, rather than by mass  

These units are useful for describing the levels of pollutants in air. For example, the concentration of NO2 in the atmosphere around a large city was 15 ppm this corresponds to 15 cm of the gas in a sample of 10 dm of air. 

For dilute aqueous solutions at room temperature, the density of the solution is close to the density of water (1 g cm ), so the volume of the solution in cubic centimetres 

These units are more convenient for low concentrations because they avoid using the very low numbers that would be involved if the concentrations were to be expressed in mol dm water pollutants are often given in ppm units. Also, we may use these units to describe trace concentrations of metals when we are not sure of the exact nature of the species involved. For example, drinking water may be found to have a total aluminium content at a concentration of 3 ppm. The nature and concentration of the different aluminium compounds present in a sample of drinking water is dependent on pH and can be a very complex problem to solve the ions AP, AlOH and Al(OH)2 are but a few species that may be found. Without exact knowledge of the species present, calculations of molar concentration cannot be made, but it is always possible to express concentration in terms of the total mass of metal present. 

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The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

Explains what is meant by pH 9-4 Other units of concentration 146... 

Notice that reaction rate has the units of concentration divided by time. We will always express concentration in moles per liter. Time, on the other hand, can be expressed in seconds, minutes, hours.A rate of 0.10 mol/L - min corresponds to... 

Rates of reaction have units of (concentration) (time)". Because time does not appear in any other term on the right-hand side of the rate law, the units of k must always include time in the denominator. The concentration... 

Material, Units of Concentration, and Other Variables Concentration9 Referenceb... 

The composition of a mixture need not be given in terms of the mole fractions of its components. Other scales of concentration are frequently used, in particular, when one of the components, say. A, can be designated as the solvent and the other (or others), B, (C,...) as the solute (or solutes). When the solute is an electrolyte capable of dissociation into ions (but not only for such cases), the molal scale is often employed. Here, the composition is stated in terms of the number of moles of the solute, m, per unit mass (1 kg) of the solvent. The symbol m is used to represent the molal scale (e.g., 5 m = 5 mol solute/1 kg solvent). The conversion between the molal and the rational scale (i.e., the mole fraction scale, which is related to ratios of numbers of moles [see Eq. (2.2)] proceeds according to Eqs. (2.32a) or (2.32b) (cf. Fig. 2.4) ... 

Others make use of concentrations in terms of atoms, as does, for example, Heumann [8,9]. Others use concentrations in terms of moles, as do Fassett and Paulsen [10] and Dean [11]. Clearly each investigator selects the form with which he or she feels most comfortable. Due caution is indicated to make sure of one s units of concentration before blindly using an equation from the literature. 

Expressing the steady state kinetics in terms of these parameters, only the Vm parameter, which has units of mass per unit time per unit volume, has units that include time. All other parameters have units of concentration (mass per unit volume). In addition, the eight concentration parameters cannot vary independently. For example we can compute Kbq in terms of the other parameters if the equilibrium constant of the reaction is known ... 

The expression obtained in this way may now be introduced into the region of velocities. The medium exercises, we have seen, a double influence, one connected with the displacement of equilibrium, while the other is perhaps to be referred to some physical property of the medium. But the influence on equilibrium vanishes if we choose saturation as the unit of concentration. It is then natural, in judging of the effect on the velocity, to choose saturation as the unit, and instead of the value expressed in terms of the constant k. 

This allows the concentration units to be changed to suit the problem, and other measures of concentration, such as mole fraction, partial pressure, or fugacity, might be introduced, g is a good measure to use for gaseous reactions with volume changes and will be mentioned later in connection with tubular reactors otherwise we will phrase our problems in terms of c, recognizing that this implies no limitation on the method. 

In other words, the decay rates of parent and daughter are equal, and their concentrations are equal, when expressed in terms of Bq/m or other units of radioactivity. This condition is known as secular equilibrium. Attainment of secular equilibrium between a parent and daughter can occur only when kp kp. In a closed system, secular equilibrium among all the daughters in a decay series may also be attained if the decay constant of the initial parent is much less than that of any of its daughters. Such is the case for and Th. If secular equilibrium is attained in such a series, then... 

Catalysis or Catalytic Power is the ratio between the reaction rate of the catalyzed reaction and that of the uncatalyzed reaction. It is defined as kcat/feun where kcat is the rate of the catalyzed reaction and kun is the rate of the uncatalyzed reaction. By definition, catalysis should be unit-less (a ratio of rate constants), thus care must be practised while determining Catalytic Power that k at and k n have the same units. Alternatively, the second order uncatalyzed reaction s rate (M s units) can be divided by kcat (s ) and the ratio then has units of concentration (M). This concentration is called effective concentration [2] and could be addressed as the concentration of functional groups or substrates in the enzyme s active site. Since that effective concentration is often in the thousands of M range, it is not a physically meaningful concentration, but rather a manifestation of the role of correct orientation, dynamic, and other catalytic effects induced by the enzyme. A similar approach used the substrate concentration in which the enzymatic and uncatalyzed rates are equal as an indicator for catalytic power [8j. The advantage of the first... 

For a large number of polymers, a plot of the reciprocal of water sorption against the reciprocal of the partial pressure of water exhibits near-linear behavior. With the expectation that the volume fraction of water will be the expression of water concentration relevant to basic pol3rmer solution thermodynamics, this measure has been used. However, a variety of other expressions of concentration can be used (weight or volume per unit weight or volume of polymer, weight percent, etc.) and substitution of these will alter the slope and Intercept, but not the linearity of the plot. 

Alternatively we could measure the 1C50 or the Ki (inhibitory constant) for the perpetrator. The A) of a perpetrator that is capable of inhibiting an enzyme (or transporter) is the dissociation constant for the enzyme-inhibitor complex. Accurate estimation of the A) requires, among other things, the appropriate definition or specification of the type of enzyme inhibition (e.g., competitive, noncompetitive, or uncompetitive). The appropriate in vitro experiments require that multiple concentrations of the inhibitor must be used as well as a range of substrate concentrations that embrace the substrate Km, and from these experiments both the type of inhibition elicited by the perpetrator can be deduced and the A) value for the perpetrator can be estimated. The Ki will have units of concentration. Alternatively, K values can be computed from /C50 values for an inhibitor. The /C50 is defined simply as the inhibitor concentration that decreases the biotransformation of a substrate at a single, specified concentration by 50%. This parameter obviously also has units of concentration (e.g., pM), and can be related to the Ki as follows. 

If the aim is to extract only some material of high purity, it is more sensible to sacrifice some of the compound of interest and take a cut that contains little or none of the peak overlap. If, on the other hand, the emphasis is on isolating the maximum yield, a broader cut should be taken with a view to subsequent purification steps to remove minor contaminants. Additionally, of course, it is often prudent to collect material in a number of fractions so that a majority of compound will be contained in a fairly pure form, and only a small proportion will need to be fiirther purified. (All of these estimations are based on the assumption that both compounds give the same detector response per unit of concentration.)... 

Other units can be imagined and a great variety of units is to be found in the literature. This variety notwithstanding, in order to reduce experimental data to useful kinetic parameters, the units of concentration have to be in terms of molar concentration per unit volume. Chemical conversion affects individual molecules of the reactant, not units of its weight. Other units that may be reported in the literature must be reduced to molar units if one intends to use mechanistic rate expressions and/or arrive at thermodynamically meaningful constants in fitting rate data. 

The density of the solution is often needed for mass balance, flow rate, and product yield calculations. Density is also needed to convert from concentration units based on solution volume to units of concentration based on mass or moles of the solution. Density is defined as the mass per unit volume and is commonly reported in g/cm, however, other units such as pounds mass (Ibm)/ft and kg/m are often used. When dealing with solutions, density refers to a homogeneous solution (not including any crystal present). Specific volume is the volume per unit mass and is equal to 1/p. 

Look carefully at this equation because it is misleading. Our goal was to nondimensionalize it. Therefore we expect the accumulation term, that is, the LHS, to be dimensionless. But how can it be The RHS clearly is not dimensionless, and it has units of concentration This is the key to seeing where we went wrong our error was in assuming that the rate constant k for this second-order rate expression had the same units as those used for the first-order system. It does not. The dimensions for this second-order rate are vol/mol/tim in other words, inverse time and inverse concentration. Why Because the accumulation term on the LHS must have the same dimensions of mol/volume/time regardless of the order or complexity of the rate expression... 

The unit of concentration as indicated by [ ] is moleAiter, but other concentration units also can be used. From this discussion we learn that the equilibrium state can be approached from both directions. 

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