Molarity units

Results are reported in energy units that correspond to those in experimental papers molar units for binding equilibria (kcal/mol) and molecular units for ligand extraction experiments (zj = pN nm). 1 kcal/mol = 6.9 zJ, and at 300 K, ktsT = 4.2 zJ. 

The dimensions of permeabiUty become clear after rearranging equation 1 to solve for P. The permeabiUty must have dimensions of quantity of permeant (either mass or molar) times thickness ia the numerator with area times a time iaterval times pressure ia the denomiaator. Table 1 contains conversion factors for several common unit sets with the permeant quantity ia molar units. The unit nmol/(m-s-GPa) is used hereia for the permeabiUty of small molecules because this unit is SI, which is preferred ia current technical encyclopedias, and it is only a factor of 2, different from the commercial permeabihty unit, (cc(STP)-mil)/(100 in. datm). The molar character is useful for oxygen permeation, which could ultimately involve a chemical reaction, or carbon dioxide permeation, which is often related to the pressure in a beverage botde. 

The solubihty coefficient must have units that are consistent with equation 3. In the hterature S has units cc(STP)/(cm atm), where cc(STP) is a molar unit for absorbed permeant (nominally cubic centimeters of gas at standard temperature and pressure) and cm is a volume of polymer. When these units are multiphed by an equihbrium pressure of permeant, concentration units result. In preferred SI units, S has units of nmol /(m GPa). 

In the mass units for flavor, aroma, and solvent molecules, the solubihty coefficient has units kg/(m Pa). Equation 6 shows how to convert from the mass units to the molar units. 

Enzymes are excellent catalysts for two reasons great specificity and high turnover rates. With but few exceptions, all reac tions in biological systems are catalyzed by enzymes, and each enzyme usually catalyzes only one reaction. For most of the important enzymes and other proteins, the amino-acid sequences and three-dimensional structures have been determined. When the molecular struc ture of an enzyme is known, a precise molecular weight could be used to state concentration in molar units. However, the amount is usually expressed in terms of catalytic activity because some of the enzyme may be denatured or otherwise inactive. An international unit (lU) of an enzyme is defined as the amount capable of producing one micromole of its reaction product in one minute under its optimal (or some defined) reaction conditions. Specific activity, the activity per unit mass, is an index of enzyme purity. 

Efficiency means component 1 made per component 3 converted, all in molar units. Data show that 89.7% of the converted propylene was accounted for by the formed acrolein. An additional 9.8% efficiency is indicated for acrylic acid. Efficiency to total useftil product was 99.5% as long as ignition of homogeneous reaction could be avoided... 

Using Eq. (2.5), one may estimate Henry s constant in molar units (mole fraction of toluene in water/mole fraction of toluene in air) to be... 

Stoichiometry in Reactive Systems. The use of molar units is preferred in chemical process calculations since the stoichiometry of a chemical reaction is always interpreted in terms of the number of molecules or number of moles. A stoichiometric equation is a balanced representation that indicates the relative proportions in which the reactants and products partake in a given reaction. For example, the following stoichiometric equation represents the combustion of propane in oxygen ... 

The logarithm of the micellar molecular weight (M) and consequently the aggregation number of sodium dodecyl sulfate at 25°C in aqueous sodium chloride solutions is linearly related to the logarithm of the CMC plus the concentration of salt (Cs), both expressed in molar units, through two equations [116]. Below 0.45 M NaCl micelles are spherical or globular, and Eq. (18) applies ... 

Fick s Law of diffusion is normally expressed in molar units or ... 

Liquid phase diffusivities are strongly dependent on the concentration of the diffusing component which is in strong contrast to gas phase diffusivities which are substantially independent of concentration. Values of liquid phase diffusivities which are normally quoted apply to very dilute concentrations of the diffusing component, the only condition under which analytical solutions can be produced for the diffusion equations. For this reason, only dilute solutions are considered here, and in these circumstances no serious error is involved in using Fick s first and second laws expressed in molar units. 

Consider the movement of an element of fluid consisting of n molar units of a mixture of two constituents A and B from a region outside the boundary layer, where the molecular concentrations are CAs and CBs, to the surface where the corresponding concentrations are CAw and CBw. The total molar concentration is everywhere Cr- The transfer is effected in a time t and takes place at an area A of surface. 

There is no net transference of the component B. When n molar units of material are transferred from outside the boundary layer to the surface ... 

Mixtures of liquids with gas or vapour, flow 181 Modified Reynolds number, non-Newtonian flow 124 Molar units 8 Mole 8... 

See Figure 1.2. A component balance can be expressed in mass units, and this is done for materials such as polymers that have ill-defined molecular weights. Usually, however, component A will be a distinct molecular species, and it is more convenient to use molar units ... 

If these equations are written in terms of mass and then summed over all components, the sum must equal Equation (1.1) since the net rate of mass formation must be zero. When written in molar units as in Equation (1.6), the sum need not be zero since chemical reactions can cause a net increase or decrease in the number of moles. 

A QSAR for the acute toxicity of new hypoglycemic agents [48] was internally cross-validated, but used LD50 instead of log LD50 as the dependent variable, and (more seriously) used LD50 values in g kg rather than in a molar unit such as mmol kg. ... 

The terms specifie conductivity and equivalent conductivity were previously used. However, these terms are not recommended for use as the SI units. They should be replaced by molar conductivity according to the SI recommendation, which states as follows, When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Thus, when we previously used equivalent conductivity, we should now use molar conductivity, where we define the molar unit so that it is equal to the equivalent unit previously used. For example, we define (l/2)Ca, (l/3)La, (l/2)CO and Alj/jF as molar units. 

Figure 5.3 A convenient scheme for performing an inhibitor titration in 96-well format. Four compounds (1-4) are assessed in duplicate at each of 11 inhibitor concentrations. The inhibitor concentrations follow a threefold serial dilution from a maximum concentration of 1000 (molarity units nM, LlM, etc.). The right most column of wells is reserved for control samples. In this illustration four of the wells of column 12 are used for zero inhibitior positive controls, and the other four are used to establish the assay background as negative controls. Negative controls could represent any sample for which one knows that the enzymatic reaction has be abrogated. For example, the negative control wells could contain all of the reaction mixture components except the enzyme. See Chapter 4 for other potential forms of negative controls.

Table 3 Values of X, and of logCH+, logaH2o> logCnsoj and logtfH2so4 in molarity units, for aqueous sulfuric acid at 25°C, at different values of wt% acid.

Table 6 Values of X and X0, and of log CH+ and log aH o in molarity units, for aqueous perchloric acid at 25°C at different values of the acid molarity.

Tables 3 and 4 contain values of the log water activity and log sulfuric acid activity in molarity units. These can be obtained at any temperature by using the polynomial coefficients supplied by Zeleznik,45 which are based on all of the preexisting thermodynamic data obtained for this medium. The numbers were converted to the molarity scale using the conversion formula given in Robinson and Stokes 46 Molarity-based water activities are given for HCIO4 in Tables 5 and 6. These are calculated from data obtained at 25°C by Pearce and Nelson,17...

The concentrations of substrate and product are invariably in molar units (M this includes mM, iM, etc.), but enzyme concentrations may be given in molar (M), milligrams per milliliter (mg/mL), or units/mL. The amount of enzyme you have can be expressed in molecules, milligrams, nanomoles (nmol), or units. A unit of enzyme is the amount of enzyme that will catalyze the formation of 1 prnol of product per minute under specifically defined conditions. A unit is an amount, not a concentration. 

Enzyme concentrations in milligrams per milliliter can be converted to molar units by dividing by the molecular weight (in mg/mmol).2... 

Velocity can be expressed in a number of different units. The most common is micromolar per minute (p,M/min) however, because the velocity depends on the amount of enzyme used in the assay, the velocity is often normalized for the amount of enzyme present by expressing the activity in units of micromoles per minute per milligram of enzyme [ jjnol/(min mg)]. This is called a specific activity. You may be wondering (or not) where the volume went—after all, product concentration is measured in molar units (M mol/L). Well, it s really still there, but it... 

When a weak acid is neutralized by a strong base, the concentration of the acid (HA) decreases by the same amount [in molar units (M)] as the concentration of the conjugate base increases. 

The product/reactant ratio may have units if there are more product terms than reactant terms, or vice versa. For example, if there are two products and one reactant, the product/reactant ratio will have molar units (M). In this case, a products/reactants ratio of 1 means that the products/reactants ratio is actually 1 M. The term molar standard state means that we re talking about a products/reactants ratio that has molar units. 

UNITS The products/reactants ratios may have units associated with them. For example, a reaction of the type A B + C has a products/reactants ratio that has molar units. What you do when you take the log of a products/reactants ratio with molar units is ignore the units. You ve not really made them disappear, you ve just ignored them. The way physical chemist types make this difficult is that they call ignoring the units an assumption of standard state. It does matter, though. If you assume the units are molar (M), the products/reactants ratio has one... 

This equation is known as a rate law. It tells you how the rate of the reaction depends on the concentration(s) of the substrate. The order of the reaction is defined as the power to which the substrate concentration is raised when it appears in the rate law. In the preceding case, [A] is raised to the first power ([A]1), so the reaction is said to be first-order with respect to the A concentration, or simply first-order in A. The rate constant k is a proportionality constant thrown in so that the equation works and so that the units work out. Since v must have units of molar per second Mls) and [A] has molar units (M), then k must have units of reciprocal seconds (1/s or s ). 

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