Unit activity, defined

The solvent strength e° is a dimensionless number and indicates the free energy of adsorption of the solvent per unit area of adsorbent with unit activity, defined as ° = 0 for n-pentane on alumina". For silica (Si02) as adsorbent, the ° values are smaller by a factor of ca. 0.8 [fi"" (SiCIj) 0.8 - ° (AI2O3)], but the ranking of solvents remains the same. 

In order to compare the thermodynamic parameters of different reactions, it is convenient to define a standard state. For solutes in a solution, the standard state is normally unit activity (often simplified to 1 M concentration). Enthalpy, internal energy, and other thermodynamic quantities are often given or determined for standard-state conditions and are then denoted by a superscript degree sign ( ° ), as in API", AE°, and so on. 

In redox couple notation, E°(HJ"/H2) = 0 at all temperatures. A hydrogen electrode in its standard state, with hydrogen gas at 1 bar and the hydrogen ions present at 1 mol-L 1 (strictly, unit activity), is called a standard hydrogen electrode (SHE). The standard hydrogen electrode is then used to define the standard potentials of all other electrodes ... 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

Mouse Bioassay. The mouse is the traditional animal of choice for detecting biological activity due to STX and TTX. Mice receive an intraperitoneal injection of sample and are observed for symptoms of intoxication, i.e., dypsnea, convulsions, and death. This method is effective for detecting biological activity of STX and TTX in numerous samples. For the standard STX assay, one mouse unit is defined as that quantity of STX injected i.p. in 1 ml solution that will... 

Pectin lyase (PNL) activity was measured spectrophotometrically by the increase in absorbance at 235 nm of the 4,5-unsaturated reaction products. Reaction mixtures containing 0.25 ml of culture filtrate, 0.25 ml of distilled water and 2.0 ml of 0.24% pectin from apple (Fluka) in 0.05M tris-HCl buffer (pH 8.0) with ImM CaCl2, were incubated at 37 C for 10 minutes. One unit of enzyme is defined as the amount of enzyme which forms Ipmol of 4,5-unsaturated product per minute under the conditions of the assay. The molar extinction coefficients of the unsaturated products is 5550 M cm [25]. Also viscosity measurements were made using Cannon-Fenske viscometers or Ostwald micro-viscosimeter, at 37°C. Reaction mixtures consisted of enzyme solution and 0.75% pectin in 0.05 M tris-HCl buffer (pH 8.0) with 0.5 mM CaCl2. One unit is defined as the amount of enzyme required to change the inverse specific viscosity by 0.001 min under the conditions of reaction. Specific viscosity (n p) is (t/to)-l, where t is the flow time (sec) of the reaction mixture and t is the flow time of the buffer. The inverse pecific viscosity (n p ) is proportional to the incubation time and the amount of enzyme used [26]. Units of enzyme activity were determined for 10 min of reaction. 

Muscle fibers are incapable of mitosis. In fact, the number of muscle fibers per muscle is likely determined by the second trimester of fetal development. Therefore, enlargement of a whole muscle is not due to an increase in the number of fibers in the muscle, but rather to the hypertrophy of existing fibers. Because muscle fibers have no gap junctions between them, electrical activity cannot spread from one cell to the next. Therefore, each muscle fiber is innervated by a branch of an alpha motor neuron. A motor unit is defined as an alpha motor neuron and all of the muscle fibers that it innervates. 

A motor unit is defined as an alpha motor neuron and all of the skeletal muscle fibers it innervates. The number of muscle fibers innervated by an alpha motor neuron varies considerably, depending upon the function of the muscle. For example, the muscles of the eyes and hands have very small motor units. In other words, each alpha motor neuron associated with these muscles synapses with only a few muscle fibers. As a result, each of these muscles is innervated by a comparatively large number of alpha motor neurons. Densely innervated muscles are capable of carrying out more precise, complex motor activities. On the other hand, antigravity muscles have very large motor units. For example, the gastrocnemius muscle of the calf has about 2000 muscle fibers in each motor unit. Muscles with large motor units tend to be more powerful and more coarsely controlled. 

The enzymatic activities of O -chymotrypsin in solution and adsorbed at the different surfaces are presented in Fig. 11, where the specific enzymatic activity (defined as activity per unit mass of protein) is plotted as a function of temperature. The enzyme loses activity due to adsorption. On the hydrophobic Teflon and PS surfaces, the activity is completely gone, whereas on the hydrophilic silica surface, or-chymotrypsin has retained most of its biological function. These differences are in agreement with the adsorption isotherms and the circular dichroism spectra. The influence of the hydrophobicity of the sorbent surface on the affinity of the protein for the sorbent surface, as judged from the rising parts of the adsorption isotherms (Fig. 8), suggests that the proteins are more perturbed and, hence, less biologically active when adsorbed at hydrophobic surfaces. Also, the CD spectra indicate that adsorption-induced structural perturbations are more severe at hydrophobic surfaces. 

The in vitro hydrogenase activity was determined by using a gas chromatograph (Hewlett Packard 5890 A Series II, column molecular Sieve 5 A, Mesh 60/80). As described before [Happe and Naber, 1993], methylviologen reduced by sodium dithionite was used as electron donor. One unit is defined as the amount of hydrogenase evolving 1 pmol Hi-min1 at 25°C. 

On the basis of crystallochemistry consideration and taking into account electron microscopy observations of the surface of crystals upon which some polymer was formed,99 Arlman and Cossee13 concluded that the active sites are located on crystal surfaces different from the basal (001) ones. In particular, these authors considered in detail active sites located on crystal surfaces parallel in the direction a — b of the unit cell defined as in Ref. 98. Figure 1.13 illustrates that, if we cut a TiCl3 layer parallel to the direction defined above, which corresponds to the line connecting two bridged Ti atoms, electroneutrality conditions impose that each Ti atom at the surface of the cut be bonded... 

In clinical chemistry the activity of an enzyme should be expressed as units and must be related to the amount of material used as enzyme source. Many authors define the unit of enzyme activity as that amount of enzyme in a given volume or weight unit of material which causes a certain change of absorbance [A log (I0//)] at 340 or 366 mp per time unit under defined, but varying conditions, e.g., A A, = 1.000 or 0.001 per minute at 25°C. In European literature activities are often given as Biicher-Einheiten (B5) where the unit is defined as the amount in 1.00 ml medium causing the change of A, of 0.1 per 100 seconds at 366 mp and 25°C. 

Standard hydrogen electrode (SHE) The standard against which redox potentials are measured. The SHE consists of a platinum electrode electroplated with Pt black (to catalyse the electrode reaction), over which hydrogen at a pressure of 1 atm is passed. The electrode is immersed in a solution containing hydrogen ions at unit activity (e.g. 1.228 mol dm of aqueous HCl at 20°C). The potential of the SHE half cell is defined as 0.000 V at all temperatures. 

A. bronchisepticus was cultivated aerobically at 30 °C for 72 h in an inorganic medium (vide supra) in 1 liter of water (pH 7.2) containing 1 % of polypeptone and 0.5 % of phenylmalonic acid. The enzyme was formed intracellularly and induced only in the presence of phenylmalonic acid. All the procedures for the purification of the enzyme were performed below 5 °C. Potassium phosphate buffer of pH 7.0 with 0.1 mM EDTA and 5 mM of 2-mercaptoethanol was used thoughout the experiments. The enzyme activity was assayed by formation of pheylacetic acid from phenylmalonic acid. The summary of the purification procedure is shown in Table 2. The specific activity of the enzyme increased by 300-fold to 377 U/mg protein with a 15% yield from cell-free extract [9]. One unit was defined as the amount of enzyme which catalyzes the formation of 1 mmol of phenylacetic acid from phenylmalonic acid per min. 

En me Treatment of LCCs. Purified Bacillus circulans xylanase (specific activity, 110 units/mg protein), purified Coriolus versicolor )9-mannanase (specific activity 179 units/mg protein), purified Thermoascus aurianticum /8-glucosidase (specific activity, 150 units/mg protein), and purified Schizophyllum commune acetyl xylan esterase (AXE specific activity, 180 units/mg protein) were used. Unit activity for xylanase and )9-mannanase was defined as the amount of enzyme catalyzing the release of 1 /xmol reducing power per minute at 50°C and pH 6.0 using oat spelts... 

CGTase Activity Assay. Aaivity was measured by the Pharmacia Phadebas Amylase Assay at pH 6.0, 60 C in O.IM sodium acetate (100 ppm Ca+ " ) for 15 minutes using B, stearothermophilus alpha-amylase as a standard. Alpha-amylase preparations were assayed under the same conditions. One Phadebas unit is defined as the amount of enzyme that will catalyze the hydrolysis of 1.0 micromole of glucosidic linkages of Lintner starch per minute at 6OOC, pH 6.0. 

The standard electrode potential (F ", sometimes referred to as Ef) is defined as the potential that exists when the electrode is immersed in a solution of ions at unit activity. The factor ajon, the actual ionic activity, is the activity of the depositing cation in the film of the plating bath at the cathode face. 

Pj), mole fraction (xj), and concentration (Cj). For these units the standard state is defined as unit activity Oj, which is typically Pj = 1 atm and 298 K, or Xj = 1 for pure liquid at 1 atm and 298 K, or C = 1 mole/liter at 298 K, respectively. Students have seen the first two of these for gases and liquids in thermodynamics. We wiU use concentration units wherever possible in this course, and the natural standard state would be a 1 molar solution. However, data are usually not available in this standard state, and therefore to calculate equilibrium composition at any temperature and pressure, one usually does the calculation with Pj or Xj and then converts to Cj ... 

Gas adsorption is the most commonly used method for characterizing the surface area of catalysts. Both physical adsorption and chemisorption may be used. Furthermore, EM can provide supplementary information. A large surface area is desirable since activity is defined as the rate per unit active surface area ((per metre) ), and this necessitates porous catalysts. Eor an idealized porous system. 

Thus, a more appropriate question to ask is Is it possible to measure the absolute potential of the hydrogen reaction, /H+(abs) Actually it is possible. Remembering the definition of a standard hydrogen electrode potential (see Section 6.3.4), this was defined as the potential obtained when a metal comes in contact with a solution containing H+ under thermodynamically reversible conditions at unit activity, and H2 at 1 atm, at 298 K. As to the identity of the metal base, it can in principle be any metal at which it is possible to observe the reaction H2 H+ + e taking place at equilibrium. In practice, the metals used as substrates can only be noble metals because most other metals enter into equilibria with their own species in solution. Usually platinum is the metal chosen. 

The universally accepted primary reference half-cell is the standard hydrogen electrode. The electrode consists of a noble metal (platinized platinum) dipping into a solution of hydrogen ions at unit activity and saturated with hydrogen gas at 1 bar (i.e. 1 X 105 Pa, which in practical terms may be taken to be equal to 1 atmosphere). In practice such a standard electrode cannot be realized, but the scale it defines can. 

Since the reactants and products need not be at unit activity, we must define the observed electrode potential E as a function of E 0 and the activities (concentrations) of A, AH2, and H+ (Eq. 6-64). 

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

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