Per-unit

Catalytic gas-phase reactions play an important role in many bulk chemical processes, such as in the production of methanol, ammonia, sulfuric acid, and nitric acid. In most processes, the effective area of the catalyst is critically important. Since these reactions take place at surfaces through processes of adsorption and desorption, any alteration of surface area naturally causes a change in the rate of reaction. Industrial catalysts are usually supported on porous materials, since this results in a much larger active area per unit of reactor volume. 

The absolute humidity is the mass of water vapour per unit mass of dry air. 

The percentage humidity is the ratio of the amount of water vapour present per unit mass of dry air to the amount the air could hold if... 

The V/L ratio is a volatility criterion seldom used in France but is used in Japan and in the United States where it has been standardized as ASTM D 2533. At a given temperature and pressure, the V/L ratio represents the volume of vapor formed per unit volume of liquid taken initially at 0°C. 

Now using a hydrocarbon component, say ethane, as an example, let us consider the other parameter, volume, using a plot of pressure versus specific volume (i.e. volume per unit mass of the component, the inverse of the density). The process to be described could be performed physically by placing the liquid sample into a closed cell (PVT cell), and then reducing the pressure of the sample by withdrawing the piston of the cell and increasing the volume contained by the sample. 

Measured in MJ/m or Btu/ft, the Wobbe Index has an advantage over the calorific value of a gas (the heating value per unit volume or weight), which varies with the density of the gas. The Wobbe Index Is commonly specified in gas contracts as a guarantee of product quality. A customer usually requires a product whose Wobbe Index lies within a narrow range, since a burner will need adjustment to a different fuel air ratio if the fuel quality varies significantly. A sudden increase in heating value of the feed can cause a flame-out. 

Pressure depletion in the reservoir can normally be assumed to be isothermal, such that the isothermal compressibility is defined as the fractional change in volume per unit change in pressure, or... 

Once the bubble point is reached, solution gas starts to become liberated from the oil, and since the liberated gas has a high compressibility, the rate of decline of pressure per unit of production slows down. 

The other main physical property of gas which distinguishes it from oil is its compressibility the fractional change in volume (V) per unit of change in pressure (P) at constant temperature (T). Recall that... 

The symbol t can be thought of as a mnemonic for time, while v/N is like the frequency measured in cycles per unit of time. 

The total free energy of the system is then made up of the molar free energy times the total number of moles of the liquid plus G, the surface free energy per unit area, times the total surface area. Thus... 

This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

Barnes cautions about using the appropriate units (molecular area with mole fraction, or area per unit mass with mass fraction) when analyzing area data [244]. 

The integral of p over all space gives the total excess charge in the solution, per unit area, and is equal in magnitude but opposite in sign to the surface charge density a ... 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

In the case of small ions, Hittorf transference cell measurements may be combined with conductivity data to give the mobility of the ion, that is, the velocity per unit potential gradient in solution, or its equivalent conductance. Alternatively, these may be measured more directly by the moving boundary method. 

Assume is -25 mV for a certain silica surface in contact with O.OOlAf aqueous NaCl at 25°C. Calculate, assuming simple Gouy-Chapman theory (a) at 200 A from the surface, (b) the concentrations of Na and of Cr ions 10 A from the surface, and (c) the surface charge density in electronic charges per unit area. 

The presence of the large repulsive potential barrier between the secondary minimum and contact prevents flocculation. One can thus see why increasing ionic strength of a solution promotes flocculation. The net potential per unit area between two planar surfaces is given approximately by the combination of Eqs. V-31 and VI-22 ... 

The interfacial free energy per unit area is given by the adhesion force Fo/lrR", estimate the Hamaker constant responsible for the adhesion force in the crossed-cylinder geometry illustrated in the inset to Fig. VI-6. 

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

Returning to the complete calculation, is then given by u multiplied by the number of atoms per unit area in the particular crystal plane. 

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