Units used to express compositions

When specifying a composition as a percentage it is important to state clearly the basis weight, molar or volume. 

The abbreviations w/w and v/v are used to designate weight basis and volume basis. 

Technical grade hydrochloric acid has a strength of 28 per cent w/w, express this as a mol fraction. 

Within the accuracy needed for technical calculations, volume fractions can be taken as equivalent to mol fractions for gases, up to moderate pressures (say 25 bar). 

Trace quantities are often expressed as parts per million (ppm). The basis, weight or volume, needs to be stated. 

The general conservation equation for any process system can be written as 

For a steady-state process, the accumulation term is zero. Except in nuclear processes, mass is neither generated nor consumed but if a chemical reaction takes place, a particular chemical species may be formed or consumed in the process. If there is no chemical reaction, the steady-state balance reduces to 

A balance equation can be written for each separately identifiable species present, elements, compounds, or radicals and for the total material. Balances can be written for mass or for number of moles. 

2000 kg of a 5% slurry of calcium hydroxide in water is to be prepared by diluting a 20% slurry. Calculate the quantities required. The percentages are by weight. 

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Of the above three expressions for supersaturation (equations 3.67 to 3.69) only Ac is dimensional, unless the solution composition is expressed in mole fractions or mass fractions. The magnitudes of these quantities depend on the units used to express concentration, as the following examples show. 

Other measures of composition such as mole fraction and mass fraction are less commonly used to express chemical reaction rates. Weight measurements are frequently used to prepare solutions or fill reactors. The resulting composition will have a known ratio of moles and masses of the various components, but the numerical value for concentration requires that the density be known. Good practice is to prepare solutions in mass units and then convert to standard concentration units based on the known or observed density of the solution under reaction conditions. To avoid ambiguity, modern analytical chemists frequently define both molarity and molality in weight units as moles per kilogram of solution or moles per kilogram of solvent. 

Membrane selectivity towards gas mixtures and mixtures of organic liquids is usually expressed in terms of the separation factor a. For a mixture consisting of components A and B the selecdvi factor a s is given by eq. 1.3. where y and yg are the concentrations of components A and B in the permeate and x. and Xg are the concentrations of the components in the feed. The SI unit for the amount of substance is the mole but the kilogram (kg) is frequently used as well. Hence, the concentrations can be expressed either as a mass concentration (c,) or a molarconcentration (nj. The composition of a solution or a mixture can also be described by means of mole fractions, weight fractions or volume fractions. The units used to describe the composition of solutions or mixtures are summarised in table 1.4. 

Molal units arc used extensively in chemistry calculations as they grcatly simplify material balances where chemical reactions are occurring. For mixtures of substances (gases, liquids, or solids), it is also convenient to express compositions in mole fractions or mole percentages instead of mass fractions. The mole fraction is the ratio of the number of moles of one component to the total number of moles in the mixture. Equations (3.6)-(3.9) express these relationships ... 

Before deriving the rate equations, we first need to think about the dimensions of the rates. As heterogeneous catalysis involves reactants and products in the three-dimensional space of gases or liquids, but with intermediates on a two-dimensional surface we cannot simply use concentrations as in the case of uncatalyzed reactions. Our choice throughout this book will be to express the macroscopic rate of a catalytic reaction in moles per unit of time. In addition, we will use the microscopic concept of turnover frequency, defined as the number of molecules converted per active site and per unit of time. The macroscopic rate can be seen as a characteristic activity per weight or per volume unit of catalyst in all its complexity with regard to shape, composition, etc., whereas the turnover frequency is a measure of the intrinsic activity of a catalytic site. 

One problem with this or any other method using gradients is that the best path obtained is dependent on the units used. If different units are used a different path will be indicated. To illustrate this, suppose it is desired to improve the yield (y) of a plug flow reactor when the feed rates and compositions are constant. At the usual operating conditions of 50 psia and 500°K a yield of 60 lb/hr is obtained. In what order should the pressure (P) and the temperature (T) be changed To reduce costs, it is desirable to minimize the number of experiments performed, hence the method of steepest ascent is to be used.When a test is performed at 50 psia and 510°K, the yield is found to be 60 lb/hr. When another experiment is run at 60 psia and 500°K, the yield is again 60 lb/hr. If the surface is linearized it can be expressed as ... 

Compositions are expressed in terms of the full unit cell content. Two compositions are provided. The CHEMICAL COMPOSITION is the nominal material composition provided in the original reference, and is usually obtained from chemical analysis. The REFINED COMPOSITION is derived from the structure refinement. Because of the complexities of structure refinements, the chemical and refined compositions do not always concur. When available, refinements of hydrated zeolites were used to calculate the patterns. For synthetic zeolites, if the zeolite had been synthesized in the presence of organic material, those refinements of the uncalcined products that contained the occluded organic molecules were chosen. The sample locality is given in the case of natural zeolites. 

The requirements set out in this publication and taken mainly from the report on the Nutrient Requirements of Poultry (NRC, 1994) are based on ME (AME), expressed as kilocalories (kcal) or megacalories (Meal)/kg feed. This energy system is used widely in North America and in many other countries. Energy units used in some countries are based on joules (J), kilojoules (kj) or megajoules (MJ). A conversion factor can be used to convert calories to joules, i.e. IMeal = 4.184 MJ 1MJ = 0.239 Meal and 1MJ = 239 kcal. Therefore, the tables of feedstuff composition in this publication show ME values expressed as MJ or kj as well as keal/kg. 

Let the unit vector in the jth characteristic direction expressed as a column matrix in the A system of coordinates be designated Remembering that alpha is always used to designate a composition vector expressed as a column matrix in the A system of coordinates, then, for any vector a/ in the jth characteristic direction, we have... 

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