Concentration, mols, partial pressure, mol fraction

Any property of a reacting system that changes regularly as the reaction proceeds can be formulated as a rate equation which should be convertible to the fundamental form, Eq 2.6. Examples are rate of change of electrical conductivity or of pH, or of optical rotation. The commonest other variables are partial pressure and mol fraction Nj. The relations between these units are, 

Other volume explicit equations of state are sometimes necessary, such as the compressibility factor equation, V = zRT/P, or the truncated virial equation, 

Designate 5a as the increase in the number of mols per mol decrease of substance A according to stoichiometric Eq 2.5, 

An equation like Eq 2.7 can be written in terms of partial pressures and mol fraction as 

Typical units of a first order reaction in terms of different variables 

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K is therefore a function of temperature through the term RT, where R is the gas constant, 8.314 J mol K and Tis the temperature expressed in Kelvin (K). The value of the constant given in Equation 6.13 depends on how the abundance of the solute or chemical is expressed i.e. partial pressure, mole fraction or molar concentration. For mole fraction the constant has a value of 1, whereby In 1 = 0 and can therefore be ignored. Rearranging Equation 6.13 to solve for AG , and then combining with the Gibbs-Helmholz equation results in... 

The computer simulation program which was available for miscible flood simulation is the Todd, Dietrich Qiase Multiflood Simulator (28). This simulator provides for seven components, of which the third is expected to be carbon dioxide and the seventh water. The third component is allowed to dissolve in the water in accordance with the partial pressure of the third component in the non-aqueous phase or pdiases. It is typically expected that the first two components will be gas components, while the fourth, fifth, and sixth will be oil components. There is provision for limited solubility of the sixth component in the non-aqueous liquid p ase, so that under specified conditions of mol fraction of other components (such as carbon dioxide) the solubility of the sixth component is reduced and some of that component may be precipitated or adsorbed in the pore space. It is possible to make the solubility of the sixth component a function of the amount of precipitated or adsorbed component six within each grid block of the mathematical model of the reservoir. This implies, conversely, a dependence of the amount adsorbed or precipitated on the concentration (mol fraction) of the sixth component in the liquid non-aqueous j ase, hence it is possible to use an adsorption isotherm to determine the degree of adsorption. 

Since the majority of flames which have been studied are open to the atmosphere, it is convenient to specify concentrations as partial pressures in atm, i.e. as mol fractions. In the unbumt gas there will be fuel, oxidant and diluent for example, a hydrogen flame at 2200 K might be fed with 0-400 atm Hg, 0-139 atm O2 and 0-460 atm of Ng. If any substance is added to the flame, these quantities will be altered—in one experiment to study the effect of chlorine on potassium a portion of the nitrogen was saturated with chloroform vapour to produce a partial pressure of 0-008 atm, while a further portion carried a spray of 0-2 M potassium chloride solution in to the flame, producing a partial pressure of 7 x 10 atm ofpotassiiun and 0-018 atm of water. The resulting composition of the unbumt gas will therefore be ... 

The equihbrium partitioning of a chemical solute between a Hquid and vapor phase is governed by Henry s law when the Hquid mixture is very dilute in the solute. Henry s law generally is vaHd at concentrations below 0.01 mol/L of solution, although the upper limit can sometimes extend to 0.1 mol/L or higher (10). Over this concentration range, a direct proportionaHty, ie, Henry s constant, is observed between the partial pressure of the chemical in the gas phase and its mole fraction in the Hquid phase. Henry s constant, when expressed in this way, has units of pressure (3). 

Henry s law constant is dimensionless when Ug and ay are in mol/m, but conventional units for Kyy are atmospheres or torr per mole fraction. Thus, the gas-phase concentration is expressed in terms of its partial pressure and the liquid-phase concentration is expressed as a mole fraction. 

The participant A is identified by subscript a. Thus the concentration is Ca, the number of mols is na, the fractional conversion is xa, the partial pressure is pa, the rate of decomposition is ra. The capital letter A also is used on occasion instead of Ca. The flow rate in terms of mols is na but the prime ( ) is left off when the meaning is clear, The volumetric flow rate is V, reactor volume is Vr or simply V of batch reactors, the total pressure is... 

Air-water partitioning can be viewed as the determination of the solubility of a gas in water as a function of pressure, as first studied by William Flenry in 1803. A plot of concentration or solubility of a chemical in water expressed as mole fraction x, versus partial pressure of the chemical in the gaseous phase P, is usually linear at low partial pressures, at least for chemicals which are not subject to significant dissociation or association in either phase. This linearity is expressed as "Henry s Law." The slope of the P-x line is designated H, the Henry s law constant (HLC) which in modern SI units has dimensions of Pa/(mol fraction). For environmental purposes, it is more convenient to use concentration units in water Cw of mol/m3 yielding H with dimensions of Pa m3/mol. 

For the absorption of a gas (like carbon dioxide) into a liquid (like water) Henry s law stales that partial pressure of the gas is proportional to the mole fraction of the gas in the liquid-gas solution with the constant of proportionality being Henry s constant. A bottle of soda pop (CO2-H2O) at room temperature has a Henry s constant of l7,l(X)kPa. If the pressure in this bottle is 120 kPa and the partial pressure of the water vapor in the gas volume at the top of the bottle is neglected, the concentration of the CO2 in the liquid HjO is (a) 0.003 mol-COj/mol (6) 0.007 mol-COj/mol... 

The osmotic pressure of a sucrose solution is 148.5 atm at 20°C. The concentration is 1.43 kg sucrose/kg water, corresponding to a mol fraction 0.0700 of sucrose. The partial molal volume of water is approx 0.018 L/g mol. Accordingly, the activity coefficient of the water is... 

Concentrations will be expressed as mole fraction of a component or species /, x = nj/E nj as molality, mole per mass of solvent, mol kg or molarity, mole per volume of solution. The concentration scale will depend on the properties of the solutes (i.e., ionic, polar, nonpolar, etc.). Pressure, p, and the gas phase partial pressure of species i, / , will be expressed in bars (approximately equal to atmospheres). 

ALTERNATE FORMS OF TRANSFER COEFFICIENTS. The gas-film coefficients reported in the literature are often based on a partial-pressure driving force instead of a mole-fraction difference and are written as kgC or K a. Their relationships to the coefficients used heretofore are simply = k/ilP and Kga = K jP, where P is the total pressure. The units of k and Kgtt are commonly mol/ft -h-atm. Similarly liquid-film coefficients may be given as kifl or Kja, where the driving force is a volumetric concentration difference is therefore the same as k defined by Eq. (21,31). Thus k a and Ki/z are equal to k jpi f and K ajp, respectively, where pi is the molar density of the liquid. The units of kjci and Kip are usually mol/ft -h-(mol/ft ) or h" ... 

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