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vb.net print barcode free ChemicalReaction Equilibria in Software
CHAPTER 13 ChemicalReaction Equilibria Encoding Quick Response Code In None Using Barcode printer for Software Control to generate, create Quick Response Code image in Software applications. QRCode Reader In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. present in each molecule of chemical species i The material balance on each element k may then be written: Draw QR Code ISO/IEC18004 In C#.NET Using Barcode generation for .NET Control to generate, create QRCode image in Visual Studio .NET applications. QR Code Drawer In Visual Studio .NET Using Barcode creator for ASP.NET Control to generate, create QR Code image in ASP.NET applications. C n i a i k  Ak = O
QR Code Printer In .NET Framework Using Barcode printer for .NET Control to generate, create QR Code image in .NET framework applications. Denso QR Bar Code Generation In Visual Basic .NET Using Barcode creation for .NET Control to generate, create Denso QR Bar Code image in .NET applications. (k = 1 , 2 , , w) EAN13 Generator In None Using Barcode drawer for Software Control to generate, create EAN13 image in Software applications. Draw Code 128 In None Using Barcode maker for Software Control to generate, create Code 128 Code Set A image in Software applications. where w is the total number of elements comprising the system 2 Next, we introduce the Lagrange multipliers hk, one for each element, by multiplying each element balance by its hk: EAN128 Maker In None Using Barcode generator for Software Control to generate, create GS1 128 image in Software applications. Generate Barcode In None Using Barcode maker for Software Control to generate, create barcode image in Software applications. These equations are summed over k, giving: Paint Barcode In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. Encoding Universal Product Code Version A In None Using Barcode maker for Software Control to generate, create UPCA Supplement 2 image in Software applications. 3 Then a new function F is formed by addition of this last sum to Gt Thus, UPCE Supplement 5 Generator In None Using Barcode creator for Software Control to generate, create UPC E image in Software applications. Create Code128 In None Using Barcode drawer for Excel Control to generate, create Code128 image in Excel applications. This new function is identical with Gt, because the summation term is zero However, the partial derivatives of F and G' with respect to ni are different, because the function F incorporates the constraints of the material balances 4 The minimum value F (and G') occurs when all of the partial derivatives (aF/ani)T,p,nJ are zero We therefore differentiate the preceding equation, and set the resulting derivative equal to zero: Bar Code Maker In Java Using Barcode generator for Java Control to generate, create bar code image in Java applications. Bar Code Printer In Java Using Barcode generation for BIRT reports Control to generate, create bar code image in BIRT applications. Since the first term on the right is the definition of the chemical potential [see Eq (1 11)], this equation can be written: Creating ECC200 In Java Using Barcode generation for Android Control to generate, create Data Matrix image in Android applications. Read Code 39 Full ASCII In .NET Framework Using Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications. + x h k a i k= O
UPC  13 Drawer In Java Using Barcode printer for Android Control to generate, create EAN13 Supplement 5 image in Android applications. Code 128A Encoder In None Using Barcode printer for Font Control to generate, create Code 128 Code Set A image in Font applications. (i = 1,2, , N) However, the chemical potential is given by Eq (139): For gasphase reactions and standard states as the pure ideal gases at 1 bar [or 1 atm]: = GP
+ RT l n ( f i / ~ " ) If GP is arbitrarily set equal to zero for all elements in their standard states, then for compounds GP = AG>i, the standard Gibbsenergy change of formation for species i In 139 Multireaction Eauilibria
addition, the fugacity is eliminated in favor of the fugacity coefficient by Eq (1 148), = yi&i P With these substitutions, the equation for pi becomes: Combination with Eq (1342) gives: Note that P o is 1 bar, expressed in the units used for pressure If species i is an element, AGYi is zero Equation (1343) represents N equilibrium equations, one for each chemical species, and Eq (1341) represents w materialbalance equations, one for each element a total of N w equations The unknowns in these equations are the ni's (note that yi = n, / ni), of which there are N, and the hk's, of which there are w a total of N w unknowns Thus the number of equations is sufficient for the determination of all unknowns The foregoing discussion has presumed that each &i is known If the phase is an ideal gas, then for each species &i = 1 If the phase is an ideal solution, 6, = I#I~, values can at and least be estimated For real gases, $iis a function of the set {yi), which is being calculated Thus an iterative procedure is indicated The calculations are initiated with Ji = 1 for all i Solution of the equations then provides a preliminary set of {yi) For low pressures or high temperatures this result is usually adequate Where it is not satisfactory, an equation of state is used together with the calculated {yi) to give a new and more nearly correct set { J i ) for use in Eq (1343) Then a new set {yi) is determined The process is repeated until successive iterations produce no significant change in {yi) All calculations are well suited to computer solution, including the calculation of {Ji) equations such as Eq (1161) by In the procedure just described, the question of what chemical reactions are involved never enters directly into any of the equations However, the choice of a set of species is entirely equivalent to the choice of a set of independent reactions among the specieany event, a set of species or an equivalent set of independent reactions must always be assumed, and different assumptions produce different results

