Stoichiometric Amounts of Reactants

Carothers derived a relationship between the extent of reaction at the gel point and the average functionality /avg of the polymerization system for the case where the two functional groups A and B are present in equivalent amounts [Carothers, 1936]. The derivation follows in a manner similar to that for Eq. 2-78. The average functionality of a mixture of monomers is the average number of functional groups per monomer molecule for all types of monomer molecules. It is defined by 

In a system containing equivalent numbers of A and B groups, the number of monomer molecules present initially is No and the corresponding total number of functional groups is Af0/avg. If IV is the number of molecules after reaction has occurred, then 2(A/ — N) is the number of functional groups that have reacted. The extent of reaction p is the fraction of functional groups lost  

Equation 2-138, often referred to as the Carothers equation, relates the extent of reaction and degree of polymerization to the average functionality of the system. 

An important consequence of Eq. 2-138 is its limiting form at the gel point where the number-average degree of polymerization becomes inhnite. The critical extent of reaction pc at the gel point is given by 

The average functionality of nonstoichiometric mixtures has been deduced [Pinner, 1956] as being equal to twice the total number of functional groups that are not in excess divided by the total number of all molecules present. This simply takes into account the fact that the extent of polymerization (and crosslinking, if it can occur) depends on the deficient reactant. The excess of the other reactant is not useful in fact, it results in a lowering of the functionality of the system. For the above nonstoichiometric mixture of 1 mol of glycerol and 5 mol of phthalic acid, the /avg value is correctly calculated as 6/6 or 1.00. This low value of /avg is indicative of the low degree of polymerization that will occur in the system. 

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Standard Heat of Reaction. This is the standard enthalpy change accompanying a chemical reaction under the assumptions that the reactants and products exist in their standard states of aggregation at the same T and P, and stoichiometric amounts of reactants take part in the reaction to completion at constant P. With P = 1 atm and T = 25°C as the standard state, AH (T,P) can be written as... 

Bach product (E, Fy G) requires different (stoichiometric) amounts of reactants according to the following mass balances ... 

Note 2 A model network is not necessarily a perfect network. If a non-linear polymerization is used to prepare the network, non-stoichiometric amounts of reactants or incomplete reaction can lead to network containing loose ends. If the crosslinking of existing polymer chains is used to prepare the network, then two loose ends per existing polymer chain result. In the absence of chain entanglements, loose ends can never be elastically active network chains. 

Polycrystalline 2201 phase formed as the major and sole superconducting component when stoichiometric amounts of reactants were heated at 875°C for several hours (7) transitions were broad with Te onsets of 84 K. Reheating at 900°C caused partial melting and an increase in the Tc onset value to 90 K (with zero resistance at 83 K) increased amounts of second-phase BaCuOz were observed. 

N,60i802 forms, and assume stoichiometric amounts of reactants are combined. 

When K has a value much greater than 1, the product concentrations are relatively large and the reactant concentrations are relatively small. In both cases, however, the rate of the forward reaction equals the rate of the reverse reaction at equilibrium (this is a definition of equilibrium). 13. No, it doesn t matter in which direction the equilibrium position is reached. Both experiments will give the same equilibrium position since both experiments started with stoichiometric amounts of reactants or products. 15. When equilibrium is reached, there is no net change in the amount of reactants and products present since the rates of the forward and reverse reactions are equal. The first diagram has 4 A2B molecules,... 

If one assumes an initial pressure of from 0 to 10 atm for ZrBr and stoichiometric amounts of reactants, then, on the basis of zirconixim, the reaction must proceed to the extent of 80 to 90% for the pressure of ZrBr to attain a value of 1 atm and hence an equilibrium constant of 1. The data of Larsen and Leddy ( ) indicate about 82% reaction at 973 K. It was assumed that around 1100 K the equilibrium constant attains a value of 1 giving -152 kcal mol" (-635.968 kJ mol" ) for the enthaply of formation of ZrBrg(cr) at 298.15 K. The limits of error were taken to be 16 kcal raol" which corresponds to a 500 K temperature spread in the above table. 

Chemists have agreed on a convention for attaching reaction enthalpy values to balanced chemical equations. A reaction enthalpy written after a balanced chemical equation refers to the enthalpy change for the complete conversion of stoichiometric amounts of reactants to products the numbers of moles of... 

The stoichiometric amount of reactant B is determined for the specific chemical reaction or reactions under consideration. For combustion reactions, the convention is to select the chemical reactions that provide complete oxidation of all the fuel components to their highest oxidation level (all carbon atoms to CO2, all sulfur atoms to SO2, etc.). Hence, although other chemical reactions may take place during the operation, generating CO and other products, the excess oxygen is defined and calculated on the basis of complete oxidation reactions. 

When there are stoichiometric amounts of reactants, for example, at the equivalence point of a titration, the equilibrium concentrations of the species in neither half-reaction is known, and an approach similar to the calculation in Example 14.1 is required. 

In a proposed preparation of tricyclic trisaminomethanes (45) (Table 6) tbe reaction of uncatalyzed exchange between etbyl ortboformate HC(OEt)3 and tbe macrocyclic triamine 1,4,7-triazacyclo-nonane (205) was initially unsuccessful. However tbe exchange reaction proceeded smoothly when the more reactive dimethylformamide dimethylacetal HC(OMe)2NMe2 was substituted for HC(OEt)3 to afford (45) in 88% yield <80JA6364> a stoichiometric amount of reactants either neat or in the presence of inert solvent at 120°C were used for performing the reaction. When (45) was treated with either Mel or methyl fluorosulfate, the dication (69) was formed. Compound (45) was reported to be prepared in 84% yield by the reaction of (205) with HC(OEt)3 in THE in the presence ofp-TsOH at 135°C for 60 h <80JA6365>. Most plausibly, such drastic conditions are needed because of the involvement of two unfavorable steps the formation of a strained formamidinium ion (95) as intermediate or the direct displacement of ethanol from the ester aminal intermediate (206) (Scheme 20). 

The stoichiometric amounts of reactants were dependent upon the bromine... 

A microwave-assisted preparation of a series of l-alkyl-3-methylimidazolium halide ILs has been described [17]. The reaction is run in solvent-free conditions with a near-stoichiometric amount of reactants, and the imidazolium halides are obtained in high yield. It is also possible to perform the subsequent metathesis reaction with sodium hexafluorophosphate by means of microwave radiation and then to form the final product in a one-pot reaction [18]. Due to the fact that ILs absorb microwave energy in a very efficient way, they are believed to be well suited for large-scale microwave-assisted synthesis (that is, for reaction mixtures of more than 100 L). 

Let F be any extensive thermodynamic property, and let/= F/N be its intensive analog. Then for any reaction , A/J represents the difference between the value of F for stoichiometric amounts of reactants and that for stoichiometric amounts of products, all in their standard states. 

The amormt of heat emitted or absorbed when a chemical reaction occurs depends on the amounts of reactants that actually react. As we have just seen, we usually specify AH xn in combination with the balanced chemical equation for the reaction. The magnitude of AHrxn is for the stoichiometric amounts of reactants and products for the reaction as xvritten. For example, the balanced equation and for the combustion of propane (the fuel used in LP gas) is ... 

Equivalence point the point in a titration when a stoichiometric amount of reactant has been added. (17.7)... 

Note the conversion from joules to kilojoules in the solutioa Note that the unit on A nG is simply kJ, because we are considering molar stoichiometric amounts of reactants and products. If we want to report Ar G in terms of unit molar amounts of reactants or products, it would be given as —231 kj/mol H2, —461 kj/mol O2, or —231 kj/mol H2O. 

Recall from Section 6.6 that Af/rxn is an extensive property it depends on the quantity of reactants undergoing reaction. Recall also that is usually reported for a reaction involving stoichiometric amounts of reactants. For example, for a reaction... 

Many industrial reactive distillation systems do not use stoichiometric amounts of reactants. An excess (10-20% above the stoichiometric amount) of one of the reactants is fed to the reactive column. There may be kinetic reasons for using an excess in some systems. These include suppressing undesirable side reactions, reducing catalyst requirements, and increasing conversion. However, even in the absence of kinetic reasons, the use of an excess of one of the reactants makes the control problem easier because the fresh feed flowrates of the components do not have to be precisely balanced in the reactive column. Achieving this exact balance may require the use of expensive and high maintenance on-line composition analyzers in some systems. In addition, the variability of product quality may be larger in the neat operation process because there arc fewer manipulated variables available and there is only one column to contain disturbances. 

At I = 0 mol, the system contains stoichiometric amounts of reactants only and at I = 1 mol, it contains stoichiometric amounts of products only. The quantities G°reactants snd G products are the Gibbs energies for stoichiometric amounts of pure, unmixed reactants and of pure, unmixed products in their standard states. 

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