Stoichiometry limiting quantities

In the schemes considered to this point, even the complex ones, the products form by a limited succession of steps. In these ordinary reaction sequences the overall process is completed when the products appear from the given quantity of reactants in accord with the stoichiometry of the net reaction. The only exception encountered to this point has been the ozone decomposition reaction presented in Chapter 5, which is a chain reaction. In this chapter we shall consider the special characteristics of elementary reactions that occur in a chain sequence. 

The limiting reactant is what will ran out fust during the reaction, i.e. the reactant whose quantity is less than that defined by the stoichiometry of the reaction. Note that the fluid volume (VL) is generally a variable, i.e. a function of time. If the volume of the reaction mixture is constant, eq.(3.71) becomes... 

Although the concentration of fluorine is the most important quantity in the control of the reaction rate and must be maintained within certain limits, in practice the stoichiometry, the molecular fluorine to substrate H-atom molar ratio, is used to determine the reaction parameters leading to a successful and efficient perfluorination. AF is most successful when sublimable solids are introduced into the hydrocarbon evaporator unit of the aerosol fluorinator as solutions by a syringe pump. This now common procedure emphasizes the individual molecule s isolation as it is fluorinated using AF. No intermolecular reactions between solute and solvent have been observed Choice of the solvent is important as it must not boil at a temperature below the melting point of the solute in order to prevent solid deposition in the tubes feeding the evaporator. It must also fluorinate to a material easily separable from the solid reactant after perfluorination. In most cases it has been found that aliphatic hydrochlorocarbons are excellent choices, but that carbon tetrachloride and chloroform and other radical-scavenging solvents are not (sec ref 6). 

If, however, 2.50 X 103 kilograms of methane is mixed with 3.00 X 103 kilograms of water, the methane will be consumed before the water runs out. The water will be in excess. In this case the quantity of products formed will be determined by the quantity of methane present. Once the methane is consumed, no more products can be formed, even though some water still remains. In this situation, because the amount of methane limits the amount of products that can be formed, it is called the limiting reactant, or limiting reagent. In any stoichiometry problem it is essential to determine which reactant is the limiting one to calculate correctly the amounts of products that will be formed. 

In Chapter 3 we covered the principles of chemical stoichiometry the procedures for calculating quantities of reactants and products involved in a chemical reaction. Recall that in performing these calculations, we first convert all quantities to moles and then use the coefficients of the balanced equation to assemble the appropriate molar ratios. In cases in which reactants are mixed, we must determine which reactant is limiting, since the reactant that is consumed first will limit the amounts of products formed. These same principles apply to reactions that take place in solutions. However, there are two points about solution reactions that need special emphasis. The first is that it is sometimes difficult to tell immediately which reaction will occur when two solutions are mixed. Usually we must think about the various possibilities and then decide what will happen. The first step in this process always should be to write down the species that are actually present in the solution, as we did in Section 4.5. 

Examining the reaction stoichiometry and the initial quantities of HCl and Zn, we note that Zn is the limiting reagent (0.260 mol of HCl is needed to completely react with 0.130 moles ofZn). The enthalpy of reaction may be obtained using tabulated enthalpies of formation ... 

Stoichiometry is the quantitative study of products and reactants in chemical reactions. Stoichiometric calculations are best done by expressing both the known and unknown quantities in terms of moles and then converting to other units if necessary. A limiting reagent is the reactant that is present in the smallest stoichiometric amount. It limits the amount of product that can be formed. The amount of product obtained in a reaction (the actual yield) may be less than the maximum possible amount (the theoretical yield). The ratio of the two is expressed as the percent yield. 

Chemical stoichiometry is the area of study that considers the quantities of materials in chemical formulas and equations. Quite simply, it is chemical arithmetic. The word itself is derived from stoicheion, the Greek word for element and metron, the Greek word for measure. When based on chemical formulas, stoichiometry is used to convert between mass and moles, to calculate the number of atoms, to calculate percent composition, and to interpret the mole ratios expressed in a chemical formula. Most topics in chemical arithmetic depend on the interpretation of balanced chemical equations. Mass/mole conversions, calculation of limiting reagent and percent yield, and various relationships among reactants and products are commonly included in this topic area. 

The actinide with the highest atomic number that has been studied in a solid phase is Es the sesquioxide is its only known oxide phase. The scarcity of this element, and more importantly the intense self-irradiation from the Es-253 isotope which destroys rapidly the oxide matrix, may limit attaining higher oxygen stoichiometries. The structural identification of ES2O3 (Haire and Baybarz 1973) was only accomplished by using very small quantities (10-100 nanograms) and electron diffraction, which provided diffraction patterns in very short times as compared to conventional X-ray techniques. 

When the quantity of the material that can be used is not of concern, classical methods of preparing the oxides are used. Thus, one may use the approach of precipitating an oxalate, and after washing and drying, calcine in air to obtain the oxide. Oxides of specific stoichiometry would be obtained by subsequent experimental treatment (e.g., hydrogen reduction of Am02 to obtain the sesquioxide). However, in many cases microtechniques are necessary for the preparation of actinide oxides. In some situations these techniques may require novel approaches to the preparation and study of the oxides. Such techniques may also limit the depth and accuracy of the study. 

All of the actinides from Th through Cf form dioxides but several of these have not been studied thermodynamically, due in part to their instability and to limited availability (e.g., it is very difficult to prepare multi-milligrams of Cf02 even though such quantities of the isotope are available). Plots of enthalpy of solution for the f elements have been established (Morss 1986) which permit estimating values for the other actinide dioxides. Although binary oxides above the dioxide stoichiometry are known for some of the actinides (Pa, U, Np), little thermodynamic data are available for these oxides. 

Always convert the amounts of reactants into molar quantities, and use the reaction stoichiometry to determine the limiting reagent. 

Whenever you are confronted with a stoichiometry problem you should always determine if you are going to have to solve a limiting reactant problem like this one, or a problem like Example 3.13 that involves a single reactant and one reactant in excess. A good rule of thumb is that when two or more reactant quantities are specified, you should approach the problem as was done here. 

In the past, many variations of the sol-gel process have been developed and used to produce powders with different Ca/P ratios, by altering not only the quantity and composition of precursors but also the processing variables. As the synthesis of HA requires a calcium to phosphorus molar ratio of 1.67 1 in the final product, a number of caldum/phosphorus precursor combinations have been used in the preparation of HA powders. For example, calcium nitrate or different calcium alkoxides and 2-ethyl-hexyl phosphate, triethyl phosphate or orthophos-phoric acid, have been used as the calcium and phosphoras precursors, respectively. The major limitation for appUcation of the sol-gel process was shown to be the very poor solubility of the calcium alkoxides in organic solvents, and the poor reactivity of the phosphorous compounds. The effective control of stoichiometry due to the volatility of the phosphorous compounds used also represented a challenge. 

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