Stoichiometry with limiting reactant

Complex stoichiometry problems should be worked slowly and carefully, one step at a time. When solving a problem that deals with limiting reactants, the idea is to find how many moles of all reactants are actually present and then compare the mole ratios of those actual amounts to the mole ratios required by the balanced equation. That comparison will identify the reactant there is too much of (the excess reactant) and the reactant there is too little of (the limiting reactant). 

Two important concepts in introductory chemislry are stoichiometry and limiting reactants. Let s look at the combustion of acetone as an example with the ideas in mind. 

The problem asks for a yield, so we identify this as a yield problem. In addition, we recognize this as a limiting reactant situation because we are given the masses of both starting materials. First, identify the limiting reactant by working with moles and stoichiometric coefficients then carry out standard stoichiometry calculations to determine the theoretical amount that could form. A table of amounts helps organize these calculations. Calculate the percent yield from the theoretical amount and the actual amount formed. 

A second-order reaction may typically involve one reactant (A -> products, ( -rA) = kAc ) or two reactants ( pa A + vb B - products, ( rA) = kAcAcB). For one reactant, the integrated form for constant density, applicable to a BR or a PFR, is contained in equation 3.4-9, with n = 2. In contrast to a first-order reaction, the half-life of a reactant, f1/2 from equation 3.4-16, is proportional to cA (if there are two reactants, both ty2 and fractional conversion refer to the limiting reactant). For two reactants, the integrated form for constant density, applicable to a BR and a PFR, is given by equation 3.4-13 (see Example 3-5). In this case, the reaction stoichiometry must be taken into account in relating concentrations, or in switching rate or rate constant from one reactant to the other. 

Two concepts are often used to describe the behaviour of a process involving reactions conversion and selectivity. Conversion is defined with respect to a particular reactant, and it describes the extent of the reaction that takes place relative to the amount that could take place. If we consider the limiting reactant, the reactant that would be consumed first, based on the stoichiometry of the reaction, the definition of conversion is straight forward ... 

The correct answer is (A). When you see two masses in a stoichiometry problem, you should be alerted that you are dealing with a limiting reactant problem. This problem will have two stages—the first is to determine the limiting reactant, and the second to determine the mass of the hydrogen gas. Before we do anything, we need to see the balanced equation for the reaction ... 

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. 

One of the tasks closely related to documentation is simple calculations that have to be performed to prepare an experiment. The number of calculations performed, for instance, in the organic synthesis laboratory is quite small, but those calculations required are very important. The calculations associated with conversion of the starting materials to the product are based on the assumption that the reaction will follow simple ideal stoichiometry. In calculating the theoretical and actual yields, it is assumed that all of the starting material is converted to the product. The first step in calculating yields is to determine the limiting reactant. The limiting reactant in a reaction that involves two or more reactants is usually the one present in lowest molar amount based on the stoichiometry of the reaction. This reactant will be consumed first and will limit any additional conversion to product. These calculations, which are simple rules of proportions, are subject to calculation errors due to their multiple dependencies. 

The experimental procedure was as follows a small amount of the catalyst (10 mg diluted with 40 mg of inactive a AI2O3) was used in order to prevent the mass and heat transfer limitations, at least for the low conversions. After heating in a flow of N2 up to 423 K the catalyst was contacted with the reactant gases (between 12 and 22 Ih l, hourly space velocity between 120 000 and 220 000). The analysis was performed at increasing and decreasing temperatures between 423 and 773 K with programmed rates of 2 K/mn. The stoichiometry of the feedstream was defined by the "s ratio" = 2(62) + (NO)/(CO) + (2x + y/2)(CxHy). 

Systematic studies of the influence of the R group and the solvents on the stoichiometry of such reactions as Eq. (8) remain limited, although the Turova group has studied ternary-phase diagrams [M(OR)n, M (OR)n, and solvent] and proposed compositions for many systems. The Ba-Ti system is one of the best characterized and has shown dependence on the R group (0x0 compound with R = /Pr nonoxo compound for R = Et) as well as on the stoichiometry of the reactants ... 

Many reactions of industrial importance are limited by chemical equilibrium, with partial conversion of the limiting reactant and, with the rate of the reverse reaction equal to the rate of the forward reaction. For a specified feed composition and final temperature and pressure, the product composition at chemical equilibrium can be computed by either of two methods (1) chemical equilibrium constants (K-values) computed from the Gibbs energy of reaction combined with material balance equations for a set of independent reactions, or (2) the minimization of the Gibbs energy of the reacting system. The first method is applicable when the stoichiometry can be specified for all reactions being considered. The second method requires only a list of the possible products. 

As for any reaction stoichiometry problem, we should start with a balanced equation. One way to proceed from there is to calculate the amount of one reactant that would combine with the given amount of the second reactant. Comparing that with the amount actually available will reveal the limiting reactant. 

All stoichiometry problems can be approached with this general pattern. In some cases, however, additional calculations may be needed. For example, if we are given (or able to measure) known amounts of two or more reactants, we must determine which of them will be completely consumed (the limiting reactant.) Once again, the mole ratios in the balanced equation hold the key. Another type of calculation that can be considered in a stoichiometry problem is determining the percentage yield of a reaction. In this case, the amount of product determined in the problem... 

In the conventional catalytically stabilized thermal (CSX) combustion approach (Beebe et al., 2000 Carroni and Griffin, 2010 Carroni et al., 2003) shown in Fig. 3.1 A, fractional fuel conversion is achieved in a catalytic honeycomb reactor operated at fuel-lean stoichiometries, while the remaining fuel is combusted in a follow-up gaseous combustion zone, again at fuel-lean stoichiometries. Nonetheless, for diffusionally imbalanced limiting reactants with Lewis numbers (Le) less than unity (such as H2 whereby Lch2 0.3 at fuel-lean stoichiometries in air), CSX is compounded by the... 

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. 

As with other problems with stoichiometry, it is the less abundant reactant that limits the product. Accordingly, we define the extent of reaction p to be the fraction of A groups that have reacted at any point. Since A and B groups... 

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. 

At least for ethylene hydrogenation, catalysis appears to be simpler over oxides than over metals. Even if we were to assume that Eqs. (1) and (2) told the whole story, this would be true. In these terms over oxides the hydrocarbon surface species in the addition of deuterium to ethylene would be limited to C2H4 and C2H4D, whereas over metals a multiplicity of species of the form CzH D and CsHs-jD, would be expected. Adsorption (18) and IR studies (19) reveal that even with ethylene alone, metals are complex. When a metal surface is exposed to ethylene, selfhydrogenation and dimerization occur. These are surface reactions, not catalysis in other words, the extent of these reactions is determined by the amount of surface available as a reactant. The over-all result is that a metal surface exposed to an olefin forms a variety of carbonaceous species of variable stoichiometry. The presence of this variety of relatively inert species confounds attempts to use physical techniques such as IR to char-... 

Detailed information on mechanistic aspects of the ligand oxidation reactions is limited by the fact that well-defined tractable kinetics is only found for systems so very dilute in the metal ion reactants that stoichiometric studies including isolation of reaction products have not yet been practicable. Some selected systems have, however, been studied in some detail, but at significantly higher metal ion concentrations than used for the kinetic studies. It is relevant to recall, however, that under such conditions the rate usually does not follow Eq. (1) and the stoichiometry does not conform to Eq. (2) with a value of n about 6. 

The amount of product is calculated by the same method used earlier for mole-to-gram stoichiometry problems. Start with the moles of the limiting factor because a limiting factor is defined as the reactant that limits or determines the amount of product that can be made. 

As seen in Table 2.1, the overall order of an elementary step and the order or orders with respect to its reactant or reactants are given by the molecularity and stoichiometry and are always integers and constant. For a multistep reaction, in contrast, the reaction order as the exponent of a concentration, or the sum of the exponents of all concentrations, in an empirical power-law rate equation may well be fractional and vary with composition. Such apparent reaction orders are useful for characterization of reactions and as a first step in the search for a mechanism (see Chapter 7). However, no mechanism produces as its rate equation a power law with fractional exponents (except orders of one half or integer multiples of one half in some specific instances, see Sections 5.6, 9.3, 10.3, and 10.4). Within a limited range of conditions in which it was fitted to available experimental results, an empirical rate equation with fractional exponents may provide a good approximation to actual kinetics, but it cannot be relied upon for any extrapolation or in scale-up. In essence, fractional reaction orders are an admission of ignorance. 

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