Theoretical yield, limiting

Theoretical yield is 100%, but usually limited by cocrystallisation of impurities. 

Under these conditions, the theoretical yield of product is the amount produced if the limiting reactant is completely consumed. In the case just cited, the theoretical yield of Sbl3 is 2.00 mol, the amount formed from the limiting reactant, I2. 

Often you will be given the amounts of two different reactants and asked to determine which is the limiting reactant, to calculate the theoretical yield of the product and to find how much of the excess reactant is unused. To do so, it helps to follow a systematic, four-step procedure. 

Choose the smaller of the two amounts calculated in (1) and (2). This is the theoretical yield of product the reactant that produces the smaller amount is the limiting reactant. The other reactant is in excess only part of it is consumed. 

To illustrate how this procedure works, suppose you want to make grilled cheese sandwiches from 6 slices of cheese and 18 pieces of bread. The available cheese is enough for six grilled cheese sandwiches the bread is enough for 9. Clearly, the cheese is the limiting reactant there is an excess of bread. The theoretical yield is 6 sandwiches. Six grilled cheese sandwiches use up 12 slices of bread. Since there are 18 pieces available, 6 pieces of bread are left over. 

Determine the limiting reactant and the theoretical yield when... 

Because 1.20 mol is the smaller amount of product, that is the theoretical yield of Sbl3. This amount of Sbl3 is produced by the antimony, so Sb is the limiting reactant. 

The reactant that yields the smaller amount (3.17 g) of Sbl3 is I2. Hence I2 is the limiting reactant. The smaller amount, 3.17 g of Sbl3, is the theoretical yield. 

The theoretical yield is the maximum amount of product that can be obtained. In calculating the theoretical yield, it is assumed that the limiting reactant is 100% converted to product. In the real world, that is unlikely to happen. Some of the limiting reactant may be consumed in competing reactions. Some of the product may be lost in separating it from the reaction mixture. For these and other reasons, the experimental yield is ordinarily less than the theoretical yield. Put another way, the percent yield is expected to be less than 100% ... 

One way of overcoming these problems is by kinetic resolution of racemic epoxides. Jacobsen has been very successful in applying chiral Co-salen catalysts, such as 21, in the kinetic resolution of terminal epoxides (Scheme 9.18) [83]. One enantiomer of the epoxide is converted into the corresponding diol, whereas the other enantiomer can be recovered intact, usually with excellent ee. The strategy works for a variety of epoxides, including vinylepoxides. The major limitation of this strategy is that the maximum theoretical yield is 50%. 

The I9e electron-reservoir complexes Fe Cp(arene) can give an electron to a large number of substrates and several such cases have been used for activation. After ET, the [FenCp(arene)]+ cation left has 18 valence electrons and thus cannot react in a radical-type way in the cage as was the case for 20e Fe°(arene)2 species. Thus the 19e Fe Cp(arene) complexes react with the organic halide RX to give the coupled product and the [FeCp(arene)]+ cation. Only half of the starting complex is used e.g., the theoretical yield is limited to 50% [48] (Scheme VI) contrary to the reaction with Fe°(arene)2 above. 

The limiting reactant is the reactant that will be completely used up. All other reactants are in excess. Because the limiting reactant is the one that limits the amounts of products that can be formed, the theoretical yield is calculated from the amount of the limiting reactant. 

STRATEGY First, the limiting reactant must be identified (Toolbox M.l). This limiting reactant determines the theoretical yield of the reaction, and so we use it to calculate the theoretical amount of product by Method 2 in Toolbox L.l. The percentage yield is the ratio of the mass produced to the theoretical mass times 100. Molar masses are j calculated using the information in the periodic table inside the front cover of this i book. 

Enzymatic KRs, as all resolutions, are limited to a maximum theoretical yield of 50%. Strategies to increase the yield are therefore of great importance. The opposite of a resolution, that is, the racemization of a chiral compound, can sometimes be highly desirable and applicable in enantioselective synthesis. By combining a... 

Despite its widespread application [31,32], the kinetic resolution has two major drawbacks (i) the maximum theoretical yield is 50% owing to the consumption of only one enantiomer, (ii) the separation of the product and the remaining starting material may be laborious. The separation is usually carried out by chromatography, which is inefficient on a large scale, and several alternative methods have been developed (Figure 6.2). For example, when a cyclic anhydride is the acyl donor in an esterification reaction, the water-soluble monoester monoacid is separable by extraction with an aqueous alkaline solution [33,34]. Also, fiuorous phase separation techniques have been combined with enzymatic kinetic resolutions [35]. To overcome the 50% yield limitation, one of the enantiomers may, in some cases, be racemized and resubmitted to the resolution procedure. 

A reaction that is carried out under limiting reactant conditions nevertheless has a yield that generally will be less than 100%. The reasons why reactions yield less than the theoretical amounts, given in Section 4-1. apply to all reactions. When a reaction operates under limiting reactant conditions, we calculate the theoretical yield assuming that the limiting reactant will be completely consumed. We then determine the percent yield as described in Section 4A. Example shows how to do this. 

The problem asks for a percent yield, so we need to compare the actual yield and the theoretical yield. Information is provided about amounts of both starting materials, so this is a limiting reactant situation. 

Use fJ = luf V to calculate amounts of each ion present in the two solutions before mixing, and determine which is limiting. Then solve for the theoretical yield, and apply Equation to calculate percent yield. 

Calculate the theoretical yield of Fe, based on the limiting reactant. 

The mass of Fe that should be produced from the limiting reactant, Fe203, is the theoretical yield. 

The limiting reactant is P4, and 111 gPCl3 should be produced. This is the theoretical yield. The actual yield is 104gPCl3. Thus, the percent yield of the reaction is... 

Seed yield in cucurbits is seldom investigated because commercial production of the carbohydrate-rich fruit is the major concern. Wide variations in sizes and weights of seeds, numbers of seeds per fruit and even numbers of fruits per plant seems the rule, particularly in wild plants and even within one species (7). Estimations from limited observations of C. foetidissima, Z. digitata and C. palmata growing wild in desert areas indicate theoretical yields Trom ot) to 3,000 lb of seeds per acre ( ,9h C. foetidissima cultivated in northwestern Texas yields approximately 700 to 2,000 lb of seeds per acre (10). C. pepo (pumpkin) produces up to 1,200 lb per acre and an improved seed-coatless line yields from 1,200 to 1,400 lb of seed per acre ( , 11). These yields are comparable to yields of oilseeds of commerce. 

In the problem above, the amount of product calculated based upon the limiting reactant concept is the maximum amount of product that will form from the specified amounts of reactants. This maximum amount of product is the theoretical yield. However, rarely is the amount that is actually formed (the actual yield) the same as the theoretical yield. Normally it is less. There are many reasons for this, but the principal one is that most reactions do not go to completion they establish an equilibrium system (see Chapter 14 for a discussion on chemical equilibrium). For whatever reason, not as much product as expected is formed. We can judge the efficiency of the reaction by calculating the percent yield. The percent yield (% yield) is the actual yield divided by the theoretical yield and the resultant multiplied by 100 in order to generate a percentage ... 

Now we can find the maximum number of moles of IF5 that can be produced (theoretical yield). We will begin with our limiting reactant rather than using the 45.2 g of IF5 given (actual yield). Remember, the limiting reagent is our key, and we don t want to lose our key once we have found it. 

In this problem, the actual yield is the amount of product found by the scientist (45.2 g IF5) therefore, we need the theoretical yield to finish the problem. Since our actual yield has the units g IF5, our theoretical yield must have identical units. To determine the grams of IF5 from the moles of limiting reactant, we need the molar mass of IF5 [126.9 g I/mol 1 + 5 (19.00 g F/mol F) = 221.9 g nymol]. 

Avogadro s number, 6.022 x 1023 4. molar mass 5. 28 g/mol 6. Limiting reagent (reactant) 7. theoretical yield... 

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