Theoretical and Percentage Yields

Substituting the right-hand side of the second equation in the first equation gives  

Simplifying that and solving, we get the mass of aluminum needed for each kilogram of the fuel mixture. 

So each kilogram of fuel should comprise 186.8 g A1 and 813.2 gNH4C104. Discussion 

The mass of fuel required for a space shuttle engine would clearly be much larger than a kilogram, but this result could easily be scaled up to the needed mass. As for most problems, there are a variety of other approaches that could be used to solve this. The particular strategy that we ve used is based on the general idea that if we have two unknown quantities (like the two masses here), we need to find two separate relationships between them to solve the problem. 

A fuel mixture comprising 600.0 g of NH4CIO4 and 400.0 g of A1 is used in a test of a laboratory scale mock-up of a shuttle engine. When the engine stops burning, some unused fuel remains. What substance is this unburned fuel, and what mass of it should be found  

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Calculate the theoretical and percentage yields of the products of a reaction, given the mass of starting material (Example M.l). 

The report should include balanced equations for the preparation of the chalcone and the Michael/aldol product. You should calculate both the theoretical and percentage yields for each step. Write your complete procedure as you actually performed it. Include the actual results of your melting-point determinations, and compare them to the expected results. 

Calculation of the theoretical yield and percentage yield can be illustrated using hypothetical data for the isopentyl acetate preparation ... 

The theoretical yield in an organic reaction is the amount which would be obtained under ideal conditions if the reaction had proceeded to completion, i.e., if the starting materials were entirely converted into the desired product and there was no loss in isolation and purification. The yield (sometimes called the actual yield) is the amount of pure product which is actually isolated in the experiment. The percentage yield is... 

To calculate percentage yield, one needs to know the theoretical value that can be obtained, based on material balance, and if 100% of the reactant(s) is converted to product. After obtaining the experimental value (actual yield), divide it by the theoretical value, then multiply by 100 to get percentage yield.8... 

STRATEGY Begin by writing the chemical equation for the complete oxidation of octane to carbon dioxide and water. Then calculate the theoretical yield (in grams) of CO, by using the procedure in Toolbox L.l. To avoid rounding errors, do all the numerical work at the end of the calculation. To obtain the percentage yield, divide the actual I mass produced by the theoretical mass of product and multiply by 100%. 

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. 

Actual yields and percentages of theoretical yield shall be determined at the conclusion of each appropriate phase of manufacturing, processing,... 

Hydrogen and Acetate Yields as Percentage of Theoretical Maximum Yield and Maximum Hydrogen Production Rates... 

In section 7.1, you looked at the reaction of hydrogen and nitrogen to produce ammonia. You assumed that all the nitrogen and hydrogen reacted. Under certain conditions of temperature and pressure, this is a reasonable assumption. When ammonia is produced industrially, however, temperature and pressure are manipulated to maximize the speed of production. Under these conditions, the actual yield is much less than the theoretical yield. Examine the next Sample Problem to learn how to calculate percentage yield. 

Often impure reactants are the cause of a percentage yield of less than 100%. Impurities cause the mass data to be incorrect. For example, suppose that you have 1.00 g of sodium chloride and you want to carry out a reaction with it. You think that the sodium chloride may have absorbed some water, so you do not know exactly how much pure sodium chloride you have. If you calculate a theoretical yield for your reaction based on... 

In this section, you have learned how the amount of products formed by experiment relates to the theoretical yield predicted by stoichiometry. You have learned about many factors that affect actual yield, including the nature of the reaction, experimental design and execution, and the purity of the reactants. Usually, when you are performing an experiment in a laboratory, you want to maximize your percentage yield. To do this, you need to be careful not to contaminate your reactants or lose any products. Either might affect your actual yield. 

To circumvent this problem it was found advantageous to use a slight excess of sodium hydroxide in the reaction, i.e., a 5% excess of the required 6 molar equivalents. This ensures that the solution is basic enough to prevent decomposition of the sodium phosphorothioate once it is formed. Yasuda and Lambert reported a percentage yield of 57% of the theoretical. In a series of three preparations on roughly a 1-mol scale where 5% excess base was used, we obtained an average yield of 67%. It was also possible to scale down the reaction to permit synthesis of 35S-labeled sodium phosphorothioate. In a series of four syntheses on a 4-5-millimol scale an average yield of 59% was achieved. 

Using 180 g. of pyridine in place of the i3o g. suggested, and a corresponding increase in the other chemicals except the sodium and alcohol, a yield of 300-326 g. of benzoyl piperidine is obtained. This is a smaller percentage yield (70-75 per cent of the theoretical amount) but the actual yield more than repays for the excess of pyridine used (see also Note 8). 

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