Calculating Theoretical Yield and Percent Yield Adipic acid, H2C6H8O4, used to produce nylon, is made commercially by a reaction between cyclohexane (C6H12) and O2: (a) Assume that you carry out this reaction with 25.0 g of cyclohexane and that cyclohexane is the limiting reactant. What is the theoretical yield of adipic acid? (b) If you obtain 33.5 g of adipic acid, what is the percent yield for the reaction? Imagine you are working on ways to improve the process by which iron ore containing Fe203 is converted into iron: (a) If you start with 150 g of Fe2O3 as the limiting reactant, what is the theoretical yield of Fe?
Answer : Step 1 We are given a chemical equation and the quantity of the limiting reactant (25.0 g of C6H12). We are asked to calculate the theoretical yield of a product H2C6H8O4 and the percent yield if only 33.5 g of product is obtained. (a) The theoretical yield, which is the calculated quantity of adipic acid formed, can be calculated using the sequence of conversions. (b) The percent yield is calculated by using the given actual yield (33.5 g) with the theoretical yield. Step 2 (a) The theoretical yield is Grams H2C6H8O4 = (125.0 g C6H122)*( 1 mol C6H12)( 84.0 g C6H12 )* ( 2 mol H2C6H8O4)( 2 mol C6H12 )* (146.0 g H2C6H8O4)( 1 mol H2C6H8O4 )=( 43.5 g H2C6H8O4). (b) Percent yield = actual yield theoretical yield * 100% = 33.5 g 43.5 g * 100% = 77.0% . Step 3 From the balanced equation we know that each mole of cyclohexane gives 1 mol adipic acid. We have 25>84 25>75 = 0.3 mol hexane, so we expect 0.3 mol adipic acid, which equals about 0.3 * 150 = 45 g, about the same magnitude as the 43.5 g obtained in the more detailed calculation given previously. In addition, our answer has the appropriate units and number of significant figures. In (b) the answer is less than 100%, as it must be from the definition of percent yield.