How to Calculate Theoretical And Practical Yeild

Calculation of % Yield Percent Yield: The percentage yield is the ratio between the actual yield and the theoretical yield multiplied by 100%.  It indicates the percent of theoretical yield that was obtained from the final product in an experiment.  The general mechanism for finding percentage yield is as follows:  1.  Balance the chemical equation 2.  Find the limiting reagent 3.  Find the theoretical yield 4.  Find the actual yield 5.  Find the percentage yield     1.  Balancing The Chemical Equation: The first step in finding theoretical and percentage yield is to balance the relevant chemical equation.  The first step in balancing any equation, is to write out the correct chemical formula: For Example:           CH4 + O2 -->  CO2 + H2O Is the reaction for the combustion of methane (CH4) in excess oxygen (O2) To balance the equation, you need to find the smallest whole number coefficients so that each element is balanced in the reaction. To solve for these coefficients, use a system of equations:  For the current example:                               aCH4 + bO2 -->  cCO2 + dH2O Multiplying each element by the coefficient gives you the following equations: Equation 1: a = c When the equation is balanced, there will be (1 x a) Carbon atoms from methane on the reactants side and (1 x c) Carbon atoms from carbon dioxide on the products side Equation 2: 4a = 2d When the equation is balanced, there will be (4 x a) Hydrogen atoms from methane on the reactants side and (2 x d) hydrogen atoms from water on the products side Equation 2(i): 2a = d Note that Equation 2 can be simplified to this format Equation 3: 2b = 2c + d When the equation is balanced, there will be (2 x b) oxygen atoms from oxygen gas on the reactant side, (2 x c) oxygen atoms from carbon dioxide on the products side and (1 x d) oxygen atoms from water on the product side. Equation 3(i): b = 2a Note that this formula results by substituting Equation 1 and Equation 2(i) into Equation 3 and simplifying  To solve for a, b, c and d: First take the smallest whole number that satisfies Equation 1, which is simply a = c =1 Then, substitute that value into Equation 2(i): 2a = d 2(1) = d d = 2 and Equation 3(i): b = 2a b = 2(1) b = 2 Your coefficients are a = 1, b = 2, c = 1 and d = 2 When writing your balanced equation, the coefficient 1 is assumed and can be omitted, yielding the formula:                    CH4 + 2O2 -->  CO2 + 2H2O 2.  Finding The Limiting Reagent:  This is the reactant which the product yield depends on, as it is not in excess. To determine which reactant is the limiting reagent:-     1(a). Divide the mass (in grams) of the reactant by its molecular weight (g/mol)                                                                   OR      (b). Multiply the amount used (in ml) by its density, then divide by its molar mass                   2.  Multiply the mass (your answer from steps 1(a) or 1(b)) by the number of moles of the reactant used in the reaction. Example:  salicylic acid + acetic anhydride « acetylsalicylic acid (ASA) + acetic acid Salicylic acid:  (0.211 g) / (138.1 g/mol) x 1 = 0.00153 mol Acetic anhydride:  (0.480 mL) x (1.08 g/mL) / (102.1 g/mol) x 1 = 0.00508 mol Therefore, salicylic acid is the limiting reagent, since there are less moles of that than there are of acetic anhydride. Pic source: www.khanacademy.org 3.  Theoretical Yield:

This is how much product will be synthesized in ideal conditions. To determine theoretical yield, multiply the amount of moles of the limiting reagent by the ratio of the limiting reagent and the synthesized product and by the molecular weight of the product.

Example: Theoretical Yield salicylic acid + acetic anhydride « acetylsalicylic acid (ASA) + acetic acid Theoretical yield =     0.00153mol sal. acid x      1 molASA      x   180.2g ASA   .                                           1 mol sal. acid          1 mol ASA                                                            = 0.276 g ASA Therefore, in a perfect experiment, 0.276 g of acetylsalicylic acid will be synthesized

Pic Source: www.premedhq.com

4.  Find the actual yield:

The actual yield you got after the completion of the reaction. 

                

5.  Percent Yield:

  

The percentage yield can be calculated using the mass of the actual product obtained and the theoretical mass of the product calculated using the balanced equation of the reaction.

Percentage Yield =     Mass of Actual Yield       x   100%

                  Mass of Theoretical Yield