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## Lecture Notes:

### Stoichiometry

• Definition
• The word  Stoichiometry comes from the Greek stoicheion, which means to measure the elements
• A good definition of the term’s meaning in the study of chemistry is the “quantitative study of reactants and products in a chemical reaction” (from Chemistry by Raymond Chang)
• Stoichiometry allows one to calculate how much of a given product a reaction is expected to produce based on how much of the reactants are available
• Given the mass, volume and density, or the number of moles of reactants, one can calculate the mass, volume (if the density is known) or moles of product
• Molar Ratios
•  Calculations using stoichiometry depend on the molar relationships in chemical equations; this is why a properly balanced chemical equation is so important
• A properly balanced chemical equation shows the molar ratios of each of the species present, whether they are reactants or products
• Take the combustion of propane as an example: C3H8 + 5O2 --> 3CO2 + 4H2O
• The ratios found in this equation are as follows:
1 mol propane:5 mol oxygen
(each mole of C3H8 requires five moles of O2 to burn completely)
1 mol propane:3 mol carbon dioxide
(each mole of completely burned C3H8 produces three moles of CO2)
1 mol propane:4 mol water
(each mole of completely burned C3H8 produces four moles of H2O)
5 mol oxygen:3 mol carbon dioxide
(for every five moles of O2 consumed, three moles of CO2 are produced)
5 mol oxygen:4 mol water
(for every five moles of O2 consumed, four moles of H2O are produced)
3 mol carbon dioxide:4 mol water
(for every three moles of CO2 produced, 4 moles of H2O are produced)
• Each of these ratios can be written in reverse order and can be thought of as a fraction or a conversion factor
• The key to using stoichiometry is to calculate using moles and to convert whatever information you are given into moles, whether it be mass or volume and density
• It is easy to calculate the number of moles needed or moles produced if the starting information is given in moles: just find the appropriate molar ratio and multiply by the moles in the starting information (be sure to write the ratio with the quantity you start with on the bottom of the ratio)
• It only requires one additional step to find the mass of a substance that is needed or produced given the number of moles of one of the substances: just convert the answer you find in moles into grams using the molar mass of the substance
• Given the mass of one of the substances you can find the mass of reactants needed or products produced by first converting the given mass into a number of moles, finding the number of moles of the other substance using the proper molar ratio, then converting that number of moles into grams
• To add another layer of complexity, say you are given a volume of a substance and asked to find the volume needed/produced; for this type of problem you always need to know the density of both the substance whose volume is known and the substance whose volume is the answer to the problem
• This type of problem is solved by converting the volume into a mass using the formula m = D·V (make sure your units all match in this equation!); next find the number of moles; next use that number to find the desired number of moles using the proper molar ratio; next use the number of moles to find the mass; finally, use the mass to find the volume using formula V = m/D
• Theoretical Yield
•  The theoretical yield is the amount of a given product one would expect would be produced based solely on the molar ratios and the amount of each starting material
• The starting materials may be present in amounts that do not match the molar ratios in the chemical equation
• When this is the case one of the reactants is a limiting reactant (or limiting reagent) and the other reactant(s) is/are said to be in excess
• An excess reactant is one that is not completely used up when the reaction is complete
• The limiting reactant is the one that will be used up before any of the others
• Because of this, the moles of the limiting reactant are what determine the theoretical yield of a reaction
• To find out which reactant is the limiting reactant you use the molar ratios given in the balanced chemical equation
• Take the combustion of propane again: if you have 10 mol C3H8 and 1 mol O2 you know that oxygen is the limiting reactant because each mole of propane requires five moles of oxygen to burn
• If you are given masses, the problem is not any harder; you just have to convert the mass of each reactant into a number of moles and multiply that number by the proper ratio to find out how many moles of the other reactant are needed
• If you have more moles of O2 than this calculation shows you will need then C3H8 is the limiting reactant
• If you have fewer moles of O2 than this calculation shows you will need then C3H8 is the excess reactant and O2 is the limiting reactant
• To find the theoretical yield of a reaction, use the number of moles of the limiting reactant only in calculating the amount of a given product produced
• Actual Yield
•  The theoretical yield tells you what to expect if everything happens exactly as described in the chemical equation
• The reality is that you usually get somewhat less than the amount predicted
• The reasons for this are many but some of them are:
• other competing reactions occur which create other products
• a reaction may be reversible and it won’t be possible to completely use up the reactants
• sometimes it is difficult to separate the desired product from other substances with which it is mixed
• the products may react with each other to form still other products
• The percent yield is a way to measure how much product can be expected from the use of a given amount of reactant
• The percent yield is calculated simply by dividing the actual yield by the theoretical yield and multiplying by 100%
• The theoretical yield is found by using the molar amount of the limiting reactant and the stoichiometric calculations already discussed
• The actual yield is a measured quantity and will either be given in problems or it will be the amount you need to find
• Given a percentage yield and the amount of each of the reactants it is possible to calculate the actual yield; simply find the limiting reactant, calculate the theoretical yield, then multiply the theoretical yield by the percentage yield
• As an aid to understanding percentage yield you could think of the percentage as representing a conversion factor; if a reaction has a percentage yield of 72% then for every 100 g of theoretical yield the actual yield is 72 g
• The conversion factor would be 72 g actual/100 g theoretical