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• 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
  
  
  

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  • 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

 

Finding Molar Ratios

Balance each of the following chemical equations. Write down all the molar ratios that are in each equation. First, write the ratios for the first reactant and each of the other substance. Second, write the ratios for the second substance with each of the others, except the first one since you have already written it. Work your way through each equation in this manner.

1.     H₂ +     O₂ -->     H₂O
2.     K +     H₂O -->     KOH +     H₂
3.     P₄O₁₀ +     H₂O -->     H₃PO₄

Calculating Moles Needed/Produced

The following equations are already balanced. You are given an amount in moles for one of the substances in the equation. Find out how many moles of each of the other substances you would need (reactants) or would be produced (products).

4. Mg(OH)₂ --> MgO + H₂O     1.5 mol MgO
5. Pb(NO₃)₂ + 2NaCl --> PbCl₂ + 2NaNO₃     3.56 mol NaCl
6. Cu + 2AgNO₃ --> 2Ag + Cu(NO₃)₂     1.78 mol Ag
7. 2C + O₂ --> 2CO     1 mol O₂
8. 2KNO₃ --> 2KNO₂ + O₂     1.3 x 10³ mol KNO₃

 

Calculating Mass Needed/Produced

The following equations are already balanced. You are given an amount in grams for one of the substances in the equation. Find out how the mass of each of the other substances you would need or would be produced. You will (obviously) need to find the molar masses of each of the reactants and products.

9. 2C + O₂ --> 2CO     14 g C
10. 2KNO₃ --> 2KNO₂ + O₂     29.8 g KNO₂
11. 3Fe + 4H₂O --> Fe₃O₄ + 4H₂     167.54 g Fe

12. Titanium (IV) oxide (TiO₂) is used as a pigment in paints and as a whitening and coating agent for paper. It can be made by reacting O₂ with TiCl₄:
    TiCl₄ + O₂ --> TiO₂ + 2Cl₂
    If 4.5 mol of TiCl₄ react with 3.5 mol O₂, identify both the limiting and the excess reactants. How many moles of the excess reactant would remain if all of the limiting reactant is used up? How many moles of each product will be formed if the reaction goes to completion?

68. Given 10 mol C, how many moles of O₂ are required to completely react with all of the C?

                1 mol O2
    10 mol C × ---------- = 5 mol O2
                2 mol C

69. Given 5.4 mol O₂ how many moles of O₃ can be produced?
70. How much ammonia can be manufactured from 1,000 mol N₂ assuming you have enough H₂?

71. How many moles of HCl do you need to completely react with 7.7 × 10^-2 mol of zinc to make ZnCl₂ and H₂?
72. How many moles of fluorine gas are needed to make 2.5 mol of SF₆ assuming no shortage of sulfur?
73. You have 4.6 mol NH₃. How many moles of O₂ do you need to completely react with all of the ammonia?