Stoichiometry

• Let’s pretend we are going to a party and we want to bring marshmallow treats. Here is our recipe.
• 3 T of butter
• 40 marshmallows
• 6 c of rice cereal
• This will make 24 treats
• We realize that we only have 4.5 cups of cereal. What do we do?
• 4.5 c cereal x 40 marshmallows/6 c cereal
• Would this be enough to feed the 20 people that are coming?
• 4.5 c cereal x 24 treats/6 c cereal = 18 treats
• We use this same process to determine how much of the products we need in chemistry to make a certain amount of reactant.
• For example, in the equation P₄ + 5O₂ —> 2P₂O₅, we know that for every 1 molecule of of P₄ and 5 molecules of O_2, we are going to end up with 2 molecules of P₂O₅. 
• This gives us various relationships in our equation:
• 1 mol P₄ reacts to form 2 mol P₂O₅ (1:2 ratio)
• 1 mol P₄ reacts with 5 mol O₂ (1:5 ratio) and
• 5 mol O₂ reacts to form 2 mol P₂O₅ (5:2 ratio)
• Even if we were to cut the original quantities in half or double them, we would still have the same ratio. These are known as mole ratios.
• We can use these ratios to do mole-to-mole conversions. This would be to determine how much of a product we would get if we added a certain amount of reactants.
• If a chemical engineer wanted to produce 25.0 mol of diphosphorus pentoxide, how many moles of phosphors would they need?
• 25.0 mol P₂O₅ x 1 mol P₄/2 mol P₂O₅ = 12.5 mol P₄
• What is the amount of oxygen needed?
• 12.5 mol P₄ x 5 mol O₂/1 mol P₄ = 62.5 mol O₂
• If 25.0 mol of diphosphorus pentoxide reacts with water to form phosphoric acid, how many moles of water is required? P₂O₅ + 3H₂O —> 2H₃PO₄ 
• 25.00 mol P₂O₅ x 3 mol H₂O/ 1 mol P₂O₅ = 75.0 mol H₂O
• Why must the conversions be done in moles? Because the recipe/balanced equation is based on moles, not mass. 
• If we wanted to know the moles of diphosphorus pentoxide that would result from the burning of 1.55 kg of phosphorus from the previous equation, we first have to convert mass to moles.
• 1550 g P₄ x 1 mol/123.9 g P₄ = 12.5 mol P₄
• Then we can use our ratio to determine the diphosphorus pentoxide that would result:
• 12.5 mol P₄ x 2 mol P₂O₅/1 mol p ₄ = 25.0 mol P₂O₅
• Example: How many moles of phosphoric acid can be formed from 3550 g of diphosphorus pentoxide? P₂O₅ + 3H₂O —> 2H₃PO₄
• First convert 3550 g P₂O₅ to moles.
• 3550 g P₂O₅ x 1 mol P₂O₅/141.9 g P₂O₅ = 25.0 mol P₂O₅ 
• Then use ratio to figure out the rest
• 25.0 mol P₂O₅ x 2 mol H₃PO₄/1 mol P₂O₅ = 50.0 mol H₃PO₄
• What if we want need to figure out mass given mass? 
• What mass of water will react with 3500 g of diphosphorus pentoxide? P₂O₅ + 3H₂O —> 2H₃PO₄
• 3550 g P₂O₅ x 1 mol P₂O₅/141.9 g P₂O₅ = 25.0 mol P₂O₅ 
• 25.0 mol P₂O₅ x 3 mol H₂O/1 mol P₂O₅ = 75.0 mol H₂O
• 75.0 mol H₂O x 18.02 g H₂O/1 mol H₂O = 1350 g H₂O