Stoichiometry – Limiting Reactants

Purpose

• When we run chemical reactions, we do not always add the reactants in the perfect ratio. Consider reacting hydrogen with oxygen to make water: 2 H2 + O2 2 H2O. The perfect ratio is 2 moles of H2 for every 1 mole ofO2. What if we reacted 2 moles of H2 with 2 mole of O2? 2 moles of H2

will still react with 1 mole of O2 leaving 1 mole of O2 unreacted. We call the H2 in this case the limiting reactant, because it limited how much oxygen could react. The oxygen is called the excess reactant, because we have excess oxygen left over after all of the hydrogen reacts.

Method

• In a limiting reactant type stoichiometry problem, you are always given amounts of each reactant.

• If they are not in the same mole ratio as the balanced equation, one of the amounts will limit the amount of product generated and is called the limiting reactant

• To determine this, convert each reactant to product and choose the one that limits the amount of product – in other words, the one that produces the smaller amount of product.

Simple example

• It takes 3 wheels, 2 pedals, and 1 frame to make a tricylcle:

3W + 2P + F T

– If you have 15 wheels and plenty of pedals and frames, how many tricycles could you build?

– If you have 12 pedals and plenty of wheels and frames, how many tricycles could you make?

– If you have 7 frames and plenty of wheels and pedals, how many tricycles can you make?

– If you have just 15 wheels, 12 pedals, and 7 frames, how many tricycles can you make?

Simple example

• It takes 3 wheels, 2 pedals, and 1 frame to make a tricylcle: 3W + 2P + F T– If you have 15 wheels and plenty of pedals and frames, how many tricycles

could you build?

• 15𝑊1 𝑇

3𝑊= 5 𝑡𝑟𝑖𝑐𝑦𝑐𝑙𝑒𝑠

– If you have 12 pedals and plenty of wheels and frames, how many tricycles could you make?

• 12𝑃1 𝑇

2 𝑃= 6 𝑡𝑟𝑖𝑐𝑦𝑐𝑙𝑒𝑠

– If you have 7 frames and plenty of wheels and pedals, how many tricycles can you make?

• 7 𝐹1 𝑇

1 𝐹= 7 𝑡𝑟𝑖𝑐𝑦𝑐𝑙𝑒𝑠

– If you have just 15 wheels, 12 pedals, and 7 frames, how many tricycles can you make?• 5 tricycles – the 15 wheels limited the amount of tricycles that could

be made.

Example Explained

• Notice how we looked at how many tricycles each part could make if they could be completely used up. The wheels could make 5, the pedals could make 6 and the frames 7. Together, they could only make 5. There were not enough wheels to make 6 or 7. The 15 wheels are the limiting reactant and the maximum yield of tricycles is 5 tricycles. There is no way to make 6 or 7 tricycles with only 15 wheels. In this case, the pedals and frames are more than enough for 5 tricycles meaning some will be left over. They are considered the excess reactants.

Chemistry Example

• What is the maximum number of moles of H2O that can be produced from the reaction of 7.3 mol H2 and 3.9 mol O2?

2 H2 + O2 2 H2O

– First, determine the amount of water that the H2 can produce if it fully reacts:

7.3 𝑚𝑜𝑙𝐻2

2 𝑚𝑜𝑙 𝐻2𝑂

2 𝑚𝑜𝑙 𝐻2= 7.3 𝑚𝑜𝑙 𝐻2𝑂

– Second, determine the amount of water that the O2 can produce if it fully reacts:

3.9 𝑚𝑜𝑙 𝑂22 𝑚𝑜𝑙 𝐻2𝑂

1 𝑚𝑜𝑙 𝑂2= 7.8 𝑚𝑜𝑙 𝐻2𝑂

– Together, the maximum that can be produced is 7.3 mol H2O

Misconception Alert

• Some students want to just look at the given numbers and choose the smaller one as the limiting reactant or the one in the balanced equation with the smaller coefficient. Do not do this! Convert each to product and look for the smaller amount of product.

• Some students like to add the two masses of product together to give the maximum amount of product. Do not do this! The smaller of the two results is the maximum amount of product.

• Some students like to call the amount of product the limiting reactant. The limiting reactant is the reactant that limited the amount of product.

Pause and practice

3 Fe(NO3)2 + 2 Na3PO4 Fe3(PO4)2 + 6 NaNO3

• How many moles of iron(II) phosphate can be produced from the reaction of 0.24 moles of iron(II) nitrate and 0.19 moles of sodium phosphate? What is the limiting reactant?

Pause and practice answer

3 Fe(NO3)2 + 2 Na3PO4 Fe3(PO4)2 + 6 NaNO3

• How many moles of iron(II) phosphate can be produced from the reaction of 0.24 moles of iron(II) nitrate and 0.19 moles of sodium phosphate? What is the limiting reactant?

0.24 𝑚𝑜𝑙 𝐹𝑒(𝑁𝑂3)21 𝑚𝑜𝑙𝐹𝑒3 𝑃𝑂4 2

3 𝑚𝑜𝑙 𝐹𝑒(𝑁𝑂3)2= 0.080 𝑚𝑜𝑙 𝐹𝑒3 𝑃𝑂4 2

0.19 𝑚𝑜𝑙 𝑁𝑎3𝑃𝑂41 𝑚𝑜𝑙𝐹𝑒3 𝑃𝑂4 2

2 𝑚𝑜𝑙𝑁𝑎3𝑃𝑂4= 0. 095 𝑚𝑜𝑙 𝐹𝑒3 𝑃𝑂4 2

• The maximum moles of iron(II) phosphate that can be produced is 0.080 mol. The limiting reactant is the 0.24 mol iron(II) nitrate.

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