4.2: Limiting & Excess Reagents

 

Learning Objectives

• Define stoichiometric proportion, limiting reagents, excess reagents, and theoretical yield
• Calculate quantities of products formed or reactants consumed based on complete consumption of limiting reagents (on both mole and mass basis) 
• Predict quantities of excess reagents left over after complete consumption of limiting reagents

Stoichiometric Proportions, Limiting and Excess Reagents

A balanced chemical equation describe the ratios at which products and reactants are respectively produced and consumed. That said, the coefficients of the balanced equation have nothing to do with the actual quantity of reactants you start with, as you can mix any amount you choose, but clearly the maximum yield (theoretical yield) must be limited by the reactant that gets consumed up first, the limiting reagent. The reagent that remains is called the excess reagent. This can be easily understood by the analogy of making bicycles, where each bike requires 2 tires and one frame. The "equation" becomes:

1 frames + 2 tires --> 1 bike

As you can see, the "balanced equation" simply tells us the ratio of number of frames and tires to the number of bikes made. So let's look at a few case scenarios: 

A) How many bikes can we theoretically make with 10 frames and 16 tires? Which is the "limiting reagent" and which is the "excess reagent"? 

With 10 frames, we can make 10 bikes. However, we also need tires to make a bike. With 16 tires, we can make 8 bikes (2 tires per bike). So, in reality we can only make 8 bikes, not 10, because the "limiting reagent" is the tires and the "excess" reagent is the frames. We have 2 frames left over. The theoretical yield of bikes will be 8 bikes (based on the limiting reagent) 

 

B) How many bikes can we theoretically make with 10 frames and 20 tires? Which is the "limiting reagent" and which is the "excess reagent"?

10 frames makes 10 bikes. 20 tires also make 10 bikes. So, we have a stoichiometric proportion and there is nothing left over. 

 

C) How many bikes can we theoretically make with 10 frames and 30 tires? Which is the "limiting reagent" and which is the "excess reagent"?

10 frames make 10 bikes. 30 tires make 15 bikes. However, we are not making 15 bikes because we ran out of frames after 10 bikes. So we used only 20 tires, with 10 tires left over. So, this time, the limiting reagent is the frames, and the excess reagent is the tires. The theoretical yield of bikes is 10 (based on the limiting reagent). 

With that being said, let's recap with a few points: 

Stoichiometric Proportions: Reactants are mixed in the ratios defined by their stoichiometric coefficients. If a reaction proceeds to completion, everything is consumed.

NonStoichiometric Proportions: Reactants are mixed in ratios that are different than the stoichiometric coefficients. One species runs out first (Limiting Reagent), while another is not completely consumed (Excess Reagent).

Theoretical Yield: the maximum possible yield based on the complete consumption of the limiting reagent

Are the limiting reagents always completely consumed? No, only if the reaction goes to completion. There can be many different reasons why the limiting reagent is not completely consumed, and these will be covered in detail in later chapters of this text. The theoretical yield is the maximum amount of product that would be produced through the complete consumption of the limiting reagent.

Excess Reagent: The quantity (mole or mass) left over after the complete consumption of the limiting reagent.

Quantity Excess = Initial Quantity - Consumed Quantity.

Where quantity can be moles or mass.

Limiting Reagent Problem Strategies:

1. Identify moles of all reactants present.
   If given mass, divide by formula weight to convert moles (this is the mass to mole step from the section 4.1.
2. Divide moles of each reactant by it's stoichiometric coefficient.
   This is the denominator of the mole-to-mole step in section 4.1.
3. Smallest number indicates limiting reagent.
4. Multiply by stoichiometric coefficient of species you are solving for, and answer the question .
   This is the numerator of the mole-to-mole step in section 4.1. If you are after moles, you are finished, if you are after mass, you need to use the molar mass of product to convert moles product to grams mass product, which is the mass-to-mole step in section 4.1.

Limiting Reagent Problem

Silver tarnishes in the presence of hydrogen sulfide and oxygen due to the following reaction

4Ag + 2H₂S + O₂ ----> 2Ag₂S + 2H₂O

What is the Limiting Reagent and Theoretical Yield of Ag₂S if 2.4 g Ag, 0.48 g H₂S and 0.16g O₂ react?

6:07 minute YouTube video showing shortcut method for determining limiting reagent and theoretical yield. [corrigenda: after dividing moles Ag by stoichiometric coef. the value is 0.00556, not 0.0556, but this this did not effect the solution as both are more than the value for oxygen of 0.00500, so oxygen is still the limiting reagent). 

What quantities of excess reagents are left over after the complete consumption of the limiting reagent if 2.4 g Ag, 0.48 g H₂S and 0.16g O₂ react?

4:36 minute YouTube determining the excess reagents after the complete consumption of the limiting reagent.

To Calculate moles of Excess reagent you subtract the amount consumed by the complete consumption of the limiting reagent from the initial quantity of the excess reagent.

 

Click the following link for more practice on limiting reagents. You will have feedback and hints to help guide you. 

http://chemcollective.org/activities/tutorials/stoich/limiting-reagents

 

Do the Following Worksheet

Limiting Reagent Worksheet
Limiting Reagent Worksheet Key