Zumdahl Chemistry Chapter 3: The concept of limiting reactant

- The limiting reactant is the reactant that consumed first. 
- The amount of product is determine by the amount of limiting reactant. 
Suppose you want to make a sandwiches made as follows: 
2 slices bread + 3 slices meat +1 slice cheese → sandwich 
And you have the following quantities of ingredients: 
8 slices bread 9 slices meat 5 slices cheese 
How many sandwiches can you make? What will be left over? To solve this problem, let’s see how many sandwiches we can make with each component.
The answer is three. When you run out of meat, you must stop making sandwiches. The meat is the limiting ingredient . 
Also you can noticed that making three sandwiches requires six pieces of bread and three cheese slices, so you have two slices of bread left and two pieces of cheese left. 
In this example, the ingredient present in the largest number (the meat) was actually the component that limited the number of sandwiches you could make.
Now, lets study the reaction of N₂(g) and H₂(g) to form NH₃(g):
N₂(g) + 3H₂(g) → 2NH₂(g)
Consider the following container of N₂(g) and H₂(g):
The container has 5 molecules of N₂ and 15 molecule of H₂, What will this container look like if the reaction between N₂ and H₂ proceeds to completion? you need to remember that each N₂ requires three H₂ molecules to form two NH₂.
In this case, the mixture of N₂ and H₂ contained just the number of molecules needed to form NH₃ with nothing left over. That is, the ratio of the number of H₂ molecules to N₂ molecules was:
This ratio is exactly matches the numbers in the balanced equation.
N₂(g) + 3H₂(g) → 2NH₂(g)
This type of mixture is called a stoichiometric mixture: contains the relative amounts of reactants that match the numbers in the balanced equation. In this case all reactants will be consumed to form products.
Assume you have the following container have 5 molecules of N₂ and 9 molecules of H₂.
In this case, the H₂ is the limiting reactant: Because when it consumed completely before N₂ the reaction stops (no more H₂) and so it limits the amount of product (NH₂) .
Limiting reactant: the reactant that runs out first and thus limits the amount of product that can form. The amount of product is calculated from limiting reactant.

Determination of limiting reactant using reactant quantities .
Example: Suppose 25.0 kg N₂ and 5.00 kg H₂ are mixed to form NH₃. What the mass of NH₃ formed? 
Balanced chemical equation:
N₂(g) + 3H₂(g) → 2NH₃(g)
to determine whether nitrogen or hydrogen is the limiting reactant and then to determine the amount of ammonia that is formed. We first calculate the moles of reactants present:
Since 1 mole of N₂ reacts with 3 moles of H₂, the number of moles of H₂ that will react exactly with 8.93x10² moles of N₂ is:
So 8.93×10² moles of N₂ required 2.68×10³ moles of H₂, and since only 2.48×10³ moles of H₂ are present , this means that the hydrogen will be consumed before the nitrogen. Thus hydrogen is the limiting reactant in this particular situation.
The second method to determine limiting reactant by comparing mole ratio required by balanced equation with actual mole ratio as following:
Since 2.78 is less than 3 then H₂ must be limiting.

Determination of limiting reactant using quantities of products formed 
In the previous example the supposed quantity of NH₃ formed from each reactant is:
Because a smaller amount of NH₃ produced from H₂ than from the N₂, the amount of H₂ must be limiting. 
The mass of NH₃ (in kg):

Example: Nitrogen gas can be prepared by passing gaseous ammonia over solid copper(II) oxide at high temperatures. The other products of the reaction are solid copper and water vapor. If a sample containing 18.1 g of NH₃ is reacted with 90.4 g of CuO, which is the limiting reactant? How many grams of N₂ will be formed?

-The amount of product calculated from limiting reactant is called theoretical yield. 
-The theoretical yield is the maximum amount of product that can be formed. 
-The actual yield is the experimentally obtain yield 
-Most of time actual yield is less than theoretical yield for many reasons (e.g.: side reactions) . 
-The actual yields given as percentage of theoretical yield:

Example: Methanol (CH₃OH), also called methyl alcohol, is the simplest alcohol. It is used as a fuel in race cars and is a potential replacement for gasoline. Methanol can be manufactured by combining gaseous carbon monoxide and hydrogen. Suppose 68.5 kg CO(g) is reacted with 8.60 kg H₂(g). Calculate the theoretical yield of methanol. If 3.57×10⁴ g CH₃OH is actually produced, what is the percent yield of methanol?