|Eggsamples of Concrete Stoichiometry
Tom Stretton, Head of Science, North
Grenville District High School,
* This article was orginally written for CHEM13 News
The first few days of stoichiometry are
often frustrating for both the students and teacher because quite often the
students do not known how to think about or go about solving a simple problem.
Though they have the required mathematical skills, the concepts elude them,
at least temporarily. Here are some example problems that I have either gone
over step by step on the board, or overhead, or I have given them out in
the form of worksheets. Both questions have been used successfully to overcome
the anxiety of the first day of stoichiometry.
Problem #1 Get Cracking!!
You are the cook at a northern mining town. It is your job to keep the miners fed, which usually means the food had better be good and there had better be lots of it. Remember, mine shafts are deep and tempers can be short!!
Your basic breakfast menu consists of 2 eggs, 4 strips of bacon, a glass of orange juice and 2 pieces of toast. We won't include the coffee because it works as a catalyst!
The equation you work with everyday for breakfast is:
2 eggs + 4 strips + 1 juice + 2 toast -----> 1 complete of bacon breakfast
Here are the supplies in your kitchen larder:
200 dozen eggs
You also have 600 miners to feed. Get cooking.
If you feed all 600 miners the first day what supplies from your stock do you use up?
From the equation below, which just happens to be balanced:
2 eggs + 4 strips
+ 1 juice + 2 toast -------->
we can get the amount of each food from the equation as follows:
Eggs 1 complete
breakfast = 2 eggs
x = 1200 eggs
1 complete breakfast = 4 strips of bacon
x = 2400 strips of bacon
1 complete breakfast = 1 juice
x = 600 glasses of juice
If each juice glass holds 300 mL of juice then we need
300 mL =
x = 180 000 mL of juice = 180 L of juice.
1 complete breakfast = 2 pieces of toast
x = 1200 pieces of toast.
From the above information you can see that in order to feed these ravenous miner type persons you must cook
1200 eggs + 2400 strips + 180 L + 1200
pieces --------> 600
Question #2: How much of each food type do you have left in your larder? The results can be found by using the following calculations.
Eggs 200 dozen
eggs = 200 dozen x 12 eggs = 2400 eggs
You originally had 2400 eggs. After breakfast you have:
2400 eggs - 1200 eggs used up = 1200 eggs still in stock.
Bacon 70 sides of
bacon x 60 strips = 4200 strips of bacon
You originally had 4200 strips of bacon. After breakfast you have:
4200 strips - 2400 strips = 1800 strips of bacon left.
Juice 300 L of juice - 180 L of juice used = 120 L of juice.
Toast 150 loaves
x 20 slices = 3000 slices of bread.
You start out with 3000 slices of bread.
After breakfast you have:
Question #3 On the second day you again need to make breakfast. Because your first day was so successful you party all night long. So you didn't go shopping. Bad move. You will have to make breakfast using the existing stock in your larder.
Your stock on hand from the question above is: 1200 eggs, 1800 strips of bacon, 120 L of juice, 1800 slices of bread
You will continue to make full breakfasts. It's really the only thing you know how to do. Nobody said you were a Cordon Bleu chef, did they! You'll keep this up until you run out of one of the ingredients. Which one of the ingredients do you run out of first?
Let's answer this by seeing how much of each ingredient will go around.
1200 eggs = 600 miners
can have eggs!
You have enough eggs on hand to feed the 600 miners. Boy are you lucky.
1800 strips = 450 miners get 4
strips of bacon!
You can only give 450 out of the 600 miners bacon!
That mineshaft looks pretty dark doesn't it?
120 L of juice = 120 000 mL of juice
= 400 miners get
Only 400 of the 600 miners get their
morning's dose of vitamin C. How fast can you run?
You can give all 600 miners their bread. You suddenly realize that each miner can have 3 pieces of bread. You blurt out that instead of bacon and juice you'll gladly give each miner an extra piece of toast. They just as gladly pick you up, carry you to the shaft and throw you in as a sacrifice to incompetence.
From the information above you can see that you run out of juice first. You are only going to feed 400 miners their full breakfasts. The other 250 are going to give you the shaft.
The thing we have the least of is the orange juice so it is called the limiting reagent. i.e. Once it runs out you are limited in your ability to make full breakfasts.
Once you've feed the 400 miners you stop making full breakfasts.
Question #4 How much stock is still in the larder?
1200 eggs - (400 miners x 2 eggs ) = 400 eggs left.
strips - (400 miners x 4 strips) = 200 strips left.
120 000 mL - (400 miners x 300 mL ) = 0 Juice left!!!
slices - (400 miners x 2 slices) = 100 slices
You used 400 miners in the equation above because they are all you can feed.
Problem #2 How to Cement a Beautiful Relationship!
You have been assigned the task of building a concrete sidewalk by your boss. The boss has left you at a secluded, out of the way spot with 900 bags of cement, 160 m3 of premixed gravel and sand, and 1000 L of water. You've got to mix and pour enough concrete to fill a sidewalk that is 1 m wide x 60 m long by 20 cm thick. (The carpenters have already been there and laid the forms.)
Your boss has left you, in addition to the above materials, a concrete mixer, (55 dm3 capacity), and a wheelbarrow that can hold 60 L and a shovel. Lucky you!
The boss tells you to mix 1 shovelful of cement with 6 shovelfuls of the gravel/sand premix, then add enough water to just mix it into a smooth mass!
The equation is: 1 cement + 6 premix + water ----> 1 load of mixed concrete
After a little experimenting you discover that an average shovelful of cement is 1 dm3. The sand/gravel premix is about the same. Okay, I know, it's a small shovel.
An average bag of cement is 6 dm3.
Question #1 How many shovelfuls of cement are in each bag?
# of shovelfuls = volume of cement
bag = 6 dm3 = 6 shovelfuls
You can now find out how many shovelfuls of cement you have on hand!
900 bags of cement * 6 shovelfuls
= 5400 shovelfuls
Question #2 How any shovelfuls of gravel/sand premix do you have on hand?
160 m3 of premix = 160 000
dm3 of premix = 160 000 shovelfuls
Again after a little experimentation you discover that you need 5 L of water for each mix so that the concrete has the right consistency.
So the equation becomes:
1 shovelful + 6 shovelfuls
+ 5 L ----> 1 load
Question #3 You mix a few more loads and find that you are averaging about 8 dm3 of concrete mixture per load, if you use the 1:6 cement:premix ratio the boss gave you. How many loads will you have to mix in order to fill the sidewalk?
Volume of sidewalk = length * width *
The number of loads you have to mix will be
# of loads = volume
of sidewalk = 12
= 1500 loads.
Lucky for you the mixer is a super duper mixmaster which can hold up to 55 L of mix at a time.
Question #4 How many loads of 8 dm3 can you do at one time?
# of loads at one time =
1 load = 8 dm3
x = 6.875 loads.
Since we can't overfill the cement mixer, we will only make up 6 full loads at any one time.
Question #5 If we use the boss's mix recipe and do 6 loads at a time, how much of each ingredient do we need?
1 cement + 6 premix + 5 L water ---> 1 load of concrete
To do six loads we need:
Cement 1 cement
= 1 load of mix
x = 6 shovelfuls of cement
6 sand/gravel = 1 load of mix
x = 18 shovelfuls of sand/gravel premix
5 L of water = 1 load of mix
x = 30 L of water
8 dm3 = 1 load of mix
x = 48 dm3 of mix
Since the mixer holds 55 dm3
you are okay.
Question #6 Do you have enough ingredients to do the complete job?
You do not have enough water to complete the job. When you run out of water you must stop, so it is the limiting reagent. It limits you in your ability to complete the mixing of any further cement and premix.
Just how much concrete can you mix?
1 cement + 6 premix + 5 L water -----> 1 load of concrete
We are looking at H2O as the limiting reagent and we are looking at how many loads of concrete we can mix therefore ignore the other two components in the equation.
5 L water = 1 load of concrete
x = 200 loads
Question #7 How much of each ingredient do we use up?
Cement 1 dm3
= 1 load of concrete
x = 200 dm3 of cement.
Number of bags of cement = volume of
= 33.3 bags
% use = 33.3
bags used x 100
= 3.7% of the cement gets used up.
6 dm3 of premix = 1 load of concrete
x = 1200 dm3 of premix gets used.
% of premix =
1200 dm3 used x
100 = 0.75%
Water All the water gets used up therefore % usage is 100%
Question #8 If you fill the mixer each time with 6 full loads and let it mix, how many times do you have to walk back and forth from the mixer to the sidewalk forms?
# of loads that can be made =
= 33.3 times.
Question #9 What percentage of the sidewalk do you complete?
Total volume of concrete mixed
= 200 loads
x 8 dm3/load
= 1600 dm3
Only 1.3% of the sidewalk gets completed. Are you in trouble? What solution can you come up with to resolve your dilemma?