Eggsamples of Concrete Stoichiometry

Tom Stretton, Head of Science, North Grenville District High School,
P.O. Box 2001, Kemptville, Ont; KOG 1JO

* 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
70 sides of bacon (averaging 60 strips of bacon per side)
300 L of orange juice (your juice glasses hold 300 mL each)
150 loaves of bread (20 slices per loaf, including the ends)

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   --------> 1 complete
                  of bacon                                                         breakfast

we can get the amount of each food from the equation as follows:

Eggs    1 complete breakfast = 2 eggs
                    600 miners                x

x = 1200 eggs

Bacon        1 complete breakfast = 4 strips of bacon
                           600 miners                        x

x = 2400 strips of bacon

Juice       1 complete breakfast = 1 juice
                       600 miners                x

x = 600 glasses of juice

If each juice glass holds 300 mL of juice then we need

           300 mL =              x
          1 glass        600 glasses

x = 180 000 mL of juice    =  180 L of juice.

Toast       1 complete breakfast = 2 pieces of toast
                      600 miners                           x

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
                        of bacon       of juice      of toast               complete
                                                                                        breakfasts

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
                                                             dozen

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
                                                 side

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.
                                      loaf

You start out with 3000 slices of bread.

After breakfast you have:
3000 slices - 1200 slices toasted = 1800 slices of bread.

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.

Eggs     1200 eggs      =   600 miners can have eggs!
           2 eggs/miner

You have enough eggs on hand to feed the 600 miners. Boy are you lucky.

Bacon        1800 strips    =   450 miners get 4 strips of bacon!
                4 strips/miner

You can only give 450 out of the 600 miners bacon!

That mineshaft looks pretty dark doesn't it?

Juice      120 L of juice =  120 000 mL of juice       =   400 miners get
                                       300 mL of juice/miner                 juice!

Only 400 of the 600 miners get their morning's dose of vitamin C. How fast can you run?
Bread         1800 slices = 900 miners get bread!
                 2 slices/miner

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?

Eggs       1200 eggs - (400 miners x 2 eggs ) = 400 eggs left.
                                                        miner

Bacon     1800 strips - (400 miners x 4 strips) = 200 strips left.
                                                           miner

Juice       120 000 mL - (400 miners x 300 mL ) = 0 Juice left!!!
                                                             miner

Bread     1800 slices - (400 miners x 2 slices) = 100 slices
                                                          miner

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
                          volume of a shovelful     1 dm3           bag

You can now find out how many shovelfuls of cement you have on hand!

900 bags of cement * 6 shovelfuls = 5400 shovelfuls
                                       bag

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
                                       1 dm3/shovelful

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 of concrete
  of cement        of premix    of water                     mixture

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 * depth
                                   = 60 m * 1 m * 20 cm
                                   = 60 m * 1 m * 0.20 m
                                   = 12 m3
                                   = 12 000 dm3

The number of loads you have to mix will be

# of loads =    volume of sidewalk        =   12 000 dm3
                     volume of a single load               8 dm3

                 = 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         55 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 loads of mix

x = 6 shovelfuls of cement

Sand/gravel premix       6 sand/gravel = 1 load of mix
                                          x                  6 loads of mix

x = 18 shovelfuls of sand/gravel premix

Water        5 L of water = 1 load of mix
                          x               6 loads of mix

x = 30 L of water

Total Volume      8 dm3 = 1 load of mix
                             x         6 loads 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?

Materials     ON HAND      NEEDED       IN EXCESS
cement          5400 dm3     1500 dm3           3900 dm3
premix     160 000 dm3      9000 dm3     151 000 dm3
water             1000 L          7000  L              -6500 L

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
 1000 L                     x

x = 200 loads

Question #7    How much of each ingredient do we use up?

Cement    1 dm3 = 1 load of concrete
                      x               200 loads

x = 200 dm3 of cement.

Number of bags of cement = volume of cement used
                                             volume of cement/bag
= 200 dm3
    6dm3/bag

= 33.3 bags

% use =     33.3 bags used      x 100
               900 bags available

= 3.7% of the cement gets used up.

Premix     6 dm3 of premix = 1 load of concrete
                        x                         200 loads

x = 1200 dm3 of premix gets used.

% of premix =      1200 dm3 used       x 100 = 0.75%
                      160 000 dm3 available

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    200 loads
# of loads in the mixer            6 loads at a time

= 33.3 times.

Question #9  What percentage of the sidewalk do you complete?

Total volume of concrete mixed  x 100
    Total volume of sidewalk

=     200 loads x 8 dm3/load           x 100
     120 000 dm3 sidewalk volume

   1600 dm3   x 100
    120 000 dm3

= 1.3%

Only 1.3% of the sidewalk gets completed. Are you in trouble?  What solution can you come up with to resolve your dilemma?