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 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 -------->
1 complete we can get the amount of each food from the equation as follows:
x = 1200 eggs
x = 2400 strips of bacon
x = 600 glasses of juice If each juice glass holds 300 mL of juice then we need x = 180 000 mL of juice = 180 L of juice.
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.
You originally had 2400 eggs. After breakfast you have: 2400 eggs - 1200 eggs used up = 1200 eggs still in stock.
You originally had 4200 strips of bacon. After breakfast you have: 4200 strips - 2400 strips = 1800 strips of bacon left.
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.
You have enough eggs on hand to feed the 600 miners. Boy are you lucky.
You can only give 450 out of the 600 miners bacon! That mineshaft looks pretty dark doesn't it?
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?
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 m Your boss has left you, in addition to
the above materials, a concrete mixer, (55 dm 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 dm An average bag of cement is 6 dm Question #1 How many shovelfuls of cement are in each bag? # of shovelfuls = You can now find out how many shovelfuls of cement you have on hand! 900 bags of cement * Question #2 How any shovelfuls of gravel/sand premix do you have on hand? 160 m 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 Question #3 You mix a few more
loads and find that you are averaging about 8 dm Volume of sidewalk = length * width *
depth The number of loads you have to mix will be # of loads = = 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 dm # of loads at one time = 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:
x = 6 shovelfuls of cement
x = 18 shovelfuls of sand/gravel premix
x = 30 L of water
1 load of mix x 6 loads of mix x = 48 dm Since the mixer holds 55 dm Question #6 Do you have enough ingredients to do the complete job? Materials ON
HAND NEEDED
IN EXCESS You Just how much concrete can you mix? 1 cement + 6 premix + 5 L water -----> 1 load of concrete We are looking at H
x = 200 loads Question #7 How much of each ingredient do we use up?
1 load of concrete x 200 loads x = 200 dm Number of bags of cement = = 33.3 bags % use = = 3.7% of the cement gets used up.
x = 1200 dm % of premix =
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?
= 33.3 times. Question #9 What percentage of the sidewalk do you complete?
= = = 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? |