Name ___________________ Block ________ Date _________
Dominoes for Unit Factor
Analysis
Chemcatalyst:
Please show all work and all units when answering the following questions.
How many eggs are in 10 dozen?
My dog weighs 50lbs. How many kilograms is that if one kilogram is 2.2 pounds?
How many minutes in a year (RENT fans are not allowed to cheat)?
New information:
Throughout this year, I will try to avoid as much math as possible. While I understand that chemistry is a math-based subject, I also understand that many of you struggle with math. I do not want that struggle to get in the way of your chemistry understanding and enjoyment. This is one case where the math cannot be avoided. Unit conversion (AKA dimensional analysis, factor conversions, my worst nightmare…) is the formal way to show the kind of math you just completed in the chemcatalyst. We will begin by using dominoes to give you the idea of what you are doing.
Procedure 1:
Play dominoes for about 10 minutes. Oh, you want the rules too? Greedy, aren’t we? I am sure you may have other rules, but these will work for our needs.
a. Turn all dominoes face down.
b. Each player picks 7 dominoes and keeps them so only he/she can see them.
c. The player with the lowest double plays first with that domino.
d. Each player in turn will build his/her own train by adding a domino that matches the number on the previous domino. (See picture) In the picture, one player may play a 1, while the other player may play a 3.
e. If you cannot play a piece, pick one, then play or pass. If you pass, anyone may play on your train.
f. Finish when one player uses all his/her dominoes.
Draw one of the trains in the space below.
Procedure 2:
Unit factor math is very much like dominoes, except that the units form trains, not the numbers.
a. Obtain a set of Unit Factor cards.
b. Play a game of dominoes with the unit factor cards.
c. Remember to link the words, not the numbers.
d. Draw one train in the space below.
New Information:
To complete a unit factor problem:
a. always start with a given number (and its unit).
b. Then form a train of unit factors that will lead you to the unit you are looking for in the problem.
1. A unit conversion is written as a fraction. For example:
2.2 pound or 1 kg .
1 kg 2.2 pound
c. To be correct, pick the unit factor that causes the units to cancel when multiplied.
So, to answer a question from the chem. catalyst:
22.7 kg
50 lbs x
1kg . =
2.2 lbs
Notice that every number has a unit and the answer is in a box.
d. Redraw your train above such that all units would cancel when multiplied.
Now rewrite your other two chemcatalyst problems using this system. Notice that #3 will require many unit factors.
10
dozen eggs x _________________ =
1 year x ____________ x
___________ x _________ = min.
Hint: For long trains like this, multiply all the top numbers first, then divide each number on the bottom separately. For Example,
1 year x 365 days x 24 hours x 60 min ÷ 1year ÷ 1day ÷ 1 hour = min.
And remember that you do not need to multiply or divide by one. The answer will not change.
Use the unit factor cards to solve the following problems.
Start with the given number and make a train with the cards to the unit requested.
1. How many feet are in 86cm?
2. How many meters are in 3.5 miles?
3. How many grams of sodium chloride (table salt) are in 3 moles?
4. How many moles of Ca(OH)2 are in 5 grams?
5. What is the volume of 28 grams of water?
Practice problems:
Solve each of the following problems using unit factor math (make trains if necessary). I expect that you already know all unit factors for the metric system (1000mm = 1m, 1kg = 1000g, etc). I will supply unit factors for English to metric conversions (1km = 1.6 mi). You may need to make new unit factor cards for some units.
State the following measured quantities in the units indicated:
a. 5.2cm of magnesium ribbon in millimeters
b. 0.049kg of sulfur in grams
c. 0.0025g of vitamin A in micrograms (1g = 1,000,000ug)
d. 1.60ml of ethanol in L
e. 0.020kg of tin in milligrams
f. 150mg of aspirin in grams
g. 2500ml of hydrochloric acid in liters
h. 0.5g of sodium in kilograms
The following will require a train of unit factors:
a. 10miles in feet (1720 yards = 1 mi, 3feet = 1 yard)
b. 2 yards in mm (1in = 2.54cm, 12in = 1foot)
c. 1 millenium in seconds
d. 5g of carbon in atoms (12g C = 1 mole, 1 mole = 6.022x1023 atoms)
