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Dimensional Analysis is a powerful way to solve problems. The power comes from the simplicity of the approach. It avoids memorization and only requires some observation of where you start and where you want to end up. As a CHM151 student, you need become very good at this kind of calculating.

Problem 1:
What goes where the "?" in order to complete this conversion.

How many inches in 2 miles?
In the tutorial, I converted miles to inches by going through two steps. I knew 440 yards was equal to 1/4 miles and I knew 36 inches equaled a yard. You can also do this conversion in one step. You just have to look up how many inches in a mile. In Google or other search engine, search for "inches in a mile". Problem 2: So what would you write in place of the "?" to do the conversion?

1 ÷  1    =  1 x 36
      36               1
 Notice that here the conversion is 1 inch per 1/36 yard because those are equal lengths. Remember when dividing by a fraction, you can invert and multiply. So dividing by 1/36 is the same as multiplying by 36. So when using the calculator, you can multiply 2 x 1760 x 36 to get 126,720 inches. Or you can turn 1/36 into a decimal fraction and divide that into 2 x 1760. Problem 3: What is the decimal fraction for 1/36 rounded to 5 significant figures?
crushed car

Mass to volume: Let's say you want to know the volume of the iron in a car that gets crushed and melted down. There's 3,000. lbs of iron in a car and iron's density is 7.874 g/cc. You calculate the volume as 173,200 cc using iron's density (see spreadsheet layout below).
Problem 4a: What goes in F2 and G2?
Problem 4b: What goes in F3 and G3?
 
A
B
C
D
E
F
G
H
I
J
1
mass of car
Conversion
Conversion
Iron's density is 7.874g/cc
      
2
3000.
 lb
1
 kg
1000
?
?
=
173,200
 cc
3
    
2.205
 lb
kilo
?
?
      
4
                    
Brewery It's a sad fact but the United States is about the last country not to convert completely to metrics. This always adds some extra conversions in chemistry. For example, in a brewery (see below), the recipe calls for a concentration of malt of 2.5 grams malt per 100mL of brew. The bags of malt come in 25 lb bags. The vat holds 1,000. gallons of brew. (equalities: 1 gallon=3785 milliliters, 1 lb=454g)
Note the dimensional analysis below. It begins with the concentration, which is mass per volume. That it multiplied by the volume of the vat. Normally, that is all that is needed to find mass because the volume cancels. However, that only works if volumes have the same units and the mass is the unit you want. Unfortunately, our units for volume don't match (mL vs. gallons). Also grams is not the weight we want. We want the weight in the number of 25 pound bags. See below dimensional analsysis that shows how to solve this.
 
A
B
C
D
E
F
G
H
I
J
K
L
M
1
malt concentration mass/vol
Volume of vat
Conversion
Conversion
Conversion
      
2
2.5
 g
1000.
 gallons
3785
mL
1
lb
1
 bag =
???
 bags
3
100
 mL
 
1
gal
454
g
25
 lb      
4
                          
Problem 5a) According the dimensional analysis setup above, what units cancel out?
Problem 5b) What units remain?
Problem 5c) How many 25-lb bags are needed (round to nearest bag) (L2)?
Let's do another problem that is almost the same but this time you will plug in the conversions. I saw one recipe that makes 9.0 gallons of beer and calls for 3.0 pounds of honey. So the honey concentration is 3.0 lb per 9.0 gallons. However, we are still using the 1,000. gallon vat. In the brewery you don't want to measure the honey in pounds. It's easier if the workers just measure it out in liters. Remember, going from weight to volume is always done by knowing density. The density of honey is 1.36 g/mL.
 
A
B
C
D
E
F
G
H
I
J
K
L
1
honey concentration mass/vol
Volume of vat
lb to grams
Use density to get grams to mL
Conversion
      
2
3.0
 lb
1000.
 gallons
?
?
?
?
0.001
 = ??? liters of honey
3
9.0
 gallons
 
1
?
?
?
milli
      
lb to grams
 Problem 6a) What goes in E2? 6b) What goes in F2? 6c) What goes in F3?  
density
 Problem 7a) What goes in G2? 7b) What goes in H2? 7c) What goes in G3? 7d) What goes in H3?
Answer
 Problem 8) How many liters of honey is needed      
Formula
 Problem 9) What is the spreadsheet formula that goes into K2? (hint: It starts like this: =A2*C2*..."
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