Transcript ppt

The factor label method
• A way to solve math problems in chemistry
• Used to convert
km to miles, m to km, mol to g, g to mol, etc.
• To use this we need: 1) desired quantity,
2)
given quantity, 3) conversion factors
• Conversion factors are valid relationships or
equities expressed as a fraction
E.g. for 1 km=0.6 miles the conversion factor is
1 km
0.6 miles
or
0.6 miles
1 km
Q. write conversion factors for 1 foot =12 inches
Q. what conversion factors can you think of that
involve meters?
Conversion factors
Conversion factors for 1 ft = 12 in
1 foot
12 inches
or
12 inches
1 foot
There are almost an infinite number of
conversion factors that include meters:
1000 m
1m
1m
,
,
1 km
100 cm 1000 mm
1m
1m
0.9144 yards
,
,
3.28 feet 39.37inches
1m
Conversion factors
• We have looked at conversion factors that are
always true. There are conversion factors
that are only true for specific questions
• E.g. A recipe calls for 2 eggs, 1 cup of flour
and 0.5 cups of sugar
• We can use these conversion factors
2 eggs
0.5 cupssugar
2 eggs
,
,
1 cup flour
1 cup flour
0.5 cupssugar
• Q - the chemical equation between H2 and O2
involves 2 H2 molecules combining with 1 O2
molecule to make 2 H2O molecules. Write all
possible conversion factors
2 molecules H2
1 molecule O2
2 molecules H2
2 molecules H2O
1 molecule O2
2 molecules H2O
2H2 + O2  2H2O
1 molecule O2
2 molecules H2
2 molecules H2O
2 molecules H2
2 molecules H2O
1 molecule O2
2 mol H2
1 mol O2
2 mol H2
2 mol H2O
1 mol O2
2 mol H2O
1 mol O2
2 mol H2
2 mol H2O
2 mol H2
2 mol H2O
1 mol O2
The steps to follow
Now we are ready to solve problems using the
factor label method. The steps involved are:
1. Write down the desired quantity/units
2. Equate the desired quantity to given quantity
3. Determine what conversion factors you can
use (both universal and question specific)
4. Multiply given quantity by the appropriate
conversion factors to eliminate units you
don’t want and leave units you do want
5. Complete the math
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km
First write down the
desired quantity
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
Next, equate desired
quantity to the given
quantity
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
Now we have to
choose a conversion
factor
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
1 km
0.621 mi
0.621 mi
1 km
What conversion
factors are possible?
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will
allow you to cancel
out miles
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will
allow you to cancel
out miles
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
1 km
0.621 mi
0.621 mi
1 km
Multiply given
quantity by chosen
conversion factor
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
x 1 km
0.621 mi
Multiply given
quantity by chosen
conversion factor
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47 mi
x 1 km
0.621 mi
Cross out common
factors
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47
x 1 km
0.621
Cross out common
factors
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47
x 1 km
0.621
Are the units now
correct?
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47
x 1 km
0.621
Yes. Both sides have
km as units.
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47
x 1 km
0.621
Yes. Both sides have
km as units.
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47
x 1 km
0.621
= 75.7 km
Now finish the math.
Factor label example
Q - How many kilometers are in 47 miles?
(note: 1 km = 0.621 miles)
# km = 47
x 1 km
0.621
= 75.7 km
The final answer is
75.7 km
Summary
The previous problem was not that hard
In other words, you probably could have
done it faster using a different method
However, for harder problems the factor
label method is easiest
More examples
1. You want to buy 100 U.S. dollars. If the
exchange rate is 1 Can$ = 0.65 US$, how
much will it cost?
# Can$ = 100 US$ x 1 Can$ = 153.85 Can$
0.65 US$
2. One mole of a gas has a volume of 22.4 L.
How many L will 300 grams of CO2 occupy?
(hint: the molar mass of CO2 is 44.01
____ g/mol).
# L CO2 =
300 g CO2 x 1 mol CO2 x 22.4 L CO2
= 152.7 L
44.01 g CO2 1 mol CO2
CO
2
More examples
3. There are 12 inches in a foot, 0.394 inches
in a centimeter, and 3 feet in a yard. How
many cm are in one yard?
# cm = 1 yd x 3 ft x 12 in x 1 cm
= 91.37 cm
1 yd 1 ft
0.394 in
4. A chemical reaction requires 3.000 moles of
sodium chloride. How many grams is this?
Sodium chloride is NaCl (58.44 g/mol)
#g NaCl =
3.000 mol NaCl x 58.44 g NaCl = 175.3 g NaCl
1 mol NaCl
Assignment
Answer questions using the factor label method:
1. How many moles of H2 are in 100 g of H2?
2. 300 g of CuSO4 is needed in an experiment.
How many moles does this represent?
3. A chemical reaction requires 23.78 moles of
silver chloride. How many grams is this?
4. Calculate how many feet are in 1 meter (use
information from the examples above).
5. With a U.S. dollar you can buy 1.1 Euros,
130 Yen, or 25 Rubles. How many Yen can
you buy with one Ruble?
Assignment
6. How many molecules are in 73 grams H2O?
(hint: form a conversion factor using Avogadro’s #)
7. 255 g of calcium phosphate are produced in a
chemical reaction. How many moles of
calcium phosphate does this represent?
8. According to the equation 2H2 + O2  2H2O,
how many grams of H2O would be produced
if 7.35 mol of O2 is used up? (hint: you will
need two conversion factors – 1 from the
balanced equation and 1 from a molar mass)
1. # mol H2 = 100 g H2 x 1 mol H2
= 49.5 mol H2
2.02 g H2
2. # mol CuSO4 =
300 g CuSO4 x 1 mol CuSO4 = 1.88 mol CuSO
4
159.61 g CuSO4
3. # g AgCl =
23.78 mol AgCl x 143.32 g AgCl = 3408 g AgCl
1 mol AgCl
4.
# ft = 1 m x 100 cm x 0.394 in x 1 ft
= 3.28 ft
1m
1 cm 12 in
5. # Yen = 1 Ruble x 1 US $ x 130 Yen
= 5.2 Yen
25 Rubles 1 US $
6. # H2O molecules =
73 g H2O x 1 mol H2O x 6.02x1023 molecules
18.02 g H2O
1 mol H2O
= 2.44 x 1024 molecules H2O
7. # mol Ca3(PO4)2 =
255 g Ca3(PO4)2 x 1 mol Ca3(PO4)2 = 0.822 mol
310.18 g Ca3(PO4)2 Ca3(PO4)2
8.
# g H2O=
7.35 mol O2 x 2 mol H2O x18.01 g H2O = 265 g
H 2O
1 mol O2
1 mol H2O
Assignment
Complete the following chart:
Formula Molar mass
Mass
(g/mol)
(g)
FeSO4
Moles
(mol)
500
(NH4)2CO3
SnO2
2
50
Sb2O5
NaClO4
0.25
100
Mg(IO3)2
CoCl2.H2O
3.2
332
Assignment
Complete the following chart:
Formula Molar mass
Mass
(g/mol)
(g)
FeSO4
Moles
(mol)
151.9
500
3.29
96.1
192.2
2
SnO2
150.7
50
0.332
Sb2O5
323.6
80.9
0.25
NaClO4
122.4
100
0.817
Mg(IO3)2
374.1
1196.8
3.2
CoCl2.H2O
147.8
332
2.246
(NH4)2CO3
Assignment
1. AgCl = 143.35 g/mol
#g = 2 mol x 143.35 g/mol = 286.7 g (2)
2. H2 = 2.016 g/mol
#mol = 100 g x mol/2.016 g = 49.6 mol (2)
3. CuSO4 = 159.62 g/mol
#mol= 300 g x mol/159.62 g=1.879 mol (2)
4. KClO = 90.55 g/mol
#mol = 250 g x mol/90.55 g = 2.76 mol (2)
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