Transcript Unit Conversion Practice Worksheet phc 10 DRB

Unit Conversion Practice Worksheet
Init 12/17/2007
by Daniel R. Barnes
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WARNING: Some images appearing in this presentation may have been swiped
without permission from the world wide web. Equally as heinous as this, I
completely ignore significant figure conventions when I round numbers.
Let’s say you want to buy a sixdollar hamburger, but all you’ve
got is pennies.
How many pennies would it
take to buy that six-dollar
burger?
How many pennies would it
take to buy that six-dollar
burger?
6x
=?x
To figure out how many
pennies six dollars is, you
need to know how many
pennies one dollar is.
=
?
100
x
Now that we know one
dollar is one hundred
cents, we can do a
unit conversion to
find out how many
pennies it takes to buy
a six dollar burger.
$6
1
x
100 ¢
$ 1
=
600 ¢
It takes 600 pennies to equal 6 dollars.
We figured this out by converting
six dollars into pennies.
Dollars and cents are both units for
measuring amounts of money.
We’ve just done a unit conversion.
$6
1
x
100 ¢
$ 1
=
600 ¢
This one was easy. You could have
probably done it in your head.
Everyone loves money, so they find it
pretty easy to do money math.
However, in chemistry, we have to
do unit conversions that are more
bizarre, using funny numbers and
weird units, so we have to learn a
procedure and stick to it.
$6
1
x
100 ¢
$ 1
=
600 ¢
You will use the method shown above to do almost all your unit
conversions in chemistry. The numbers are sometimes fancier,
and the units are weirder, but the procedure remains the same.
Remember that when you perform a unit conversion, the
original quantity does not really change. It’s still the same
size. It just looks different.
“$6” looks quite different than “600¢”, but they mean exactly
the same thing.
How many nickels would it take to buy a $12.50 taco combo?
$12.50
1
20 nickels
x
$1
= 250 nickels
How many hours can you talk if you have 3600 minutes left on
your cell plan this month?
3600 min
x
1
1h
60 min
= 60 h
If you’re pressed for time, click the button below.
If you have all the time in the world, click anywhere else.
Let’s assume that you live to be 100 years old.
100 years
365 days
x
x
1
1 year
24 hours 60 minutes
60 seconds
x
x
1 day
1 hour
1 minute
100 yr x 365 days/yr = 36,500 days
36,500 days x 24 hr/day = 876,000 hr
876,000 hr x 60 min/hr = 52,560,000 min
52,560,000 min x 60 s/min = 3,153,600,000 s
In scientific notation, 3,153,600,000 s = 3.1536 x 109 s
That’s about three billion seconds.
Let’s assume that you live to be 100 years old.
100 years
365 days
x
x
1
1 year
24 hours 60 minutes
60 seconds
x
x
1 day
1 hour
1 minute
100 yr x 365 days/yr = 36,500 days
36,500 days x 24 hr/day = 876,000 hr
876,000 hr x 60 min/hr = 52,560,000 min
52,560,000 min x 60 s/min = 3,153,600,000 s
In scientific notation, 3,153,600,000 s = 3.1536 x 109 s
That’s about three billion seconds.
A mole of anything is . . . 6.022 x 1023 molecules.
Let’s say you can count one molecule per second.
6.022 x 1023 seconds
1
lifetime
x
3.1536 x 109 seconds
1
1.9095636
(23-9) lifetimes
=
1.91
x
10
3.1536) 6.022
= 1.91 x 1014
lifetimes
That’s about 200 trillion lifetimes
3.1536 x 109 s
That’s about three billion seconds.
= 1.91 x 1014
That’s about 200 trillion lifetimes
lifetimes
http://www.flinnsci.com/moleconcept
Very short video above about the mole.
If you’re pressed for time, click the button below.
If you have all the time in the world, click anywhere else.
Proxima Centauri, a red dwarf,
is the second closest star to the earth.
The closest star to the earth is . . .
. . . the sun. It’s only 93,000,000 miles
away from the earth.
Proxima Centauri is so far away that
the distance between it and the earth
is not measured in miles, but in . . . light years.
Proxima Centauri is 4.2 light years
away from the earth.
How many miles is that?
A light year is how far light travels in one year.
The speed of light is 186,000 miles per second.
How fast is that in miles per year?
A light year is how far light travels in one year.
The speed of light is 186,000 miles per second.
How fast is that in miles per year?
186,000 mi
60 s
60 min
24 h
365 days
x
x
x
x
s
1 min
1 h
1 day
1
yr
= 5,865,696,000,000 mi/yr
A light year is how far light travels in one year.
The speed of light is 186,000 miles per second.
How fast is that in miles per year?
186,000 mi
60 s
60 min
24 h
365 days
x
x
x
x
s
1 min
1 h
1 day
1
yr
= 5,865,696,000,000 mi/yr = 5.866 x 1012 mi/yr
A light year is about six
trillion miles.
trillion
billion
million
thousand
5.866
x 4.2
24.6372
Proxima Centauri is 4.2 light-years
away, so how far does light travel
in 4.2 years?
24.6372 trillion miles
= 2.4 x 10 13 miles
Proxima
Centauri
Earth
UNIT CONVERSION STEPS
original
amount
x
1
#new new unit . . .
#old old unit
1. Original amount over one
2. Times a fraction
3. Old unit on the bottom
4. New unit on the top
5. Put in #’s to make top equal bottom
6. If new unit is not target unit, build another fraction.
YOU TRY IT:
four weeks?
4 weeks
1
x
How many meals does a person eat in
(Assume B/L/D)
7 days
1 week
x
3 meals
1 day
= 84 meals
This has all been very interesting, but now we
need to focus on the kinds of unit conversions that
you’re actually going to have to do on the test.
This has all been very interesting, but now we
need to focus on the kinds of unit conversions that
you’re actually going to have to do on the test.
Before actually doing some true mole math
problems, you’re going to take a good look at your
tool box.
Volume of Gas at STP
(L)
Standard temperature =
0oC = 273 K = 32oF
See Prentice Hall’s
Chemistry textbook,
page 303
MOLE
Mass (g)
Representative Particles
(atoms, molecules)
P = 0 atm
in outer
space
“Standard Temperature and Pressure”
O oC
P = 0.3 atm
on top of
Mt Everest
P = 1 atm at sea level
1 atm
These are all different ways of saying standard pressure.
One mole of gas at
STP occupies 22.4
liters of volume.
It doesn’t matter
what gas it is.
At STP,
6.022 x 1023 gas
molecules takes up
22.4 liters of space.
22.4 L = 1 mol
That’s just a bit
more than the
combined volume
of 11 two-liter soda
bottles.
If you don’t memorize it, you better know where to look.
A mole of any gas takes up 22.4 L of space at STP.
Therefore, you can measure # of molecules, which is hard,
by measuring volume, which is easy.
The thing is, if you change the temperature or pressure of a
gas, it will expand or shrink.
Therefore, in order to use the 22.4 L thingie to figure out
how many moles of gas you’ve got, you have to get the gas
to STP, or your answers will be wrong.
Volume of Gas at STP
(L)
Standard temperature =
0oC = 273 K = 32oF
See Prentice Hall’s
Chemistry textbook,
page 303
MOLE
Mass (g)
Representative Particles
(atoms, molecules)
Volume of Gas at STP
(L)
In what units is each
quantity measured?
MOLE
Mass (g)
Representative Particles
(atoms, molecules)
If the material is a covalently-bonded compound,
the “representative particle” unit will be molecules.
Representative Particles
(atoms, molecules)
If the material is a polyatomic non-metal element,
the “representative particle” unit will be molecules.
Representative Particles
(atoms, molecules)
If the material is a noble gas, a lattice-forming non-metal,
or a metal, the “representative particle” will be atoms.
Representative Particles
(atoms, molecules)
If the material is ionic, technically, the “representative
particle” unit would be “formula units”.
Na
Na
Na
Cl
Na
Cl
Na
Cl
Cl
Na
Cl
Na
Na
Cl
Cl
Cl
Representative Particles
(atoms, molecules)
Volume of Gas at STP
(L)
How do you convert
from one quantity
to another?
MOLE
Mass (g)
Representative Particles
(atoms, molecules)
Before we answer that
question, do remember what
piece of information you
needed to know in order to
turn $6 into 600¢?
$1 = 100¢
Or, in another way of saying it . . .
100¢ per $
or
100¢/$
Volume of Gas at STP
(L)
How do you convert
from one quantity
to another?
MOLE
Mass (g)
Representative Particles
(atoms, molecules)
Volume of Gas at STP
(L)
To go from grams to moles
or from moles to grams
you need . . .
MOLAR
MASS
In what units is molar
mass given?
MOLE
g/mol
Mass (g)
Representative Particles
(atoms, molecules)
Volume of Gas at STP
(L)
To go from particles to moles
or from moles to particles,
you need . . .
In what units is Avogadro’s
number given?
MOLE
AVOGADRO’S
NUMBER
molecules/mol
Mass (g)
Representative Particles
(atoms, molecules)
Do you remember Avogadro’s Number? What is it?
NA =
6.022 x 1023
formula
molecules/mol
atoms/mol
units/mol
It’s not on your CST Reference Sheet, so you’d better memorize it.
Volume of Gas at STP
(L)
To go from volume of gas
at STP to moles, or from
moles to volume of gas
at STP, you need . . .
22.4 L/mol
MOLE
Mass (g)
This is a constant, and it
Can be found on your
CST Reference Sheet.
Representative Particles
(atoms, molecules)
Volume of Gas at STP
(L)
These three pieces of
information are your
“mole math tool box”.
MOLAR
MASS
22.4 L/mol
MOLE
g/mol
Mass (g)
AVOGADRO’S
NUMBER
molecules/mol
Representative Particles
(atoms, molecules)
Volume of Gas at STP
(L)
22.4 L/mol
MOLAR
MASS
MOLE
g/mol
Mass (g)
AVOGADRO’S
NUMBER
molecules/mol
Representative Particles
(atoms, molecules)
Q1: What “tool” allows you to convert grams into moles or convert
moles into grams?
A: molar mass
Q2: Why is molar mass the right tool for converting grams into
moles or converting moles into grams?
A: Molar mass is given in grams per mol = g/mol
Q3: What is Avogadro’s number?
A: 6 x 1023
Q4: What is Avogadro’s number useful for?
A: converting molecules into moles or moles into molecules
Q5: When you see “STP” in a question, what mathematical
quantity should immediately pop into your head?
A: 22.4 liters per mole of gas = 22.4 L/mol
Q6: What does “STP” stand for?
A: Standard temperature and pressure
Q7: What are the conditions at STP?
A: a temperature of zero degrees Celsius (273 Kelvins = 32oF)
and a pressure of 1 atm = 101.3 kPa = 14.7 psi = 760 mmHg = . . .
Q8: How do you get molar mass?
A: calculate it using the chemical’s formula and the atomic
masses from the periodic table.
Q9: Where can you get Avogadro’s # during a test?
A: Sorry. You have to memorize it.
Q10: Where can you get that 22.4 L/mol thingie?
A: It’s on the back side of the reference sheet.
Q11: How many representative particles are in a mole?
A: 6 x 1023 representative particles = 1 mole
Q12: What does “representative particles” usually mean?
A: “molecules”
http://what-if.xkcd.com/4/
Unit Conversion Practice Worksheet
Try each problem in pencil before you
look at the answer.
Then, make whatever corrections you
need to make to your answer.
Don’t just look at the answer first, or you
won’t learn as much.
1. How many grams is 72 kilograms?
72 kg
1
x
1000 g
=
1 kg
1 kilogram = 1000 grams
72,000 g
2. How many Ag atoms are there in 3.4 moles of silver?
3.4 mol
1
x
6 x 1023 atoms
=
20.4 x 1023 atoms
1 mol
2.04 x 1024 atoms
1 mole = 6.022 x 1023 atoms
3.4
x6
20.4
3. How many milliliters is 2 liters?
2L
1
x
1000 mL
1 L
1 liter = 1000 milliliters
=
2,000 mL
4. How many grams of carbon are there in 78 moles
of carbon?
78 mol
1
x
12.01 g
=
937 g
1 mol
The periodic table lists carbon’s
average atomic mass as 12.01.
1 mole of carbon = 12.01 grams of carbon
12.01
x 78
936.78
5. How many liters does 3200 grams of CH4 occupy at STP?
3200 g
1
molL
x
g
Now, it would be nice if we could convert directly from grams to
liters, but I don’t know of any number that tells us how many
grams per liter or how many liters per gram.
(Well, actually, I do. It’s called density, but we don’t use density in
this chapter, so we’ll have to do something else instead.)
Your CST Reference Sheet says that one mole of ideal gas at
STP takes up 22.4 liters of volume. (It’s the first fact listed under
“Constants”.)
Now if we could just convert grams into moles, then we could
convert moles into liters.
This problem is going to take two steps.
5. How many liters does 3200 grams of CH4 occupy at STP?
3200 g
1
1 mol
x
22.4 L
x
16.05 g
CH4:
C: 1 x 12.01 = 12.01
H: 4 x 1.01 = 4.04
= 4467 L
1 mol
199.37694
16.05) 3200.0000000
16.05 g/mol
199.4
x 22.4
4466.56
To convert grams into moles, we’re going to need to calculate the
molar mass of methane.
Now that we’re set up to convert grams into moles, we need to get
set up to convert moles into liters.
Once again, according to your reference sheet, one mole of ideal
gas occupies 22.4 liters of space under STP conditions, so . . .
6. How many moles of zinc are there in 124 grams of zinc?
124 g
1
1 mol
x
=
1.9 mol
65.39 g
The periodic table list’s zinc’s
average atomic mass as
65.39.
1 mole of zinc = 65.39 grams of zinc
1.8963144
65.39) 124.0000000000
To convert Celsius to Kelvins . . . add 273.
To convert Kelvins to Celsius . . . subtract 273.
7. How many degrees Celsius is 310 Kelvins?
oC
oC
= K – 273
= 310 – 273 =
37 oC
310
-273
37
Your chemistry CST
reference sheet says that
K = oC +273.
Therefore, oC = K – 273.
PLEASE NOTE that converting between degrees Celsius and Kelvins is just about
the only time that you don’t multiply fractions times fractions to perform a unit
conversion. You don’t really need to work with Celsius and Kelvins until
chapter 14 (gases) anyway, but I thought I’d throw this in here just so you’d
know that unit conversions don’t always follow the same pattern.
Time to think-pair-share the rest of the back side of the
worksheet.
8. What volume does 2.2 grams of carbon dioxide (CO2) occupy
at STP?
2.2 g
1
1 mol
x
44.01 g
CO2:
C: 1 x 12.01 = 12.01
O: 2 x 16.00 = 32.00
22.4 L
x
1 mol
= 1.12 L
0.0499886
44.01 ) 2.2000000
44.01 g/mol
0.04999
x 22.4
1.119776
9. How many atoms of helium are there in 67.308 moles of
helium?
67.308
23
6.02 x 10 atoms
67.308 mol
x
6.02
x
1
mol
1
405.19416
= 405.19416 x 1023 atoms
1 mole is 6.02 x 1023 particles
(whether it’s helium, carbon dioxide, salt, gold, or whatever)
This answer is correct, but it’s not in
proper scientific notation.
There should be only one digit in front of the
decimal, not three.
9. How many atoms of helium are there in 67.308 moles of
helium?
That move made
405.19416 get 100
times smaller.
Therefore, to keep our answer the
same size, we need to make the
power of 10 get 100 times bigger.
25 atoms
23
405.19416
x
10
.
This decimal point
needs to move . . .
. . . two spaces to
the left.
100 is 10 to the 2nd power, so we
need to make the exponent get
bigger by 2.
23 + 2 = 25
9. How many atoms of helium are there in 67.308 moles of
helium?
67.308
23
6.02 x 10 atoms
67.308 mol
x
6.02
x
1
mol
1
405.19416
= 405.19416 x 1023 atoms
25
= 4.0519416 x 1025 atoms He
4.0519416 x 10 atoms
Now, the answer has been properly converted into scientific
notation.
Converting it into proper scientific notation didn’t make it get
bigger or smaller; it just changed what it looks like.
9. How many atoms of helium are there in 67.308 moles of
helium?
67.308
23
6.02 x 10 atoms
67.308 mol
x
6.02
x
1
mol
1
405.19416
= 405.19416 x 1023 atoms
= 4.0519416 x 1025 atoms
10. How many molecules are there in 126 grams of water (H2O)?
126 g
1
x
molecules
g
It would be nice if there were a number that told us how
many molecules per gram of water, but there isn’t.
However, there is a number that tells us how many
molecules per mole.
There are 6.022 x 1023 molecules per mole. (Avogadro’s #)
If we can just convert grams into moles, then we can convert
moles into molecules using Avogadro’s number.
10. How many molecules are there in 126 grams of water (H2O)?
126 g
1
x
mol
g
It would be nice if there were a number that told us how
many molecules per gram of water, but there isn’t.
However, there is a number that tells us how many
molecules per mole.
There are 6.022 x 1023 molecules per mole. (Avogadro’s #)
If we can just convert grams into moles, then we can convert
moles into molecules using Avogadro’s number.
Calculating the molar mass of water will tell us how many
grams per mole for water. Let’s do that next.
10. How many molecules are there in 126 grams of water (H2O)?
126 g
1
x
1 mol
x
18 g
6 x 1023 molecules
1
H: 2 x 1 = 2
? molecules
mol
7
18 )126.0000
H2O:
=
7
x6
42
O: 1 x 16 = 16
18 g/mol
42 x 1023 molecules
4.2 x 1024 molecules
4
x 1024 molecules
(If you care about sig figs, you’re only allowed to keep one digit.)
11. How many moles of bismuth are there in 2.56 kg of
bismuth?
1000 mol
g
1 mol
2.56 kg
x
x
= 12.25 mol
1
1 kg
209 g
2.56
x 1000
2560.00
12.248803
209 ) 2560.000000
The periodic table list’s bismuth’s average atomic mass as
208.98 1 mole of bismuth = 208.98 grams of bismuth
Too bad it doesn’t say how many KILOGRAMS one mole is.
We’re going to have to convert kg into g first, and THEN turn
g into mol. This is going to take two steps.
1 kilogram = 1000 grams.
This is always true, not just for bismuth.
11. How many moles of bismuth are there in 2.56 kg of
bismuth?
1000 g
1 mol
2.56 kg
x
x
= 12.25 mol
1
1 kg
209 g
2.56
x 1000
2560.00
12.248803
209 ) 2560.000000
12. What is the mass, in kilograms, of 8 x 1028 copper atoms?
8 x 1028 atoms
1 mol
63.55 g
1 kg
x
x
x
23
1
6 x 10 atoms
1 mol
1000 g
63.55
x
8
508.40
84.733
6 ) 508.40
= 84.733 x 10 (28-23-3) kg
= 84.733 x 10 2 kg
= 8.4733 x 10 3 kg
= 8 x 103 kg if you care
about sig figs
103
For one guy’s take on the effects of exposure to a vacuum on the human body:
http://www.geoffreylandis.com/vacuum.html
Slide needed: How many atoms are in a grain of sand?
oC
K
Title Page
#1
SWBATS
#2
#7
$6 Burger
#3
#8
S/Lifetime
#4
#9
Lifetimes/mol
STP
#10
Miles/ly
(Prox. Cent.)
#5
#11
The Mole
Road Map
#6
#12