Pirate Chemistry
Molar Mass
http://www.rocksforkids.com/images/copper%20pellets.jpg
In the last unit we saw that we were able to count atoms and group them together by using the
idea of the mole. We were able to turn moles into atoms and vice versa. However, that idea
itself is not terribly useful to a Chemist on a practical laboratory setting. If a chemist had a
sample of copper pellets, for instance, how would he determine how many atoms or moles there
were? He would need some way of measuring how much is there. There is no device in the lab
that directly measures atoms; an “atom-ometer”. Even if there was, you would need a different
“atom-ometer” for every substance because atoms are all different sizes; some big, some small.
How are we going to count atoms?
How can you count the atoms in this sample of copper?
What we need to count atoms is some device that is useful for virtually any element or compound and is very easy to use. Luckily, all chemistry labs have many of these devices; a common scale or balance!
How can a balance or scale tell us how many atoms are present? A scale simply tells us the
mass of a sample. Since atoms all have different masses how this work? It will work if we
know how much each atom weighs.
Let me give you an example. Let’s say you want to count how many M&Ms were in a bag but
you didn’t want to take the time to count each individual one. If you knew that each plain
M&M had a mass of 0.2 grams and each peanut M&M had a mass of 1.5 grams you could set
up an equality like we did before:
1 plain M&M = 0.2 grams
1 peanut M&M = 1.5 grams
Who would want to take the time
to count all the candies in these big
56 ounce (1585 gram) bags?
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
By using the factor-label method, we can count the M&M’s in the bag without counting them;
we can mass them!
Example 1: How many plain M&M’s are in a 1585 gram (56 ounce) bag?
1585 grams
1 plain M&M = 0.2 grams
1 plain M&M 1585 grams
X
0.2 grams
1
=
7925 plain M&M’s
Example 2: How many peanut M&M’s are in a 1585 gram (56 ounce) bag?
1585 grams
1 peanut M&M = 1.5 grams
1 peanut M&M 1585 grams
X
1.5 grams
1
=
1057 peanut M&M’s
http://www.awesomescales.net/images/orbit.jpg
We are counting the candies by massing them. The same thing can be done with atoms if we
know something about their masses. What we need is a list that tells us how much atoms of a
particular type weigh. Luckily, such a list exists and has been right in front of us the whole
time!
A scale can count
things if you know
how much each one
weighs
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
The Periodic Table of elements is the link between counting atoms and massing them. We
know that a listing on the table can tell us the atomic number which is the number of protons;
37 in the case of Copper, listed below. But the table also tells us the atomic mass, 63.5 for Copper. What does that do for us? The atomic mass tells us the number of grams that are in 1
mole or 6x1023 atoms of that element. Consequently, we can set up an equation for each atom
simply by looking at the atomic mass off of the Periodic Table. For Copper we can say:
63.5 grams Cu = 1 mole Cu
29
Cu
Copper has a mass of 63.5 off of the Periodic Table. That means that 63.5 grams of
copper will give you 1 mole of copper atoms.
63.5
The Periodic Table of elements is the link between counting atoms and massing them. We
know that a listing on the table can tell us the atomic number which is the number of protons;
37 in the case of Copper, listed below. But the table also tells us the atomic mass, 63.5 for Copper. What does that do for us? The atomic mass tells us the number of grams that are in 1
mole or 6x1023 atoms of that element. This is also called the molar mass. Consequently, we
can set up an equation for each atom simply by looking at the atomic mass off of the Periodic
Table. For Copper we can say:
63.5 grams Cu = 1 mole Cu
Combining this information with what we learned in the previous chapter, we can now calculate
the number of atoms of copper in the sample.
Example 3: How many atoms of copper are in 25.01 grams of it?
25.01 grams
63.5 grams = 1 mole
1 mole = 6x1023 atoms
6x1023 atoms 1 mole 25.01 g
X
1 mole X 63.5 g
1
=
2.36x1023 atoms Cu
Atoms are way too tiny to count individually but knowing the molar
mass of a substance lets us count them by massing them and doing a
little math!
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
Remember that the mass of each kind of element is different. If you wanted to do the same
thing with other elements you would have a different mass in your equation. But regardless of
the element you choose, the number on the Periodic Table tells you the number of grams in 1
mole of the substance, the molar mass:
http://goldprice.org/buying-gold/uploaded_images/how-do-you-buy-gold781694.jpg
79
Au
197.0
For gold
197 g Au = 1 mole Au
http://www.monex.com/images/photos/prodSilver01.jpg
47
Ag
107.9
For silver
107.9 g Ag = 1 mole Ag
24.3
6
C
12.0
For magnesium
24.3 g Mg = 1 mole Mg
http://www.freewebs.com/symbolc/hardwood-charcoal.jpg
Mg
http://catalog.miniscience.com/Catalog/Metals/Images/
Magnesium_Ribbon.jpg
12
For carbon
12 g C = 1 mole C
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
This also works with compounds. Since water is the combination of 2 hydrogen atoms and 1
oxygen atom, its mass will simply be the sum of those atoms:
1
8
H
O
1.0
16.0
H2O
2 H atoms each at a mass of 1 = 2
1 O atom at a mass of 16 = 16
H2O = 1 + 1 + 16 = 18
So for H2O
18 g H2O = 1 mole H2O
Let’s practice this with other compounds:
Example 4: What is the molar mass of CO2?
C = 12
O = 16
CO2 = 12 + 16 + 16 = 44
44 g CO2 = 1 mole CO2
Example 5: What is the molar mass of Br2?
Br = 79.9
Br2 = 2 (79.9) = 159.8
159.8 g Br2 = 1 mole Br2
Example 6: What is the molar mass of Al(NO3)3?
Al = 27
N = 14
O = 16
Al(NO3)3 = 27 + 3(14) + 9(16) = 213
213 g Al(NO3)3 = 1 mole Al(NO3)3
Example 7: What is the molar mass of Ca(OH)2?
Ca = 40.1
H=1
O = 16
Ca(OH)2 = 40.1 + 2(16) + 2(1) = 74.1
74.1 g Ca(OH)2 = 1 mole Ca(OH)2
Example 8: What is the molar mass of Fe2(Cr2O7)3?
Fe = 55.8
Cr = 52
O = 16
Fe2(Cr2O7)3 = 2(55.8) + 6(52) + 21(16) = 759.6
759.6 g Fe2(Cr2O7)3 = 1 mole Fe2(Cr2O7)3
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
Knowing all of this information, we can now calculate moles, atoms, and grams for any substance!
atoms
1 mole = 6x1023 atoms
Periodic Table
grams
moles
x grams = 1 mole
This is the beginnings of a very simple “mole map”. All you have to do is to figure out how
many steps you have to take on the map and that is number of equations you will need to solve
the problem. For instance:
Example 9: How many grams are in 2.3 moles of sodium chloride?
11
atoms
Na
1 mole = 6x1023 atoms
23.0
Periodic Table
grams
17
moles
x grams = 1 mole
Cl
You are only trying to go from moles to grams. This is one step on the
map so you should only need 1 equation to solve it. Since you are incorporating grams, you need to know the molar mass like we learned
before. Na is 23 and Cl is 35.5 so its molar mass is 58.5
35.5
2.3 moles NaCl
58.5 grams NaCl = 1 mole NaCl
58.5 g NaCl
1 mole
X
2.3 moles
1
=
134.6 g NaCl
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
Example 10: How many moles are in 50 grams of CO2?
6
atoms
C
1 mole = 6x1023 atoms
12.0
Periodic Table
grams
8
x grams = 1 mole
O
You are only trying to go from grams to moles. This is one step on the
map so you should only need 1 equation to solve it. We need to know
the molar mass of CO2 by including 1 C at 12 and 2 O each at 16 so its
molar mass is 12 + 16 + 16 = 44
16.0
1 mole
44 g
moles
50 g CO2
44 g CO2 = 1 mole CO2
X
50 g
1
=
1.14 moles CO2
Example 11: How many atoms are in 4 moles of carbon?
atoms
1 mole = 6x1023 atoms
Periodic Table
grams
moles
x grams = 1 mole
You are only trying to go from moles to atoms so this is just like we did in the last chapter. It is
only a 1 step problem. Notice how we don’t need to look up the mass on the Periodic Table.
Since grams are not involved, we can skip that step.
4 moles
1 mole = 6x1023 atoms
6x1023 atoms
X
1 mole
4 moles
1
=
24x1023 atoms
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
Example 12: How many atoms are in 5 grams of Zinc (Zn)?
30
atoms
Zn
1 mole = 6x1023 atoms
65.4
Periodic Table
grams
moles
x grams = 1 mole
In this problem you are going from grams to atoms. It is going to take you 2 steps so therefore
you will need to write down 2 equations. The first equation is the molar mass equation so you
need to look at the Periodic Table for the mass. The second equation never changes, it is always
that 1 mole equals 6x1023 atoms or molecules.
5 grams
65.4 grams = 1 mole
1 mole = 6x1023 atoms
6x1023 atoms
1 mole
X
1 mole
65.4 g
X
5g
1
=
0.459x1023 or 4.59x1022 atoms Zn
Example 13: How many grams are in 8x1023 molecules of HCl?
atoms
8x1023 molecules
36.5 grams = 1 mole
1 mole = 6x1023 atoms
1
17
H
Cl
1.0
35.5
36.5 g
1 mole
X
1 mole = 6x1023 atoms
Periodic Table
grams
1 mole
6x1023 molecules
moles
x grams = 1 mole
X
8x1023 molecules
1
=
48.7 g HCl
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org
Pirate Chemistry
Questions
1. What device do chemists use to count atoms or molecules?
2. Define molar mass.
3. Calculate the molar mass for each substance listed below:
A. Ba
B. O2
C. LiNO3
D. Na3PO4
E. Al2O3
F. Cl2
G. Ca(ClO3)2
H. Fe3(PO4)2
I. I2
J. K2CO3
4. Calculate the number of atoms or molecules in:
A. 4.5 moles of Fe
B. 81 moles of H2O
5. Calculate the number of moles in:
A. 4x1023 atoms of Li
B. 9x1023 molecules of NO2
6. Calculate the number of moles in:
A. 35 grams of TiO2
B. 75 grams of F2
7. Calculate the number of grams in:
A. 4.7 moles of K2SO4
B. 9.2 moles of Br2
8. Calculate the number of atoms or molecules in:
A. 36 grams of ClF3
B. 82 grams of I2
9. Calculate the number of grams in:
A. 4x1023 molecules of SiCl4
B. 9x1023 atoms of Hg
atoms
1 mole = 6x1023 atoms
Periodic Table
grams
moles
x grams = 1 mole
All text copyright Chris Smith 2009. All pictures obtained from internet and are copyright of their owners but assumed to be public accessible. If you are the owner of a picture and want it removed, email csmith@d211.org