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The Mole Concept and Atomic Weights
Text Reference: Tro, Chemistry: Structure and Properties
Section 2.8 - Atoms and the Mole: How Many Particles?
Section 1.9 – Atomic Mass: The Average of an Element’s Atoms
The purpose of this activity is to better understand the concepts of relative atomic mass, counting by weighing and the mole. Per cent composition and average atomic mass are included.
Part I. Relative Atomic Masses and the Mole – Early Method
When John Dalton proposed his atomic theory, he stated that the atoms of each element had a characteristic mass. He carried out experiments to determine the relative atomic mass of each element. To do this, he had to establish a standard because a single atom was too small to weigh. The standard he chose was that the mass of hydrogen would be set equal to 1.000. In a simple experiment, Dalton would measure the grams of an element such as sulfur that reacted with 1.00 gram of hydrogen. For sulfur, the reacting mass was found to be 32.0 grams, and so 32.0 was the relative mass of sulfur with respect to the standard hydrogen. (Note:
The current standard for atomic mass is the most abundant isotope of carbon, C-12, with an assigned mass of exactly 12.000 amu.)
The following activity will demonstrate how the relative mass method works.
1. Weigh five of the red color balls to three decimal places. Be sure to tare out the mass of the plastic cup. Record the mass in the table below.
2. Weigh five colorless balls. Record mass. Weigh five green balls. Record mass.
3. Set the “Relative Mass” of the red balls equal to 1.000. Calculate the relative mass of the colorless and green balls by dividing their mass by the mass of the red balls.
4. Now, weigh 1.000 gram of red balls. Try to get the mass as close as possible to 1.000 gram. Count the number of red balls in this mass and record it. Be as precise as possible.
5. For the colorless balls, weigh out a mass in grams equal to its relative mass. Count the number of colorless balls in this mass. Repeat this for the green balls.
Ball size

Mass (g)

Relative Mass

Small (red)

1.000

Medium (colorless)
Large (green)
What do you notice about the number of balls in the gram-relative mass?
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Number of balls contained in the gramrelative mass

This number is the “unit of count” for the balls, similar to Avogadro’s number for atoms.
When the relative mass of any ball is weighed in grams, they contain the same number of balls.
1 unit of balls = ______ balls = gram-relative mass of that color of ball
Part II. Counting by Weighing
A. Use the above relationships to calculate mass of red balls needed to have a count of 60 balls.
Show your work!

Next, weigh out this calculated mass of red balls as closely as possible.
Now count the number of balls in this mass and record it. ________________
How close did you come to 60?

B. Use these relationships to determine the number of colorless balls in the beaker.
Weigh all the colorless balls in the beaker. ________________
(Be sure to exclude the mass of the beaker.)
Next, calculate how many colorless balls are in the beaker. Show work!

Now, count how many nuts are in the bottle. ______________
C. Describe how you could “count” 150 green balls without actually counting them

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The unit of count and the relative masses depend on the size of the smallest particle. Atoms are very small, thus the “unit of count” Avogadro’s number is very large 6.02 x 1023 atoms. Chemists call this unit of count the mole.
The mole is related to the relative mass of the atom, just like the exercise you did with the colored balls. The relative atomic masses of the elements are listed in the Periodic Table. When this amount of the element is weighed in grams, you have one mole of atoms of that particular element.
Gram relative mass = 1 mole of atoms = 6.02 x 1023 atoms
Examples
12.01 grams of C = 1 mole of carbon atoms = 6.02 x 1023 carbon atoms
55.85 grams of Fe = 1 mole of iron atoms
= 6.02 x 1023 iron atoms
Using these relationships, we easily convert between mass, moles, and the number of atoms.
Write the relationships for sulfur.
__________ grams of S = 1 mole of S = ________________ atoms of S
Use these relationships with dimensional analysis:
a. to calculate how many sulfur atoms are in 48.00 grams of sulfur. Show your work!
48.00 grams S → moles S → atoms S

in a stepwise manner or use only the “end” terms

b. How many grams would 1.00 billion atoms of sulfur weigh?

48.00 grams S → atoms S

Show your work!

c. What mass of sulfur would contain 0.400 mole of sulfur atoms? Show your work!

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Part III. Isotopes and Average Atomic Mass – Modern Method
In the 1920’s, an instrument called the mass spectrometer was developed by J.J. Thomson and F.W.
Aston from their work with cathode ray tubes. This invention allowed atomic, and molecular, masses to be measured directly. In the instrument, positively charged atoms or molecules were produced in collisions of electrons with neutral atoms or molecules. The positive charged ions were drawn toward negatively charged plates (accelerated), passing through apertures in the plates to enter a magnetic field. From physics, it is known charged particles will follow curved paths with the radius of curvature depending on the particles’ charge, velocity, and mass. Lighter ions take tightly curved paths, heavier ion loosely curved paths. In
Thomson and Aston’s original experiment, the particle beams struck a phosphorescent screen. Individual particle masses were easily calculated from the particle positions on the screen, the magnetic field strength and accelerating voltages. An image showing the isotopes of neon from Thomson and Aston’s 1913 paper is reproduced to the left.
Over time, a statistical profile of ion masses and ion numbers can be generated. The results showed that most elements are composed of collections of atoms of two or more unique masses in more or less fixed ratios. Much later, the differences in masses were attributed to variations in the number of neutrons contained in the nucleus of each element. The atoms of different masses in a single element were named isotopes, indicating the atoms occupied the same (iso) position in the periodic table (tope).
For example, the CRC Handbook of Chemistry and Physics lists the three naturally occurring isotopes of the element silicon and their mass in amu. The “amu” is the abbreviations for “atomic mass unit”.
Si-28 92.21% relative abundance with an exact mass of 27.97693 amu
Si-29 4.70%
28.97649 amu
Si-30. 3.09%
29.97376 amu
The average atomic mass of silicon can be calculated using the weighted average method, wehre the relative
% abundance is expressed as the decimal equivalent, as follows:
Ave. Mass Si = (0.9221)(27.97693) + ( 0.0470) (28.97649) + 0.0309 (29.97376)
= 25.80
+ 1.36
+ 0.926
= 28.09 amu (pay attention to sig figs and use all digits)
When this value for the average atomic mass of silicon is compared with the value determined experimentally by the chemists in the 1800’s the two agreed to within 0.1% error!

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Calculate the average atomic mass of iron from the following isotopic composition: iron-54 iron-56 iron-57 iron-58

53.9396 amu
55.9349 amu
56.9354 amu
57.9333 amu

5.82%
91.66%
2.19%
0.33%

Show your work as was done for the silicon example above, paying particular attention to significant figures and units.

Part IV. Further Calculations
From the mass of one mole of iron atoms, calculate the mass of one iron atom in grams.
(Remember that an atom is very small.) Show your work!

If you weighed out 5.000 grams of iron atoms on the balance in our lab, what is the uncertainty in the measured mass? Hint: Think how balance display behaves with a mass on the pan.
5.000 + / -- __________ grams
Based on this uncertainty, calculate how many atoms of iron you could be “off” by.

A Geiger counter is a device that is used to “count” the decay events of radioactive isotopes like Uranium238. In one minute, a Geiger counter detected the decay of 35,000 uranium-238 atoms. Using dimensional analysis, calculate the mass corresponding to 35,000 uranium-238 atoms.

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Part V. Compounds and Molar Masses
Atoms are bonded together to make the particles of a compound. The chemical formula tells how many of each atom is in this particle. Parentheses are used for polyatomic ions.
The smallest particle of a covalent compound is called a ______________________.
The smallest particle of an ionic compound is called a ________________________.
The mass of one mole of a compound is calculated by adding up the average atomic masses of each of the elements that make up the compound. For example, the molar mass of dihydrogen sulfide H2S would be
2(1.01 g) + 1(32.06 g) = 34.07 grams.
Calculate the molar masses of
a. N2H4
b. Ca(OH)2
c. Ca(NO3)2
How many molecules are in 0.200 moles of N2H4 ?

Calculate how many molecules of N2H4 are in 40.0 grams of the substance.

How many grams of N2H4 contain 1.50 x 1020 molecules?

Calculate how many grams of Ca(OH)2 should be weighed out to give 1.5 moles of the substance?

How many atoms of hydrogen are in 1.5 moles of Ca(OH)2

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Part VI. Chemical Formulas and Per Cent Composition by Mass
% of element in compound = (number of atoms of the element in the formula)(atomic mass) formula mass