Name
Period
Date
DETERMINING AN EMPIRICAL FORMULA
PROBLEM
Determining the elements that a mineral contains may be challenging, because
some minerals contain the same elements, just in different proportions, as shown
in the table below.
Some Silicon-Containing Minerals Found in Meteorites
Mineral
Chemical formula
Cristobalite
Quartz
Enstatite
Forsterite
Diopside
Monticellite
SiO2
SiO4
MgSiO3
Mg2SiO4
MgCa(SiO3)2
MgCaSiO4
Background
Minerals such as the compounds in the table are actually formed in networks of
repeating atoms, instead of as isolated molecules. To distinguish between two
minerals with the same elements, such as cristobalite (SiO2) and quartz (SiO4),
determine the ratios of the atoms. Cristobalite has two oxygen atoms for every
silicon atom, and quartz has four oxygen atoms for every silicon atom.
Determining Empirical Formula Example
A mineral from a rock sample is analyzed. Its composition is 48.0% oxygen,
27.9% iron, and 24.1% sulfur. What is the empirical formula for this compound?
Analyze
Given: percentage composition:
Unknown: empirical formula
48.0% O
27.9% Fe
24.1% S
Plan and Solve
percentage composition → mass composition → composition in moles
smallest whole number molar ratio
→
Mass composition (mass of each element in an imaginary 100.0 g sample):
48.0 g O, 27.9 g Fe, 24.1 g S
Composition in moles:
48.0 g O × (1 mol O/16.00 g O) = 3.00 mol O
27.9 g Fe × (1 mol Fe/55.84 g Fe) = 0.500 mol Fe
24.1 g S × (1 mol S/32.06 g S) = 0.752 mol S
Smallest whole-number mole ratio of atoms:
These mole quantities do not provide a whole-number ratio. To find the
whole-number ratio, start by dividing each of the values by the smallest
mole amount.
(3.00 mol O/0.500) : (0.500 mol Fe/0.500) : (0.752 mol S/0.500)
= 6.00 mol O : 1 mol Fe : 1.50 mol S
This is not a whole-number ratio. Take a closer look to see if multiplying
each amount by a small number (usually 2 or 3) will result in a wholenumber ratio. In this case, doubling each amount will work.
12.00 mol O : 2.00 mol Fe : 3.00 mol S
The empirical formula of the compound is:
Fe2S3O12 (or Fe2(SO4)3)
Check Your Work
In this compound, the mass of sulfur is twice as much as the mass of
oxygen. Because sulfur has twice the atomic mass of oxygen, that
means there should be four times as many oxygen atoms as sulfur
atoms in the empirical formula.
Practice
1. A student calculates the empirical formula of a compound to be C1.5H3.5.
Express this as a correct empirical formula.
2. The formula for acetic acid, an ingredient of vinegar, is C2H4O2. What is the
empirical formula for acetic acid?
3. A compound contains 69.9% iron and 30.1% oxygen. What is its empirical
formula?
PLANNING
Goal
Use relative masses of elements to determine an empirical formula and identity for
a mineral compound found in a meteorite.
Objectives
Observe and make measurements of a sample of a mineral compound from a
meteorite.
Analyze the sample with a mass spectrometer to determine the relative masses of
each clement present.
Convert these relative masses into mole amounts.
Determine the empirical formula and the identity of the substance.
Your Plan
4. Adjust or replace the following sample procedure to suit your plan for
performing the virtual lab. You can also edit the data tables in Observations.
For example, you might delete the line for Element 3 if your sample does not
have a third element.
a. Select an area of the meteorite that appears to contain a single
mineral to study.
b. Make and record observations about the mineral in the data
table below.
c. Measure the mass of the mineral sample and record it in the
data table.
d. Dissolve the mineral sample in the test tube, and place the test
tube in the mass spectrometer.
e. Analyze the output from the mass spectrometer, and record it in
the data table. Each peak corresponds to a different element with a
different atomic mass, as indicated along the horizontal axis. The
height of the peak along the vertical axis corresponds to the mass
of that element in the sample. The specific values can be seen by
clicking on the top of each peak.
5. Identifying Elements Examine the mass per atom (u) values from your output
and compare them to the values for atomic mass on the periodic table. (There
is a periodic table available in the Tools menu of the virtual lab.) Which
elements have atomic masses that match? Record these elements in the
calculation and analysis table.
6. Determining Molar Mass of Elements In the space below, describe the
relationship between molar mass and atomic mass. Referring to the periodic
table, record the molar mass of the elements in the calculation and analysis
table above.
7. Calculating Amounts of Elements Using the mass amounts from the mass
spectrometer output and the molar mass of the elements, calculate the
amounts of each element present, in moles. Enter the results of your
calculations in the space below. (Hint: Remember that your results are in
micrograms. You’ll need to convert your mass values to grams before
converting to moles.)
8. Working with Significant Figures Examine the data you used for your
calculation. How many significant figures should your results have? If you
haven’t already rounded them to the appropriate number of significant figures,
do so, and record the results in the calculation and analysis table.
9. Finding Subscripts Divide the amount of each element in moles by the smallest
mole amount in your data table, showing your work below. If the numbers are
close to whole numbers, these are the subscripts for the elements in your
empirical formula. If they are not, multiply them by a small number, such as 2
or 3, that provides near whole-number results. Record both the unrounded ratio
and the rounded whole-number subscripts for each element in the calculation
and analysis table.
10. The Empirical Formula What is the empirical formula for your mineral? A
sample formula is provided below to help you with the formatting of the
formula. Edit it as needed to reflect your results. (XaYbZc)
11. Error Analysis Typically, empirical formula calculations provide results that
are close to whole-number ratios, but not exactly. Were your results higher or
lower than you expected? What are some potential sources of error in the data
and calculations?
12. Making Judgments What criteria would you use for rounding off empirical
formula data to get to whole-number coefficients? Would you round 5.51 to 6?
What about 5.75 or 5.90?
SUMMARY AND CONCLUSION
13. Results Using the table at the beginning of this lab report, determine which
mineral is the likeliest candidate for your sample’s identity.
14. Reflections Based on what you know about how a mass spectrometer works,
would you expect that a trace impurity (less than 0.5%) would measurably
impact your results? Explain why or why not.
15. Conclusions Describe the level of confidence you have in your results and
your identification of the mineral. Is there more than one possible answer? Can
you rule out any of the possibilities for sure? Explain what scientific reasons you
have for your level of confidence.
EXTEND 1
If you will be performing additional analyses on other samples, adjust or replace
these tables to suit your plan for performing this activity. Once they fit your plan,
you can copy and paste the tables into this lab report as many times as you will
need them.
Observations of Sample
EXTEND 2
Goal
You will analyze an element sample with a mass spectrometer to identify and
determine the relative masses of each isotope present.
Your Plan
17. List the steps of your plan for using the equipment in the virtual lab to
achieve the goal. Your plan should include what you will do and the order in
which you will do it.
18. Adjust or replace the tables below to suit your plan for performing this
activity. Once they fit your plan, you can copy and paste the tables into this lab
report as many times as you will need them.
Calculation and Analysis Table
19. Totaling Accumulated Mass For each element whose isotopes you test, total
the accumulated mass from all of the isotopes of that element. Record the
result in the bottom row of the data table.
20. Calculating Relative Abundance For each isotope, calculate its relative
abundance by dividing its accumulated mass by the total accumulated mass
from the previous item. Record the result in the calculations and analysis table.
21. Calculating the Weighted Average Atomic Masses For each isotope, calculate
a weighted atomic mass in units of u by multiplying the mass per atom by the
relative abundance, calculated in the previous item. Record your results in the
calculation and analysis table.
22. Calculating the Average Atomic Mass of an Element Calculate the average
atomic mass of the element by totaling the weighted average atomic masses,
and record the value in the calculation and analysis table.
23. Comparing Your Results Using a periodic table, identify the expected value
for the atomic mass of your element, and compare it to the one you recorded in
the table. If there is a difference, calculate the percent error.
Magnesium
Chlorine
Copper
Observations of Sample
Total mass (µg):
Sample ID:
Other observations:
Data Table
Element
Element 1
Accumulated mass (µg)
Mass per atom (u)
Element 2
Element 3 (if needed)
Calculation and Analysis Table
Element
Identity
Molar mass
(g/mol)
Amount
(umol)
Ratio
(unrounded)
Subscript in
empirical
formula
Element 1
Element 2
Element 3 (if
needed)
The Empirical Formula What is the empirical formula for your mineral? A sample formula
is provided below to help you with the formatting of the formula. Edit it as needed to reflect your results.
Observations of Sample
Total mass (µg):
Sample ID:
Other observations:
Data Table
Element
Element 1
Accumulated mass (µg)
Mass per atom (u)
Element 2
Element 3 (if needed)
Calculation and Analysis Table
Element
Identity
Molar mass
(g/mol)
Amount
(umol)
Ratio
(unrounded)
Subscript in
empirical
formula
Element 1
Element 2
Element 3 (if
needed)
The Empirical Formula What is the empirical formula for your mineral? A sample formula
is provided below to help you with the formatting of the formula. Edit it as needed to reflect your results.
Observations of Sample
Total mass (µg):
Sample ID:
Other observations:
Data Table
Element
Element 1
Accumulated mass (µg)
Mass per atom (u)
Element 2
Element 3 (if needed)
Calculation and Analysis Table
Element
Identity
Molar mass
(g/mol)
Amount
(umol)
Ratio
(unrounded)
Subscript in
empirical
formula
Element 1
Element 2
Element 3 (if
needed)
The Empirical Formula What is the empirical formula for your mineral? A sample formula
is provided below to help you with the formatting of the formula. Edit it as needed to reflect your results.
Observations of Sample
Total mass (µg):
Sample ID:
Other observations:
Data Table
Element
Element 1
Accumulated mass (µg)
Mass per atom (u)
Element 2
Element 3 (if needed)
Calculation and Analysis Table
Element
Identity
Molar mass
(g/mol)
Amount
(umol)
Ratio
(unrounded)
Subscript in
empirical
formula
Element 1
Element 2
Element 3 (if
needed)
The Empirical Formula What is the empirical formula for your mineral? A sample formula
is provided below to help you with the formatting of the formula. Edit it as needed to reflect your results.
EXTEND 2
Element:
Data Table
Isotope
Mass per atom (u)
Accumulated mass (µg)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total accumulated mass:
Calculation and Analysis Table
Isotope
Percentage abundance
Weighted average atomic mass
(u)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total average atomic mass (u):
Comparing Your Results Using a periodic table, identify the expected value for the
atomic mass of your element, and compare it to the one you recorded in the table. If there is a
difference, Calculate percent error.
EXTEND 2
Element:
Data Table
Isotope
Mass per atom (u)
Accumulated mass (µg)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total accumulated mass:
Calculation and Analysis Table
Isotope
Percentage abundance
Weighted average atomic mass
(u)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total average atomic mass (u):
Comparing Your Results Using a periodic table, identify the expected value for the
atomic mass of your element, and compare it to the one you recorded in the table. If there is a
difference, Calculate percent error.
EXTEND 2
Element:
Data Table
Isotope
Mass per atom (u)
Accumulated mass (µg)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total accumulated mass:
Calculation and Analysis Table
Isotope
Percentage abundance
Weighted average atomic mass
(u)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total average atomic mass (u):
Comparing Your Results Using a periodic table, identify the expected value for the
atomic mass of your element, and compare it to the one you recorded in the table. If there is a
difference, Calculate percent error.
EXTEND 2
Element:
Data Table
Isotope
Mass per atom (u)
Accumulated mass (µg)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total accumulated mass:
Calculation and Analysis Table
Isotope
Percentage abundance
Weighted average atomic mass
(u)
Isotope 1
Isotope 2
Isotope 3 (if needed)
Total average atomic mass (u):
Comparing Your Results Using a periodic table, identify the expected value for the
atomic mass of your element, and compare it to the one you recorded in the table. If there is a
difference, Calculate percent error.