Permanganate reaction with oxalic acid

Handouts for Inquiry-Based Redox and Electrochemistry Labs
Steve Sogo
Laguna Beach High School
[email protected]
Instructor’s Notes for #138: Color by Number
Instructional video from ACR92651: http://youtu.be/ZIwhDIzZVCA
Each lab group needs:
1x Erlenmeyer flask (125 or 250 mL)
1x 150 mL beaker
One or two graduated cylinders (25 mL recommended size)
Set-Up for 32 lab groups
 Need about 1-liter of 3 M H2SO4 (count on each lab group using 30 mL). Distribute into
4 or 5 reagent bottles on buffet table
 Make about 1-liter of 0.015-M KMnO4 solution (2.37 g KMnO4 per 1-liter distilled
water). Distribute into 4 or 5 reagent bottles on buffet table (keep remainder in reserve).
If doing the Shadow of Doubt and Let There be Light labs, make 2-liters of 0.015 M
KMnO4.
 Set out solid oxalic acid next to weighing scales (actual compound is the dehydrate, but
you can pretend that it is anhydrous for student calculations)
 1-liter waste beaker on buffet table
Have available (in reserve--produce these upon student request):
 manganese(II) salts (MnSO4, MnCl2, Mn(NO3)2) solids are fine--students to use 0.10
grams for catalytic trials
 6 M H2SO4 (2 x 200 mL bottles)
 Sparkling water (club soda)
 3x concentrated KMnO4 solution (.045 M) (one or two 200 mL bottles)
What to expect:
Typically, the initial reaction and analysis requires 45 minutes of class time. Part Two of the
lab (unscripted experiments) will take 30-45 minutes for students to formulate a hypothesis,
design an experiment (with some input from the instructor), and carry out the experiment. The
instructor will need to provide materials for many of the experiments--the goal is for each lab
group to try a different experiment, so limiting the number of bottles of each “extra” chemical
helps-- students should be instructed not to share their special reagents with any other groups.
If students are investigating the use of heat, it is best to start the experimental reaction with
pre-heated reactants (the oxalic acid + sulfuric acid mixture can be preheated using a microwave
or Bunsen burner). A temperature of 50-70C is a good place to start, but even near boiling is
OK (reaction will be instantaneous at such a high temperature).
Assignment #138: Color By Number (Lab)
Permanganate reaction with oxalic acid
Write-Up: Everyone will turn in the question page of the lab (on Monday) for
7.5 points. If you want a better grade than this, you will also need to make a
paragraph-based write-up describing the experiments you designed in step #8.
Your paragraphs should be thoughtful, explaining your ideas instead of just
stating what you did.
Procedure: (Bring a calculator, periodic table, and pink page to your table)
1. You will need 1 clean beaker and 1 clean flask for this lab. The flask will be to create a
solution of oxalic acid solution, and the beaker will be used to run redox reactions.
2. Weigh out between 0.62 and 0.74 grams of solid oxalic acid. Then dissolve this
solute in enough water to make the concentration equal to 0.20-molar. Hint: your
calculated volume should be in the range between 30 and 45 mL.
3. Using a graduated cylinder, measure out 10 mL of your oxalic acid solution into the
REACTION BEAKER (save the remaining 30-45 mL of oxalic acid solution for future experiments). Place a
SMALL MAGIC BEAN in the REACTION BEAKER and place it atop the magnetic stir plate.
4. Add 10 ml of 3-molar sulfuric acid (H2SO4) to the reaction beaker. Sulfuric acid is a 150 mL beaker
strong acid that is very effective at burning holes in clothing. Because the H2SO4 molecule can
form many friendship bonds (hydrogen bonds), the acid evaporates very slowly, so a drop that
gets on your clothes will remain there for hours, slowly eating away the fabric. Note: don’t expect
to see any reaction between the sulfuric ACID and the oxalic ACID.
5. To start the redox reaction, add 10 ml of 0.015-molar potassium permanganate solution
(KMnO4) to your reaction beaker and stir with the magic bean for a few seconds. After the
solutions are mixed, STOP stirring. Watch the beaker as it goes through several color changes
and RECORD THE TIME it takes for the reaction to go to completion (start timing as soon as you
mix the purple KMnO4 into the beaker). Expect the reaction to take a FEW MINUTES to run to
completion. The reaction is done when the solution is colorless.
6.Look carefully at the solution once the reaction is done to see subtle clues as to the products of
the reaction (in particular, look for some TINY BUBBLES that may accumulate on the magic bean).
7. AFTER THE REACTION HAS FINISHED, answer the questions on the next page. You should be
able to figure out all the answers if you apply the theories you have learned this week!
8. Once you understand the chemistry of the reaction, try to perform experiments of your own
design to accomplish the following tasks:
i. eliminate the "lag time" in the beginning of the reaction (when it is purple and just sits there)
ii. arrest the progress of the reaction at one of the intermediate colors so that you can keep the
color permanently (or at least for a long time)
Note: When faced with a challenge of this sort, a chemist would consider three general ways of
changing a reaction’s rate:
a) Alter the TEMPERATURE of the reaction
b) Alter the CONCENTRATIONS of reactants (your instructor has solutions of varying molarities
available for your use!)
c) Include a CATALYST in the reaction (this is the most interesting idea to try if you have a clue as
to what the catalyst might be!!!!)
Assignment #138 (continued) Color By Number Lab Questions:
A. What is the OXIDATION NUMBER of the Mn atom in KMnO4? Hint: K is a +1 ion.
B. The manganese atom ends this reaction as a free-swimming Mn2+ ion. Based on your experimental
results, what is the COLOR of manganese in a +2 oxidation state?
C. Explain how the REDUCTION of manganese can produce the many colors seen during the reaction.
Hint: consider the TITLE of this lab!!!
D. The structure of the oxalic acid molecule is shown below. Assign an oxidation number to each atom
in the structure.
E. When manganese is reduced (gaining electrons), something must be oxidized (losing electrons). In
this case, the element that is oxidized is in the oxalic acid molecule. Based on your understanding of
oxidation numbers, WHICH ELEMENT in the oxalic acid is being oxidized? Hint: Your choices are limited to
H, C, and O. Only one of these is a “variable” that can change its number. . .
F. Determine the OXIDATION NUMBER OF CARBON in each of the molecules shown below. Then EXPLAIN
why only CO2 is a plausible identity for the molecule produced when oxalic acid is OXIDIZED.
H2CO
CO2
HCOOH
G. Using the idea of wolves and goats, fill in the appropriate coefficients to balance the chemical
equation for the reaction of permanganate with oxalic acid:
___ MnO4- + ___ H2C2O4
+ ___ H+
 ___ Mn2+ + ____ CO2 + ____ H2O
Mn (wolf) goes from +7 to +2, gobbling up ___ e-.
C (goat) goes from ___ to ___, providing ___ e-.
H+ ions are
supplied by H2SO4
(strong acid)!
Each oxalic acid
molecule contains
TWO carbon atoms!
Need ___ carbons to “feed” each Mn.
H. You may have noticed that the reaction in this lab starts very slowly, but appears to speed up after a
minute or two. The reason for this acceleration in rate is that the reaction is “autocatalytic”. Use the
suggestions below to come up with a hypothesis for how the catalyst works its “magic”. Note: you are
encouraged to test your hypothesis by performing appropriate experiments in procedure #8.
a) The catalyst is one of the reactant molecules
b) The catalyst is one of the product molecules
c) The catalyst is a substance that does not appear in the chemical equation
Explain your choice in the space below.
Note: after completing the question page, return to the previous page to complete step #8.
Notes for #142: Oxidizing anions (now called A Shadow of Doubt)
Instructional Video from ACR92651: http://youtu.be/wwrgx4daWrc
This is a beautiful lab--many vibrant colors and miraculous transformations. The write-up for
this lab requires students to develop cogent arguments that take into account various types of
data in an internally consistent manner. This is quite a challenge for high school sophomores,
who often double back in their logic to contradict themselves!
For this lab, students are provided with a table of half-reactions (see last page of this handout for
a sample).
The set-up for the lab is fairly simple—solution to be made are
100 mL each of
0.15 M NaBr (or KBr)
0.15 M NaI (or KI)
0.25 M NaCl (or KCl)
0.15 M Na2SO3
Solutions placed in color-coded 2 x 50 mL portions polystyrene widemouth jars (with color
coded matching pipets). Available on the buffet table
ABCD salt solutions can be refrigerated overnight—important for preservation of the sulfite,
which is susceptible to air oxidation. If the sulfite is left unrefrigerated overnight, it may be
best to make a fresh solution. Longer storage of the sulfite solution is not recommended.
Buffet Table also provides:
 0.015 M KMnO4 provided in 5 reagent bottles with pipets in bottles. Do not reuse the
same bottles provided in the Color by Number lab, as they may contain traces of sulfuric
acid, which will allow partial oxidation of Br- in the Shadow of Doubt lab.
 3 M H2SO4 provided in 5 or 6 reagent bottles (with pipets in sidecar test tubes)
 Heptane provided in 3 reagent bottles with pipets in sidecar test tubes
 1-liter WASTE beaker (add a scoop of sodium bisulfite to decolorize this solution
(reduces I2, Br2, Cl2, MnO4-))
Each student lab station requires:
 6x small test tubes (13 x 100 mm)
 1x test tube rack
 Vortex mixer
 centrifuge may be helpful
In past years, students have misidentified bromide and chloride because they believe that the
yellow reaction with the big smell is chlorine. They are unwilling to admit that Br2 might have
an odor similar to that of chlorine. I’m hoping that with the “Shadow of a Doubt” title, more
students will be willing to admit that they have conflicting evidence (or incomplete evidence).
Assignment #142: A Shadow of Doubt?
(LAB)
Overview: In this lab, you will perform redox reactions with a variety of common anions
(ANION = A NEGATIVELY CHARGED ION). Each reaction can be understood using half-reactions to
identify the products of oxidation and reduction. At the start of the lab, you will NOT KNOW
the identities of the various ions, but you may be able to DEDUCE them based on the experimental
evidence you collect. However, it is quite likely that (as the title of the lab implies) you may be
faced with some doubt as to which anion is which.
Write-up instructions: Please make a multi-paragraph write-up that does NOT copy any
phrases or sentences from the instruction page. Be sure to write balanced chemical equations for
all reactions that occur (that means 6 total equations!) and explain WHY things worked the way
they did. Include pictures that show the COLORS present in the test tubes, and explain what
molecules/ions create these colors. Present your evidence in as convincing a manner as possible.
If you are left with a shadow of doubt, please explain the reasons for your doubt.
Procedures: As always, start by equipping yourself with proper safety gear!
1. To do this lab, each individual will need a half-reaction chart and some scratch paper.
2. At your lab station, you should find 4 clean test tubes in the test tube rack.
3. Your instructor will show you bottles containing the 4 salt solutions you will be using in
this lab. Each bottle is filled with a solution of a sodium or potassium salt containing a
particular anion. It is the anion that is of importance in today's experiments. The salts are
labeled A, B, C, & D, and the four anions (in random order) are CHLORIDE, BROMIDE, IODIDE,
and SULFITE.
4. Use your half-rxn chart to find an OXIDATION HALF-REACTION for chloride, bromide and
iodide. Copy these onto your note page. Also copy the following half-reaction for the
oxidation of sulfite ion onto your note page:
SO32- (aq) + H2O (l)  SO42- (aq) + 2 H+ (aq) + 2 eE° = -0.20 Volts
5. Use the pipets provided in the stock jars to accurately measure 1 mL of Salt A
into a labeled test tube. Then measure out 1 mL of Salt B into a second tube.
Continue with salts C and D in your two remaining test tubes. After collecting all
four salt solutions, check your test tubes to see that they all contain the same volume of
liquid. If one seems to be “off”, send it back for a refill.
6. Use a graduated pipet to accurately add 1 mL of 0.015-molar potassium
permanganate (KMnO4) solution to each of your four test tubes. Note: please
“borrow” a bottle of permanganate from the buffet table.
7. Look for signs of reaction. Describe (sketch?) the changes that you see. You should have
TWO tubes that have reacted (and two tubes that have not reacted). At this point, you have
added KMnO4 without any acid (H+). In the absence of acid, permanganate undergoes the
following half-reaction (note the electrode potential).
MnO4- (aq) + 2 H2O (l) + 3 e-  MnO2 (s) + 4 OH- (aq)
E = +.59 volts
Use this half-reaction to determine why you have TWO tubes that have reacted and TWO tubes
that have NOT reacted. Write BALANCED EQUATIONS for the TWO reactions that have
occurred.
8. Thoughtfully consider the chemical equations you have written, looking for evidence of
reaction products in your test tubes. You may find it helpful to test the pH of a drop of liquid from
the tubes that have reacted!
Assignment #142: A Shadow of Doubt? (continued)
9. In the presence of acid, MnO4- undergoes the following half-reaction, with a potential of
+1.50 volts:
MnO4- (aq) + 8 H+ (aq) + 5 e-  Mn2+ (aq) + 4 H2O (l)
Question: If the reaction mixture is acidified to increase permanganate’s potential to +1.50 volts,
which of the anions (Cl-, Br-, I-, SO32-) should become oxidized?
10. Write FOUR balanced redox equations for the reaction of ACIDIFIED MnO4- with all the anions
in this lab (include electrode potentials). Hint: this is not much work if you realize the
similarities between the oxidation half-reactions!
11. Based on your BALANCED EQUATIONS and the hints provided below, make predictions of
what you should expect to see (and smell) in your 4 test tubes.
Cl-, Br-, I-, SO32-: these are the ions your started with--you already know that all of these ions are
colorless with no particular odors.
Mn2+: you saw this ion last week in your Color by Number lab!
Chlorine (Cl2) from the Greek chloros, meaning “yellow-green”: Chlorine gas dissolves well in water to
produce a pale yellow-green color. As you know, chlorine has a powerful odor.
Bromine (Br2) from the Greek bromos, meaning “stench”: Orange-red when concentrated, yellow when
dilute. Some swimming pools utilize bromine instead of chlorine as a disinfectant.
Iodine (I2) from the Greek iodes, meaning “violet”: Yellow, orange, brown or red when in aqueous
solution. Violet when dissolved in non-polar solvent. Also can produce violet vapors.
Sulfate (SO42-) The color of sulfate ion is evident in the bottle of 3-M sulfuric acid.
12. Use a plastic pipet to add 1 mL of 3-molar H2SO4 to all four tubes. Agitate and look for
color changes. Please borrow a bottle of sulfuric acid from the buffet table to perform this step.
13. Sketch the appearance of your test tubes at this stage. If you still have a purple color at this
stage, it means that the PERMANGANATE has NOT yet been REDUCED.
14. Carefully smell the contents of each tube. Wafting recommended!
15. Compare the results observed with the results you expected based on your balanced
equations. You should have some discrepancies between expected and observed results, which
will lead to doubt, but you should be able to identify some of the anions.
16. Remove 1 mL of solution from your purple test tube and transfer to a clean test tube. This
tube should remain heptane-free and will be used in step #19.
17. To gather further evidence, you will use heptane as a non-polar organic solvent to “extract”
the non-polar chemicals present in your test tubes. Heptane is a hydrocarbon with the formula
C7H16 that will form a layer on top of the water.
Use a pipet to add about 1 mL of heptane to each of your 4 original tubes and vortex
vigorously. Heptane (although flammable) is rather inert in most situations. It is NOT reacting
with anything in this experiment. Its only purpose here is to act as a solvent. The heptane will
extract any non-polar molecules produced in the reactions. Look for signs of these non-polar
molecules in the heptanes layers
18. Identify the molecules that are producing colors in your test tubes. Try to label the contents
of each tube in BOTH the TOP AND BOTTOM LAYERS (i.e. what non-polar molecules are in the
heptane layer? What ions and molecules are in the aqueous layer??).
19. At this point, you still have one tube that has undergone very little reaction. Therefore, it
hasn’t progressed to make products that would give it a unique color or smell. In order to speed
the rate of this reaction, you should put 60 mL of tap water in a beaker, microwave the water for
1 minute, and immerse the tube containing the purple solution that you reserved in step #16 in
the hot water bath. Look for signs of reaction. A smell test may help identify products that are
forming.
20. When you are finished, pour the contents of all your tubes into the waste beaker on the
buffet table. Rinse your tubes with water and set them upside-down in your test tube rack.
Notes for #146: Let There Be Light!
Instructional video from ACR92651: http://youtu.be/MoR9TjOamQM
This lab is an exciting day, in which students discover the power of electrochemistry. Students
must make some intelligent decisions in the design of their galvanic cells in order to produce a
battery capable of lighting up an LED. For those students who successfully achieve this task
with time left on the clock, a second challenge is to wire two student-made cells together in
series to create a higher voltage.
The initial hands-on challenge is to create a standard copper/zinc galvanic cell, which will be
easy for students who have done their homework. This standard cell utilizes a salt bridge.
Students measure the functionality of their galvanic cell using a volt/ammeter (both voltage and
current output are measured). Typically, the voltage is very close to the standard potential of
1.10 volts, but the current is very low (less than 1 milliamp). In order to light an LED, a voltage
of 1.7 volts and at least 10 mA are required.
During the second part of the lab, each lab group is asked to build a better battery (one capable of
lighting an LED) using an assigned "special" chemical. The special chemicals are assigned using
index cards. Each card says, “Your special chemical is. . .” and provides guidelines on volumes
to use.
3x KMnO4 Back of card suggests that a second chemical is needed!
3x FeCl3 Back of card suggests using the alkaline zinc half-reaction!
3x Mg(s)
Examples of Cards:
Your Special Chemical is:
KMnO4 (aq)
Use about 45 mL of 0.015 M
KMnO4
Your Special Chemical is:
FeCl3 (s)
Dissolve about 0.5 grams in
75 mL distilled H2O
Your Special Chemical is:
Mg (s)
Front
of card
Back
of card
Front
of card
Back
of card
Front
of card
Back
of card
Hint: Consider what chemical
you should add to help the
MnO4- reach its full
potential!
Hint: To make a bright light,
try to find a way to make
your oxidation ½-cell produce
1.25 volts!
Lab Set-up:
Materials required
a) zinc and copper strips to use as electrodes
b) Solid CuSO45 H2O
c) Solid ZnSO47 H2O
d) 0.25 M Na2SO4 (1 liter) for salt bridges distributed into several beakers for student use
e) 0.015 M KMnO4 solution (about 1-liter needed for this lab)
f) Ground ferric chloride solid
g) 3 strips of magnesium ribbon (labeled)
h) graphite electrodes
i) voltmeters and appropriate electrical cables
j) 1-liter waste beaker (labeled) for permanganate waste
Buffet table provides:
Table 1 = salt bridges, cotton, salt bridge solution, waste beaker, CuSO4 recycling beaker
Table 2 =
1 bucket of porous cups (soaking in lightly salted water): one cup per lab group
3 bottles 0.015 M permanganate
3 bottles 1 M H2SO4
3 jars solid FeCl3
3 strips Mg(s)
3 jars MgSO4 (s)
6 graphite rods (for use as electrodes)
Each lab table needs
1 voltmeter (in box?)
2 patch cords of differing colors
1 copper electrode
1 zinc electrode
Examples of LEDs used in this lab (obtained from RadioShack)
Red
Yellow
Flat Blue
Bullet Blue
Mystery #1 (jumbo)
Mystery #2 (jumbo)
7-color flashing LED
1.7 volts
2.1 volts
3.2 volts
3.7 volts
2.4 volts
3.5 volts
3.2 volts
20 mA
20 mA
20 mA
20 mA
20 mA
20 mA
20 mA
For write-up, make it clear that the battery desired is a single cell, NOT the super battery.
For this lab, students are provided with a table of half-reactions (see last page of this packet for
an example).
Assignment #146: Let There Be Light!
Building batteries in the lab
In the beginning, God created the heavens and the earth, and the earth
was without form and void. . .And God said, “Let there be Light”. And
there was light. Genesis 1:1-1:3
Overview: Your goal in this lab is to make a powerful battery, capable of lighting up some
miniature light bulbs (LED’s). You will all start by making a standard copper/zinc cell. Then
you will try to make a BETTER battery using a particular “special ingredient”.
Part One: For the zinc/copper cell, you should use:
1. Two 250 mL beakers, each containing 75 mL of distilled water
2. A strip of zinc metal (for use as an electrode)
3. A strip of copper metal (for use as an electrode)
4. Between 1.2 and 1.6 grams of solid copper sulfate
5. Between 1.2 and 1.6 grams of solid zinc sulfate
6. A salt bridge (filled with .25 M Na2SO4).
Use the materials described above to construct a battery in the manner you have seen in your
homework assignments.
In order to determine how well your battery works, you will use a digital voltmeter to measure
the voltage and current output of your battery.
a) Measure VOLTAGE by turning the dial on your voltmeter to the 20 V setting (indicating DC
voltage). Use an alligator clip to connect the black lead of the voltmeter to the ANODE of your
battery. Use a second alligator clip to connect the red lead of the voltmeter to the CATHODE of your
battery.
Your voltage should measure close to 1.10 volts (the theoretical potential of the redox reaction). If
your voltage is not close to 1.10 volts (or if it jumps around wildly), you probably have a bad
electrical connection. Check to make sure your alligator clips are secure. You may also want to
shine up your metal electrodes using a Scotchbrite scrubbing pad (available at any of the sinks).
b) To measure MILLIAMPS, first remove the plugs on the meter. Turn the dial to the 20m setting in
the A section of the meter (indicating DC amps). Reconnect the leads to the voltmeter (black to
anode and red to cathode). You should get a current reading less than 1 milliamp.
Record your voltage and current readings and show them to your instructor when he/she passes
by your table.
Remove the salt bridge from your battery set-up while measuring the voltage (or current). Your
voltage/current should drop to zero. Then reinstate the salt bridge to complete your circuit—thus
restoring your voltage/current. This demonstration should emphasize the importance of the t salt
bridge.
Make a rough sketch of your battery set-up and identify the direction of electron flow
through the wires. Include the two relevant half-reactions (with potentials) in your sketch.
Assignment #146: Let There Be Light! (continued)
Part Two: You will now try to make a better battery. In order to do this, you will need new
chemical species so that you can run more powerful half-reactions.
1. For the better battery, REPLACE YOUR SALT BRIDGE with a POROUS CUP to maximize electrical
current (milliamps). The porous cups provided on the buffet table are designed to fit inside a 400
mL beaker. This set-up will allow you to have TWO COMPARTMENTS within a single beaker.
Note: a porous cup allows MIGRATION OF IONS between the two compartments. Since the ions have a LOT
of surface area through which they can migrate, a porous cup provides less resistance than a salt bridge.
2. Your instructor will give you a CARD which specifies a “special” chemical that you will use to
improve your existing set-up. These chemicals will be available on the buffet table.
3. You will use your special chemical to create a new half-cell, which you will combine with
one of your original half-cells to make a superior battery. You must decide which of your
original half-cells (the zinc or copper half-cell) you will keep for use in your better battery.
4. If you are using a powerful “wolf”, you will need to employ an inert GRAPHITE ELECTRODE
(non-oxidizable). Graphite electrodes are available on the buffet table.
5. Design your improved battery on paper before you try to construct it in real-life. Remember
that you need a wolf (oxidizing agent) and a goat (reducing agent) in separate compartments in
order to make a functional battery.
6. After constructing your “new and improved” battery, MEASURE THE VOLTAGE and MILLIAMPS
produced by the cell (USE THE 200m SETTING IN THE A SECTION TO ACCURATELY MEASURE
MILLIAMPS). You should achieve a voltage  1.5 volts and a current  10 mA. Note: voltage and
current data should be included in the scientific diagram that you turn in for a grade.
7. Let There Be Light! If your voltage and current readings exceed the lower limits
described in step #6, you should attempt to light an LED. Disconnect the voltmeter and use
alligator clips to hook up your battery to the red LED provided at your lab station. When using
an LED, the longer lead (marked with a + sign) should be attached to the cathode of your
battery. Note: it is expected that every group will light a red LED. To get the other LEDs to light, you
should combine volts with another group as outlined below.
8. If you have time, connect your battery to your neighbors’ battery to create a
“super” battery of very high voltage. In order to do this, you will have to make
intelligent connections (a physicist would say that you have to connect your cells
in SERIES). Measure the VOLTAGE and CURRENT of your super battery. Then try
to light some of the high voltage LEDs.
Batteries
in series
9. When cleaning up, you should pour your copper sulfate solution into the
CuSO4 RECYCLING beaker. Permanganate goes in the WASTE beaker on buffet
table. All other solutions that you used in the lab can go down the drain.
Write-up instructions: Draw a careful SCIENTIFIC DIAGRAM of the BEST SINGLE battery that you
constructed during the lab period. Label everything that is important, and try to show HOW THE
CHEMISTRY WORKS. You may want to have “windows” in your diagram where you zoom in to
show the details of the chemistry that is occurring at each electrode.
Please do NOT try to draw a picture of a “super battery” (a combination of your cell with another
group’s cell). Show only a single cell in your diagram.
Minimum size for the scientific diagram = 8.5 x 11”
Maximum size = 11 x 17”