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Introduction to Graphing
Investigation
Manual
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DISTANCE
INTRODUCTION TO GRAPHING
Table of Contents
2
Overview
2
Objectives
2
Time Requirements
3
Background
7
Materials
7
Safety
7
Activity
9
Activity 2
11 Activity 3
Overview
Scientific investigation requires the analysis and interpretation of
data. Knowing how to graph and what the different components
mean allow for an accurate analysis and understanding of data. In
this investigation you will practice creating graphs and use some
simple statistical tools to analyze graphs and datasets.
Objectives
• Create graphs from datasets, both by hand and electronically.
• Analyze the data in the graphs.
• Compare the slope of trendlines to interpret the results of an
experiment.
Time Requirements
Activity 1: Graphing by Hand ………………………………….. 20 minutes
Activity 2: Computer Graphing………………………………… 20 minutes
Activity 3: Linear Regression …………………………………… 20 minutes
Key
Personal protective
equipment
(PPE)
goggles gloves apron
(i)
• 47 •
follow
link to
video
photograph stopwatch
results and
required
submit
warning corrosion flammable toxic environment health hazard
Made ADA compliant by
NetCentric Technologies using
the CommonLook® software
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Background
Science requires the collection of data to test
hypotheses in order to see if it supports or
does not support ideas behind the experiment.
Collecting data creates a record of observations
from experiments that is needed to ensure the
ideas in a hypothesis are accurate. This allows
the scientist to better understand the processes
they are investigating. Sharing data is critical
since it allows other scientists to examine the
experimental setting and draw conclusions
based on the data obtained. It also allows for
the replication and comparison of data obtained
in the experiment to confirm results and conclusions. This will aid in the understanding of a
scientific principle.
The aim of this experiment was to examine
growth rates of the two plant types in
comparison with each other in order to
find out which grows under a certain set of
environmental circumstances.
When looking at an experiment, the
experimenter is typically looking at variables that
will impact the result. A variable is something
that can be changed within an experiment.
An independent variable is something the
experimenter has control over and is able
to change in the experiment. Time can be a
common independent variable as the total
duration of the experiment can be changed or
the intervals at which data is collected can be
changed. A dependent variable changes based
on its association with an independent variable.
In the data from Table 1, the measured height of
the plant was the dependent variable. The aim of
Table 1, shows data from a study of plants. Two
types of plants, wheat and rye, were grown
over 8 weeks, and the height of the plants were
measured in centimeters (cm).
Table 1.
Height in cm
Week
Wheat Plant 1 Wheat Plant 2 Wheat Plant 3 Rye Plant 1
Rye Plant 2
Rye Plant 3
1
2.0
3.0
0.0
0.0
1.0
0.0
2
3.0
3.0
2.0
1.0
2.0
1.0
3
5.0
5.0
3.0
1.0
2.0
2.0
4
6.0
6.0
4.0
2.0
3.0
3.0
5
7.0
7.0
5.0
3.0
4.0
3.0
6
9.0
8.0
7.0
3.0
4.0
3.0
7
10.0
9.0
7.0
4.0
5.0
4.0
8
10.0
10.0
7.0
5.0
6.0
5.0
continued on next page
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INTRODUCTION TO GRAPHING
Background continued
experiments is to determine how an independent
variable impacts the dependent variable. This
data can then be used to test the hypothesis
which has been made at the beginning of the
experiment.
Data can be presented in different ways. One
way is to organize it into a table as it is being
collected. When working with a limited amount
of data points, this can be the best option; for
larger studies, the data in data tables can be
overwhelming and difficult to interpret. To help
see the trends in large data sets, a scientist
may rely on summary statistics and graphical
representations of the data.
Summary Statistics
Summary statistics are methods of taking many
data points and combining them into just a few
numbers. The most common summary statistic
is an average, or arithmetic mean. An average
is the sum of a group of numbers, divided by
how many numbers were in the set. To find
the arithmetic mean you find the sum of the data
to be averaged and divide by the number of
data points. For instance: If we wanted to find
the average wheat plant height in week 8 from
the above data we would perform the following
calculations:
Equation 1:
average=
In this equation, x1 indicates the first number in
a data set, x2 would be the second number, and
so on. xn is the last number in the set. The “n”
is the number of items in the set. So a dataset
with 8 numbers would go up to x8. This is the
4
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same “n” that the sum of the numbers is divided
by. Using equation 1 for the wheat plant height
in week 8 would give the following equation.
average = ___3_ __
Since there are 3 wheat plants in week 8, there
are 3 numbers that would be added together
(x1 x2 x3) divided by the number of plants (3).
average= 10 + 10 + 7 = 9 cm
3
In science it is important to know how much
variation is found in the data collected. The
most common measurement of variation is the
standard deviation. To calculate the standard
deviation:
1. Calculate the average of a data set.
2. Calculate the difference between each data
point and the average.
3. Square the result.
4. Find the average of these squares. This
yields the variance (σ2).
5. Taking the square root of the variance gives
the standard deviation (SD) as seen in
Table 2.
The standard deviation is an indication of the
distribution of your data. In the example above,
the average height of the plants was 9 cm. The
standard deviation was 1.4 cm. Statistically this
indicates that 68% of the data was within
1.4 cm of the average. In this way it is a useful
tool to gauge how close the results on an
experiment are to each other.
continued on next page
CAR@UNA~
Table 2.
Height at Week 8 (cm)
Difference from Average
Difference Squared
Wheat Plant 1
10
10 – 9 = 1
(1)2 = 1
Wheat Plant 2
10
10 – 9 = 1
(1)2 = 1
Wheat Plant 3
7
7 – 9 = -2
(-2)2 = 4
(10+ 10+ 7)
=9cm
3
Variance
Average
Standard Deviation
=
(1 + 1 + 4)
=2
3
= -)variance = J2 = 1 .4
that the variance in Groups 1 and 2 is much
greater than in Groups A and B (Figure 2).
Interpreting Graphs in Scientific Literature
and Popular Press
Graphs are an excellent way to summarize
and easily visualize data. Care must be taken
when interpreting data from a graph or chart.
Information can be lost in summarization and
this may be critical to our
interpretation. For example,
Figure 1.
in Figure 1, the average age
of 4 groups of people was
graphed using a bar graph. A
45
bar graph is most useful when
40
directly comparing data as it
allows for differences to be
35
more easily seen at a glance.
30
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Looking at Figure 1, it is
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ACTIVITY
Materials
ACTIVITY 1
Needed but not supplied:
• Graphing Software (Excel®, Open Office®, etc.)
• Printer to print graphing paper
A Graphing by Hand
■
A common method to look at data is to create
Safety
There are no safety concerns for this lab.
an x,y scatter graph. In this first activity, you will
create two graphs of the data from Table 1.
1. Print 2 copies of the graphing sheet found on
page 13.
2. Title the first graph “Wheat plant height by
week.”
3. Title the second graph “Rye plant height by
week” and set aside for later.
4. At the bottom of the graph there is a space to
label the x-axis. The x-axis runs from left to
right, with smaller numbers starting on the left
and the numbers increasing as you move to
the right.
5. At the left of the graph there is a space to
label the y-axis. The y-axis runs from the
bottom to top of the graph, with smaller
numbers starting at the bottom and the size
of the numbers increasing as you move up.
6. You will now label each axis and decide which
pieces of data will be our x-values and our
y-values, respectively.
7. One method to determine which data should
be your x versus y axis is to think about the
goal of the experiment. The y-axis should be
for data that you measured for, the dependent
variable. In the data set in Table 1, the
scientists were measuring the height each
week. This means that the height is the
dependent variable.
8. Label the y-axis “Height (cm).” It is important
to always include the unit of measurement on
the axis. In this case the unit is centimeters
(cm).
continued on next page
www.carolina.com/distancelearning 7
ACTIVITY
ACTIVITY 1 continued
9. The x-axis is the independent variable, the
parameter of the experiment that can be
controlled. In this experiment the scientists
were controlling when they measured the
height.
10. Label the x-axis “Time (weeks).” This
indicates that a measurement was taken
each week.
11. Locate the lower left corner of the graph.
This will be the origin of your graph. The
origin on a graph is where both the values of
x and the values of y are 0. If the numbers
in a data set are all positive (i.e. there are no
negative numbers) it is a best practice to set
the origin in the lower left corner. This allows
the view of the data to be maximized.
12. The axes then need to be numerically
labeled. Referring to Figure 4, label each
axis from 0 to 14 along the darker lines.
13. Starting with the “Wheat Plant 1” data in
Table 1, count over 1 (for week 1) on the
x-axis for time, then count up to 2 from there
to indicate 2 cm. Place a dot at this point
14. Repeat this process for the remaining data
points for “Wheat Plant 1.” Your graph
should now look like Figure 4.
15. Using this same process, graph the data
for “Wheat Plant 2” and “Wheat Plant 3” on
the same graph. You will need to be able to
distinguish the data from each set from each
other. Use different colors, or symbols to
make this differentiation.
16. When complete, compare your graph to
Figure 5. Your exact colors or symbols may
be different, but the data should be in the
same locations.
continued on next page
Figure 5.
HEIGHT OF WHEAT PLANT BY WEEK
Figure 4.
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HEIGHT OF WHEAT PLANT BY WEEK
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TIME (WEEKS)
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♦ Wheat Plant 1
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t;. Wheat Plant 3
CAR@UNA~
ACTIVITY 1 continued
17. You can now create a legend. The legend is
what shows another person what the points
on your graph represent. Refer to Figure 5
for an example legend for this graph.
18. Create your legend. It is below the x-axis
label as in Figure 5. The legend can be
anywhere on the graph, so long as it does
not interfere with the reading of the graph.
19. Create your own graph of the data for “Rye
plant height by week.” Use the process
outlined in this activity to graph all of the
data for each plant.
ACTIVITY 2
A Computer Graphing
■
Graphing by hand can be useful for observing
trends in small data sets. However, as the quantity of the data grows it can be useful to graph
using a computer. This activity will give a general
outline of how to graph on a computer. Please
note Microsoft Excel® was used to generate
the figures for this activity. Your exact software may look different or have slightly
different labeling than what you will see here.
You may need to refer to the documentation
of your exact program to determine how to
perform a particular step.
In this activity you will graph the data from
Table 1 into your computer.
1. Open a new workbook. This will open a new
sheet (Figure 6).
2. You will see a large sheet with lettered
columns and numbered rows. These letters
and numbers can be used to refer to a
specific cell (the box
where information
can be typed.) For
example the upper left
cell is A1 representing
column A, row 1.
Figure 6.
New
[ search for online templates
Suggested searches:
3. Starting in cell A1
type “Week.” In cell
B1 type “Wheat Plant
1.” Continue across
putting each title in
a new cell in the first
row.
A
1
2
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Business
Personal
B
C
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–
3
4
–
5
–
6
7
Blank woricbook
4. Move to row 2. Type the corresponding
numbers under the correct column.
5. Continue until your table looks like Table 1.
6. Select the data for Week thru Wheat Plant 3.
You can do this by clicking on cell A1 and
then dragging down and over to cell D9. All
of the data and titles should be selected for
the wheat plant (Figure 7).
Figure 7.
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B
Week
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–
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continued on next page
www.carolina.com/distancelearning 9
ACTIVITY
ACTIVITY 2 continued
NOTE: The next several
steps may vary greatly
depending on the exact
software you are using, but
the goal is the same.
7. Find the menu labeled
“Insert.”
8. Among the “Charts” find
“Scatter,” or “x,y Scatter,”
and click it.
Figure 8.
Chart Title
12
10
8
6
4
••
•
2
0
0
1
9. A basic graph similar to
Figure 8 should appear.
10. Edit the chart title so that
it matches the one created
in Activity 1. This can
usually be accomplished
by clicking (or double
clicking) on the title and
then typing.
11. You can then add a label
to each axis. This step in
particular is very different
depending on your
software. You will typically
be looking for a menu
option titled “Axis Title.”
You will need to do this
twice, once for each axis.
Your graph should now
look like Figure 9. You will
use this graph again in
Activity 3.
10
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•
•
••
3
2
•
•
•
•
4
• Wheat Plant 1
5
• Wheat Plant 2
•••
••
•
•
•
6
7
8
9
• Wheat Plant 3
Figure 9.
Height of Wheat Plant by Week
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•
•
6
7
8
9
Time (weeks)
• Wheat Plant 1
• Wheat Plant 2
• wheat Plant 3
CAR@UNA~
ACTIVITY 3
A Linear Regression
■
Typically if you are graphing using an x,y scatter
plot you are looking for trends (a recognizable
pattern) in your data. In this activity you are
looking to see if there is a trend in height of
the plants over time. More specifically, you are
looking for the rate at which the plants grew.
This rate can be determined from the graph
produced in Activity 2.
1. In your graph from Activity 2, click on a point
from the Wheat Plant 1 dataset.
2. Right-click on the data point and select “Add
Trendline.”
3. Select “Linear.”
4. Select “Display Equation on chart.”
5. The equation displayed on the graph should
read y = 1.2381x + 0.9286. Write this in
“Wheat Plant 1 trendline equation” in the Data
Table.
This is the equation of the line. In its general
form is y = mx + b . The “m” symbol stands for
the slope of the line. The slope is how far the line
rises (y) over a certain distance (x.) The “b” is
called the y-intercept; this is the point at which
the line crosses the y-axis. For the equation from
step 6, this would mean that “1.2381” would be
the slope and “0.9286” would be the y-intercept.
This equation allows you to find the length of
a plant at a certain time. For example, if you
wanted to determine the height of the plant in
week 9, based on this equation the estimated
height would be 12.0715 cm.
Y = 1.2381 * 9 + 0.9286
Y = 12.0715 cm
change in y
Since the slope is calculated from change in x
it uses the same units as the dataset. In this
case, this means that the slope has units of __f_!!l_
.
week
The slope then means that on average, Wheat
Plant 1 grew 1.2381 centimeters per week.
The y-intercept indicates that at week 0 the
plant was likely 0.9286 cm tall. However, in
this experiment the plants were all grown from
seeds, so at week 0 they should have a height of
0. This information can be added to a trendline
without having to add to a dataset.
6. Right click on the trendline and select
“Format Trendline.”
7. Select “Set Intercept” and set the number to
0. This is setting the y-intercept to 0. You can
do this whenever you know the exact value
of your dependent variable at the 0 for the
x-axis.
8. Write the new trendline in “Wheat Plant 1
trendline corrected” in the Data Table.
9. Using the same procedure, create a corrected
trendline for each additional wheat plant on
the graph. Write the corrected equation for
each in the data table.
10. Based on the corrected trend lines, which
wheat plant grew fastest? Record your
answer in the data table.
continued on next page
www.carolina.com/distancelearning 11
ACTIVITY
ACTIVITY 3 continued
Data Table.
Wheat Plant 1 trendline equation
Wheat Plant 1 trendline corrected
Wheat Plant 2 trendline corrected
Wheat Plant 3 trendline corrected
Wheat plant with fastest growth
continued on next page
12
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CAR@UNAe
Label (y-axis): _________________________________________________
Title: __________________________________________________________
I
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Label (x-axis): _________________________________________________
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NOTES
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Introduction to Graphing
Investigation Manual
www.carolina.com/distancelearning
866.332.4478
Carolina Biological Supply Company
www.carolina.com • 800.334.5551
©2016 Carolina Biological Supply Company
CB781021610
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CAR@UnA
DISTANCE
LEARNING
CHEMISTRY
Isolation of Casein
Investigation
Manual
ISOLATION OF CASEIN
Table of Contents
2
Overview
2
Outcomes
2
Time Requirements
3
Background
4
Materials
5
Safety
5
Preparation
6
Activity 1
7
Disposal and Cleanup
Overview
Students will take a provided sample of milk and through the addition of an acid, determine the pH at the isoelectric point of casein.
The mass of casein will be measured and the percentage of casein
in the milk sample will be calculated. As an extension, students
can test their own milk sample to compare the percentage of
protein.
Outcomes
• Examine the properties of proteins in general and casein
specifically.
• Explain and apply the principles of protein isolation.
Time Requirements
Preparation ………………………………………………………………5 minutes
Activity 1: Isolation of Casein from Dried Milk…………..45 minutes +
Drying Time
Key
Personal protective
equipment
(PPE)
goggles gloves apron
follow
link to
video
photograph stopwatch
results and
required
submit
warning corrosion flammable toxic environment health hazard
Made ADA compliant by
NetCentric Technologies using
the CommonLook® software
2
Carolina Distance Learning
Background
Proteins are complex organic compounds
composed of monomers called amino acids.
Amino acids contain hydrogen, oxygen, carbon,
and nitrogen in three functional groups, with
the general chemical formula NH2–RCH–COOH,
where NH2 is an amine group and the –COOH
is the carboxylic acid functional group. The
–R represents a side chain, which can be an
–H, a carbon chain, or a carbon ring structure.
All amino acids are identical except for the –R
group. All organisms require nitrogen for the
construction of proteins, nucleic acids, and other
compounds.
Twenty amino acids are encoded by the
universal genetic code; these are known as the
natural amino acids. These 20 amino acids
can be linked together by peptide bonds to form
proteins. The linked amino acids can form dipeptides, tripeptides, and polypeptides. The polypeptides may contain any number, sequence,
and/or configuration of amino acids to form a
vast number of proteins. Proteins contained
in foods are a source of prefabricated amino
acid groups. Nine amino acids are considered
essential; these essential amino acids must
be supplied in prefabricated form via the diet.
However, the remaining eleven amino acids can
be synthesized in the human body. The absence
of any of these essential amino acids halts the
synthesis of crucial proteins, resulting in disease,
and in prolonged cases of deprivation, death.
A common source of dietary protein is milk.
Casein is the most prevalent protein in mammalian milks: 80% of the protein in cow’s milk is
casein. Casein is very poorly soluble in water,
which is the base solvent of milk. The casein
in milk is part of a suspension; an undissolved
solid floating in the solvent. The protein is
highly hydrophobic, meaning it is negatively
attracted to water, causing the protein to form
micelles (small bubbles of protein) within the
water. The exact structure of these micelles is
not completely understood, but one hypothesis
is that the κ-casein proteins (one type of casein
protein in the micelles) are arranged such that
their polar (charged) regions are on the surface
of the micelles. Calcium and phosphate ions are
present on the surface of the micelles. These
ions and the polar regions of the κ-casein molecules interact with water molecules, which are
also polar. The interaction of the micelles with
the charged water molecules keeps the micelles
suspended in the liquid phase of the milk. There
are several methods of removing a suspended
solid from solution. One method is to use a
centrifuge. A centrifuge is an apparatus that
can spin a sample at a high speed and essentially force heavy materials to the bottom of a
sample centrifuge tube, similar to how the spin
cycle on a clothes washer helps separate the
clothes from excess water. This method obviously requires expensive laboratory equipment
and would not be suitable for an at-home
investigation.
There is another way to separate these particles,
which involves changing the pH of the milk. In
this investigation, acetic acid will be added to a
milk sample until the isoelectric point, the point
at which the molecule carries no net electric
charge, of the protein is reached. The addition of
acid changes the pH of the solution and disrupts
the intermolecular forces holding the micelles
together. At the isoelectric point, the hydrogen
continued on next page
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3
ISOLATION OF CASEIN
Background continued
ions (H+) from the acid balance out any negative charges on the protein, breaking up the salt
bridges that give the protein their shape, and
thereby reducing the strength of the intermolecular forces. This process of adding acid denatures the protein, meaning that it is no longer
in its natural molecular conformation (shape).
This disruption pops the protein bubble, and the
insoluble casein coagulates and precipitates out
of solution.
Materials
Included in the materials kit:
2 Filter paper
Dried milk
Glass stirring
rod
Figure 1.
Filtration funnel pH indicator
strips
Casein micelles
suspended in milk;
before the addition
of acid
Network formed
during coagulation;
after the addition
of acid
Casein, while being a source of essential amino
acids, is also the protein primarily responsible
for the formation of cheese; it is the protein that
coagulates to form the solid portion of cheese.
In fact, the method used in this investigation is
similar to ones used in the production of many
cheeses. In this investigation, the percentage
by weight of casein in a milk sample will be
calculated.
4
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Needed from the chemical kit #1:
Vinegar
continued on next page
Safety
Needed from the equipment kit:
Beaker, 250 mL Medicine cup
Wear your safety
goggles, chemical apron,
and gloves at all times while conducting this
investigation.
Dropping pipet
Read all the instructions for this laboratory
activity before beginning. Follow the instructions
closely, and observe established laboratory
safety practices, including the use of appropriate personal protective equipment (PPE) as
described in the Safety and Procedure sections.
Acetic acid is a corrosive material.
Use this chemical near a source of
running water that can be used as a
safety eye wash or safety shower if any corrosive material comes in contact with skin or eyes.
Plastic cup,
8 oz
Balance
Needed but not supplied:
• Non-fat milk sample (optional)
Reorder Information: Replacement supplies
for the Isolation of Casein investigation can
be ordered from Carolina Biological Supply
Company, kit 580360.
Call 800-334-5551 to order.
Do not eat, drink, or chew gum while performing
this activity. Wash your hands with soap and
water before and after performing the activity.
Clean up the work area with soap and water
after completing the investigation. Keep pets
and children away from lab materials and
equipment.
Preparation
1. With the balance, weigh 10 grams of dry milk
into a 250-mL beaker.
2. Fill beaker to 100-mL line.
3. Stir using glass stir rod until thoroughly
mixed.
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5
ACTIVITY
Activity 1
A Isolation of Casein from Dried Milk
1. Weigh a small medicine cup, and record the
mass in Data Table 1.
8. Dip a clean stirring rod in the clear, yellow
liquid, and touch it to a pH indicator strip.
Record color and pH in Data Table 1.
9. Weigh a piece of filter paper, and record the
mass in Data Table 1.
2. Add approximately 10 mL of rehydrated milk
to the medicine cup.
10. Assemble the filtration apparatus as shown
in Figure 2 with the weighed filter paper.
3. Weigh the medicine cup with the milk, and
record the mass in Data Table 1.
Figure 2.
4. Calculate the mass of milk in the medicine
cup, and record in Data Table 1.
5. Take the glass stir rod, and dip it into the milk
sample.
6. Touch the milk sample to a pH indicator strip.
Record color and pH in Data Table 1.
7. Add acetic acid drop-wise with dropping
pipet while stirring with the glass stirring rod.
Add drops until a precipitate ceases to form.
continued on next page
Data Table 1.
Dry Milk Sample
Mass of Cup
Mass of Cup + Milk
Mass of Milk
pH of Milk Pre-Acid
pH of Milk Post-Acid
Mass of Filter Paper
Mass of Filter Paper + Casein
Mass of Casein
Percentage of Casein in Milk
6
Carolina Distance Learning
Optional Milk Sample
11. Place the folded filter paper into the funnel.
It may be necessary to wet the funnel with
water to get it to stay.
12. Set the funnel into the 8-oz plastic cup.
13. Pour the milk in the filter, and collect the
solid protein in the filter paper.
14.
Remove the filter paper containing the
protein (casein) from the funnel, and
allow to dry overnight in a cool, dry location
away from pets, children, and food sources.
47
Disposal and Cleanup
1. Dispose of solutions down the drain with the
water running. Allow the faucet to run a few
minutes to dilute the solutions.
2. Solid waste may be disposed of in the trash.
3. Rinse and dry the lab equipment, and return
the materials to your equipment kit.
4. Sanitize the workspace.
15. Weigh the dried casein and filter paper, and
record the mass in Data Table 1.
16. Calculate the mass of casein, and record in
Data Table 1.
17. Calculate the percentage of casein in the
milk sample, and record in Data Table 1.
mass of casein
× 100
mass of milk sample
= percentage of casein in milk
18. *Optional* Repeat activity with non-fat or
low-fat fresh milk sample.
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7
CHEMISTRY
Isolation of Casein
Investigation Manual
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