emmaburgin.weebly.com · web viewone such freezing point depression experiment was published by a...

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Introduction

Every year, somewhere around 3,400 people and countless numbers of

household pets die from ingesting ethylene glycol, the most common component

of antifreeze (Antifreeze Factsheet). Ethylene glycol is a sweet-tasting, odorless

chemical that can kill a grown man with as little as 120 milliliters. Victims that

consume ethylene glycol are afflicted by mental symptoms that mimic

drunkenness and physiological symptoms such as seizures, arrhythmias,

respiratory distress, and even heart failure or coma. If no medical help is sought,

the victim may suffer irreparable renal damage and will ultimately die.

An alternative to ethylene glycol is propylene glycol, a chemical commonly used

in food preservatives, but the use of propylene glycol is expensive, averaging

$100 dollars per gallon (“Propylene Glycol, 500 mL”), while ethylene glycol is

comparably cheaper, approximately $60 per gallon (“Ethylene Glycol, 500 mL”).

Another potential alternative for use in antifreeze is the chemical glycerin, a

byproduct of biodiesel.

Glycerin is a natural, non-toxic, easily accessible chemical. It was first

used in antifreeze as early as the 1900’s, but because biodiesel was uncommon,

it was very expensive and difficult to come by in its naturally occurring form.

Ethylene glycol was cheaper antifreeze that eventually made the use of glycerin

obsolete. However, since biodiesel production has been growing steadily for the

last three years, reaching 1.1 billion gallons annually in 2011 and 2012, there

now exists a surplus of glycerin (“Production Statistics”). Today, one gallon of

glycerin costs about $87 (“Glycerin, 500 mL”). Although more expensive then the

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toxic ethylene glycol, it is cheaper than the other nontoxic antifreeze, propylene

glycol.

This research intended to discover if a safer and less expensive antifreeze

than ethylene glycol or propylene glycol exists, concentrating on glycerin. The

purpose of this research was to determine if glycerin, now readily available, is as

effective an antifreeze as the commonly used chemicals ethylene and propylene

glycol. Glycerin as an antifreeze would be a safe, environmentally friendly

alternative.

Since the purpose of antifreeze is to lower the freezing point of water so

that fluid in car engines does not freeze in the winter, the experiment tested the

freezing point depression of different concentrations of solutions made with

ethylene glycol, propylene glycol, and glycerin. A control of pure water was also

tested. The experiment tried to discover which chemical depressed the freezing

point the most by finding which solution had the smallest change in temperature.

This was done by measuring the change in temperature after a certain amount of

time after the solutions were submersed in an ice-water bath. The chemical that

allowed the temperature of the solution to change by the smallest amount was

the most effective antifreeze. This is because the solution froze at a slower rate.

If it was determined that glycerin was as or more effective than the more

commonly used chemicals in antifreeze, it could potentially replace the harsh and

dangerous chemicals. Non-toxic antifreeze would be safer for humans, pets, and

the environment. Because glycerin is being made more abundant in recent times

do to its status as a byproduct of biodiesel production, this antifreeze that is safe

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to humans and to the environments is also cheaper than what is currently on the

market. If glycerin was proven effective, the results of this experiment could be

used in the future to employ glycerin as safer, inexpensive antifreeze to replace

the common, toxic chemicals used today.

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Review of Literature

Antifreeze is a substance that lowers the freezing temperature of a water

solution. There are numerous different antifreezes with different uses. Some

types are used in car engines while some are used in the environment. Road

salt, for instance is an antifreeze that allows ice to melt at lower temperatures by

adding ions that disrupt water molecules to make it harder for them to join

together and form ice, so that roads are not icy (Marder). Antifreeze agents can

also be used to keep brittle items that contain water from cracking in cold

conditions due to the expansion of water as it freezes. Antifreeze also elevates

the boiling point of a solution so that water will not boil until higher temperatures

are reached, so that engines in cars do not overheat (“How Does Antifreeze…”).

Perhaps the most well-known application of antifreeze chemicals is the use of a

mixture of antifreeze and water as coolant in automobile engines.

Figure 1. Diagram of Vehicle Engine (Jenkins)

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Figure 1above shows a diagram of a vehicle engine with components vital

to making the vehicle move labeled. In an engine, there are pistons situated

inside of cylinders in the chamber of the engine. These pistons are attached to

cams which are attached to cam shafts. Inside each of the chambers, there are

fuel injection systems. In a timed fashion, a small amount of gasoline is sprayed

into the cylinder. At the exact moment that the fuel is sprayed into the cylinder,

the spark plug sparks and a small explosion occurs. This explosion forces the

piston down into the cylinder head. When the piston is pushed down the cylinder,

the cam shaft rotates, and lobes on the cam shaft turn other pistons back up

toward the top. The cam shaft is connected to a drive shaft that turns the wheels,

and this process repeats at a fast pace to make the car move. However, the

burning gas in the combustion makes the engine get very hot, which can

potentially cause the engine to overheat (Brain).

Figure 2. Diagram of Vehicle Cooling System and Radiator (Dasan)

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When an engine overheats, the car does not function properly. Thus, a

cooling system must be used to keep the engine running at a safe temperature.

Such a system is shown above in Figure 2. This system involves a radiator that is

typically located in the front of the engine. Various tubes are attached to radiator

and go to other points in the engine that need to be cooled (Jennings). A mixture

of water and antifreeze circulates through the system to keep the engine cool, as

the heat from the system is transferred to the coolant, due to the Law of

Thermodynamics which states that energy cannot be created or destroyed.

Energy is always transferred, and is therefore changed and transferred in the

system. The coolant circulates through and around the head of engine to keep it

cool and eventually goes back to the radiator where it is cooled by fans and

circulated back through the system (Nice).

Water alone cannot be used as a coolant in the engine. Water alone

freezes at too high of a temperature, 0 °C, and boils at too low of a temperature,

100 °C, to keep from freezing or boiling inside the engine in extreme

temperatures. For this reason, it is necessary to use a solution of antifreeze and

water inside of the car to keep the coolant from boiling or freezing when

temperature extremes are reached because adding a solution to the water may

lower the freezing point or raise the boiling point of water due to the disruption of

molecules created by the addition of solution (“Antifreeze Factsheet”). As

temperatures inside the engine can rise above the boiling point of water, a

solution must be used to elevate the boiling point of the coolant so that it does

not boil inside the radiator. However, this solution also serves as a freezing point

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depressant in the winter when temperatures drop below freezing to keep the

coolant from freezing when the engine is not running. Antifreeze is therefore an

important feature in automobiles.

To understand how antifreeze works, one must understand why water

freezes when its temperature reaches freezing point, 0°C. Liquid water becomes

solid as the temperature decreases due to a loss of heat that slows the

molecules down. Bonds between molecules are formed as more energy is

released, and the water becomes solid. The molecules then form a crystalline

structure and freeze to form ice (Luedtke).

Figure 3. The Freezing of Pure Water vs. the Freezing of a Solution (Snelling)

Antifreeze changes the freezing point of water so that water does not

freeze until a lower temperature has been reached.. When the temperature of

pure water drops to 0ºC, the water molecules have slowed down enough for ice

to form. When a dissolvable substance, known as the solute, is added to water,

ions are introduced to the water that disrupt the placement of the molecules of

water and the formation of the crystalline structure of ice is impeded. The water

molecules are forced to move farther apart from each other, and more energy

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must be removed before the molecules slow down enough to form bonds and

become solid. Therefore, a lower temperature must be reached before water can

freeze when a solute is added (“Solutions and Colligative Properties:

Antifreeze”). The difference in how pure water and solutions change is shown in

the graphs in Figure 3. This difference is called freezing point depression, as the

freezing point of the solution is lower than the freezing point of water.

When water boils, it changes from its liquid phase to its gas phase, water

vapor. This occurs because when water reaches its boiling point of 100ºC, its

vapor pressure is equal to the vapor pressure of the outside air, and water vapor

escapes in the form of steam. This pressure is caused by the movement of

molecules, which increases as the molecules gain energy in the form of heat.

Figure 4. Boiling Point Elevation (Smith)

When solutes are added to the water, the vapor pressure of the water

decreases as additional ions are added to disrupt the water molecules so that it

takes a higher temperature for the liquid water to change to steam. This is called

boiling point elevation, as the boiling point of the solution is higher than the

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boiling point of water (Widom). This process is shown in Figure 4 above, as the

boiling point of the solution, the curve labeled 1, is higher than the boiling point of

water, the curve labeled 2.

Freezing point and boiling point of water are colligative properties. This

means that they depend on the concentration of the dissolved substance, the

antifreeze, and not on the chemical properties of the solute added. This is the

case because it depends on the number of ions introduced to displace the water

molecules, and not on the identity of said ions. However, not just any chemical

solutes can be put into cars and expected to be safe to use as antifreeze. The

chemicals used as antifreeze must be nonvolatile, non-corrosive, and safe to use

at the temperatures required in an engine. That is, they must not evaporate

under normal conditions, and they must not be damaging to the chemical

makeup of the engine of the car.

In automobiles today, the most common antifreeze used is composed of

ethylene glycol (C2H6O2), dyes, and corrosion inhibitors. This chemical is non-

corrosive and stable at high temperatures and is safe to use in cars.

Unfortunately, ethylene glycol is a toxic chemical, and ethylene glycol poisoning

is not uncommon. Ethylene glycol is sweet tasting substance that can be

accidentally ingested by animals and children. As the chemical metabolizes in

the body, it forms metabolites that are toxic to humans, and that inhibit many

systems that are necessary to keep the body functioning. As these toxins move

through the system, the body is subject to damage that is often irreparable.

Ingesting as little as 100 mL of ethylene glycol can prove to be fatal, and

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ingesting any of the substance can cause mental symptoms that mimic

drunkenness, and physiological symptoms such as seizures, arrhythmias, coma,

and renal damage that may take over a year to fully recover from (Bannerjee).

Using a nontoxic antifreeze in automobiles would therefore be a sensible choice.

Another chemical, propylene glycol (C3H8O2), is used as a “green,” safe,

antifreeze by some people, but it is more expensive than ethylene glycol. Today,

one gallon of pure ethylene glycol can be purchased for about $60 (“Ethylene

Glycol, 500 mL”) while one gallon of pure propylene glycol can be purchased for

about $100 (“Propylene Glycol, 500 mL”). Although ethylene glycol and

propylene glycol are generally the only antifreeze agents used in cars, another

substance, glycerin (C3H8O3), has being considered as an alternative antifreeze

in recent years.

In the past, glycerin was used as automobile antifreeze but it was not as

readily available as ethylene glycol. In recent times, however, glycerin is more

readily available, as it is a product of biofuel production that is becoming more

and more common (Treacy). If glycerin is as effective at lowering the freezing

point and raising the boiling point of water, it could be used as antifreeze today,

as a safer alternative to ethylene glycol.

To determine if glycerin was as effective an antifreeze as the more

commonly used chemicals, a freezing point depression laboratory experiment

was performed. A boiling point elevation procedure was planned, but could not

be carried out due to safety issues that arose after reviewing the Material Safety

Data Sheets (MSDS).

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One such freezing point depression experiment was published by a

Wisconsin AP Chemistry school teacher, Michael Nikson. In his experiment, a

solution made of a chemical and distilled water was placed into a test tube and

the tube was placed into an ice-salt bath inside of a beaker. The test tube

solution was stirred until ice crystals formed and the temperature at that point

was recorded to be the freezing point of the solution (Nikson). The methods used

in Nikson's experiment are similar to the methods used in this experiment in that

a chemical-water solution in a test tube is placed into an ice-water-salt bath in a

beaker. However, Nikson's methods differ from methods used in this experiment

because the solution does not get stirred. A temperature probe measures the

change in temperature as the solution remains in the ice water, and the freezing

point is calculated that way.

Another way the effectiveness of glycerin as an antifreeze could be tested

was through a boiling point elevation laboratory experiment. One experiment that

tested this was published by a teacher at a notable Korean school, Jeong S. Joo.

The boiling point was found using this experiment by recording the temperature

of each chemical solution as they were heated until the solution boiled. The

boiling point was reached when the temperature remained constant for three

readings at 30 second intervals (Joo). Unfortunately, due to laboratory limitations

and safety issues that were brought up after reviewing the MSDS, an experiment

comparing the boiling points of these chemicals could not be performed. The

hypothesis was tested by carrying out an experiment that compares freezing

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point. Glycerin’s ability to change the rate at which water freezes will be used as

judgment of how effective it is as an antifreeze.

Common antifreeze, although useful, is dangerous to humans, animals,

and the environment when it is made with ethylene glycol. Unfortunately,

ethylene glycol is cost-effective compared to a less harmful antifreeze chemical,

propylene glycol. As a byproduct of biodiesel production, glycerin could

potentially be a cost-effective, eco-friendly alternative to the chemicals most

commonly used in antifreeze.

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Problem Statement

Problem:

To determine if glycerin is an effective antifreeze by comparing the change

in temperature of glycerin solutions to solutions of ethylene glycol and propylene

glycol at three different concentrations.

Hypothesis:

There will be no statistical difference between the mean changes in

temperatures of the solutions, and glycerin will therefore be an effective

antifreeze.

Data Measured:

The independent variables in the experiment were the type of chemical,

either glycerin, ethylene glycol, or propylene glycol, and the concentration of the

solution which was measured in molarity (M). The dependent variable in the

experiment was the change in temperature of the solution, measured in °C. An

analysis of variance (ANOVA) test was carried out to determine if there was a

significant difference in the mean changes in temperature of each concentration

of each temperature.

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Experimental Design

Materials:

Ethylene Glycol, C2H6O2

Propylene Glycol, C3H8O2

Glycerin, C3H8O3

Graduated Cylinder, 10 mLGraduated Cylinder, 50 mL (2) Stir Rod(10) Beaker, 50 mL(1) Beaker, 600 mLRing Stand(2) Test Tube Clamp

(4) Test Tube, 50 mLTemperature ProbeLabQuestDistilled WaterIceRock Salt, NaClSpoon(3) Weighboat 1000 mL BeakerRefrigerator

Procedures:

1. Fill a 1000 mL beaker with water and place in refrigerator to keep the

water cold.

2. In the 50 mL beakers, prepare three solutions each of ethylene glycol,

propylene glycol and glycerin by using the graduated cylinders to measure

the necessary volume of the chemical with the necessary volume of

distilled water. Refer to Appendix A for detailed procedures on how the

solutions were made.

3. Fill the last 50 mL beaker with 30 mL of distilled water.

4. Setup the LabQuest by attaching the temperature probe and verifying that

the data collection is set to time based, and that the trial will run for 20

minutes, taking a data point every 0.1 minute.

5. Measure three 15 g samples of rock salt into three separate weigh boats.

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6. Fill the 600 mL beaker with approximately 200 mL of ice, and add water

from the refrigerated beaker until the ice water reaches the 200 mL line on

the beaker.

7. Set up the ring stand by placing the 600 mL beaker containing the ice

water on the stand and attaching the two test tube clamps so that they are

close together and nearly touching the top of the beaker.

8. Place 10 mL of the first solution in the test tube.

9. Place the test tube in the lower test tube clamp.

10. Place the temperature probe in the test tube, and secure by tightening the

top test tube clamp on the temperature probe.

11. Start data collection.

12. Quickly lower the test tube clamps so that the test tube with temperature

probe is inside the ice water bath.

13. When 0.5 minutes have passed since the data collection started, add one

of the 15 g samples of salt to the ice water and stir with a stirring rod until

the salt is no longer sitting on top of the ice.

14. After seven minutes have passed, add another 200 mL of ice and

refrigerated water and another 15 g of salt to the ice water bath and stir.

15. Repeat the process with a final 200 mL of ice water and the final weigh

boat of 15 g of salt after 14 minutes have passed.

16. When the 20 minutes are up, save the data and record the change in

temperature that occurred.

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17. Repeat for four trials each of the other solutions and the control of pure

distilled water.

Diagram:

Figure 5. Materials

Figure 5 shows all of the materials used in the experiment.

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Temperature Probe

Rock Salt

Ethylene Glycol Glycerin

Propylene Glycol

Ring Stand

Clamps

Distilled Water

Cold Water

Spoon

Graduated Cylinder600 mL Beaker

WeighBoats

LabQuest50 mL BeakerStir Rod

Ice

50 mL Test Tube

1000 mL Beaker

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Figure 6. Setup of Experiment

Figure 6 shows the setup of the experiment. The solution is inside the test

tube in the ice water bath and is being measured by the temperature probe.

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Clamps

50 mL beaker

600 mL beaker

Stir rod

Ring stand

Test tube

Temperature probe

Chemicals

Salt

Weigh boatLabQuest

1000 mL beaker

Burgin – Drylie

Data and ObservationsTable 1Average Temperature Change of 3M Solutions

3M Solutions of Ethylene Glycol, Glycerin, and Propylene Glycol

Chemical Trial

Initial Volume

of Solution

(mL)

Starting Temp. of Solution

(°C)

Ending Temp. of Solution

(°C)

Temp. Change

(°C)

Avg. Change in Temp.

(°C)

Ethylene Glycol

5 10.0 21.1 0.2 20.9

22.816 10.1 21.6 -0.6 22.229 10.0 23.0 -1.6 24.636 10.0 21.6 -2.0 23.6

Glycerin

2 10.0 20.1 -0.4 20.5

22.911 9.9 22.2 -2.4 24.630 10.0 21.9 -2.5 24.440 10.0 21.9 -0.3 22.2

Propylene Glycol

13 9.9 19.5 -3.4 22.9

23.923 10.0 23.9 -2.3 26.228 10.1 22.7 0.0 22.732 10.0 23.8 -0.1 23.9

Table 1 above shows the raw data from the trials that used 3M

concentrations of solutions. The trial numbers were randomized along with the

6M and 9M solutions and the control, and 40 total trials were carried out. The

Starting Temperature and Ending Temperature columns were found from directly

reading information from the LabQuest, and the Temperature Change was found

my subtracting the ending temperature from the starting temperature to find a

positive value for the decrease in temperature. The Initial Volume column is the

initial volume of solution that was measured in a graduated cylinder and placed

into the test tube. The average change in temperature for each chemical solution

was found by adding the changes in temperature for each solution and dividing

the result by four, the number of trials for each chemical.

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Table 2Average Temperature Change of 6M Solutions

6M Solutions of Ethylene Glycol, Glycerin, and Propylene Glycol

Chemical Trial

Initial Volume

of Solution

(mL)


(°C)


(°C)

Temp. Change

(°C)


(°C)

Ethylene Glycol

3 10.0 20.2 -0.8 21.0

24.110 9.9 21.2 -1.4 22.619 10.1 20.4 -3.8 24.235 10.0 27.0 -1.5 28.5

Glycerin

8 10.0 20.9 0.9 20.0

22.918 10.0 22.1 -0.9 23.021 10.0 21.8 -0.9 22.733 10.0 23.2 -2.6 25.8

Propylene Glycol

6 10.0 19.9 0.2 19.7

21.920 10.0 21.8 0.6 21.227 10.0 21.7 -0.5 22.238 10.0 22.3 -2.3 24.6


concentrations of solutions. It also shows the average change in temperature for

each chemical solution at 6M concentration.

Table 3

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Average Temperature Change of 9M Solutions9M Solutions of Ethylene Glycol, Glycerin, and Propylene Glycol

Chemical Trial

Initial Volume

of Solution

(mL)


(°C)


(°C)

Temp. Change

(°C)


(°C)

Ethylene Glycol

9 10.0 21.5 -0.9 22.4

22.612 10.0 22.9 0.3 22.617 10.0 21.9 -2.9 24.839 10.0 20.6 0.1 20.5

Glycerin

22 10.0 23.9 -1.4 25.3

25.924 10.1 22.1 -3.6 25.726 10.0 24.0 -1.1 25.131 10.0 25.0 -2.5 27.5

Propylene Glycol

1 10.0 22.0 0.5 21.5

22.34 10.1 20.8 -1.3 22.17 9.9 21.4 0.0 21.437 10.0 22.3 -1.8 24.1


concentrations of solutions. It also displays the average change in temperature

for each chemical solution at 9M concentration.

Table 4Control Data

Table 4 above shows the raw data from the control trials that used distilled

water instead of a chemical solution.

FinalTemperature=StartingTemperature−EndingTemperatureFigure 7. Final Temperature Formula

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Control, H20

Trial Initial Volume (mL)

Starting Temperatur

e (°C)

Ending Temperatur

e (°C)

Temperature Change

(°C)14 10.0 23.4 -1.6 25.015 10.0 22.8 -1.0 23.825 10.0 22.0 -2.5 24.534 10.1 24.1 -2.4 26.5

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Figure 7 shows the formula used to find the final temperature of the

solution. The ending temperature was subtracted from the starting temperature to

find the change in temperature as a positive value, although each temperature

change was a decrease in temperature.

Table 5

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ObservationsConcentratio

nTria

l Chemical Observations

3M

13 Propylene Glycol

LabQuest 1, Channel 2. Researcher 2. The second batch of new ice was added 0.5 minutes early, after 13.5 minutes had passed.

32 Propylene Glycol

LabQuest 1, Channel 2. Researcher 1. The first batch of new ice went in after 8.2 minutes, 1.2 minutes later than it should have been.

36 Ethylene Glycol

LabQuest 1, Channel 2. Researcher 2. This trial was redone because the temperature probe was never lowered into the solution the first time.

40 GlycerinLabQuest 1, Channel 2. Researcher 2. There was a little more than the 200 mL of ice water that there should have been at the start of the trial.

6M

3 Ethylene Glycol

LabQuest 2, Channel 1. Researcher 2. Temperature increased after first batch new of ice, the water added was too warm because it was early in the day and had not been refrigerator very long. Second batch of new ice went in at 14.5 minutes, 0.5 minutes late.

21 GlycerinLabQuest 1, Channel 2. Researcher 2. This trial had to be redone because of evaporation that affected the original solution concentration.

27 Propylene Glycol

LabQuest 2, Channel 1. Researcher 1. This trial had to be redone because of evaporation that affected the original solution concentration.

38 Propylene Glycol

LabQuest 2, Channel 1. Researcher 1. This trial was started before the other trials were ran at the same time because the LabQuest would not load.

9M

12 Ethylene Glycol

LabQuest 2, Channel 1. Researcher 1. The graph shown on the LabQuest was unusually wavy, but the trial was carried out in the same way as the other trials. Added ice water at 14.9 minutes, 0.9 minutes late.

17 Ethylene Glycol

LabQuest 2, Channel 1. Researcher 1. This trial was redone because the solution used the first time was affected by evaporation and the molarity may have been off.

31 Glycerin

LabQuest 1, Channel 1. Researcher 1. Approximately 1 mL of solution dripped down the side of the test tube before the trial started, so there was not as much solution in the test tube to be frozen. The first batch of new ice went in 1 minute late, after 8.0 minutes.

37 Propylene Glycol

LabQuest 1, Channel 1. Researcher 2. The second batch of new ice went in after 14.5 minutes, slightly

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later than it should have been.Table 5 shows the important and unusual observations that were taken

throughout the experiment. Note that Trials 17, 21, 27, and 36 were redone due

to evaporation that led to a possible change in concentration or other

experimental errors. Trials 3, 31, and 40 had errors that may have affected the

resulting temperature change. Also, many of the trials had batches of ice go in

slightly early or late, which may change the results of the experiment slightly.

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Data Analysis and Interpretation

The data was collected by reading the final temperature off of the

LabQuest after the solution had been in the ice water bath for the 20 minute trial.

This final temperature was subtracted from the initial temperature to find the

change in temperature. The final, lower temperature was subtracted from the

higher, initial temperature so that the change in temperature was a positive

value. To produce valid and viable data, the experiment had elements of control,

randomization, and repetition. These elements were used to ensure that the

effects of lurking variables were minimized and that the data can be trusted.

Trials with distilled water as opposed to the different concentrations of

solutions were run to act as controls in the experiment. These control trials were

used to see if the experiment was done correctly, because the data from the

controls should have been relatively horizontal.

0 1 2 3 4 5 60

2

4

6

8

10

12

Controls

Control Trial

Chan

ge in

Tem

pera

ture

(ºC)

Figure 8. Data From Control Trials

They acted as a valid control because lurking variables in the experiment

would have affected these trials in the same way they affected the experimental

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trials. However, as shown in Figure 8, the controls were not perfectly horizontal,

and the experiment may therefore have been affected by some lurking variables.

Randomization was used in the experiment as the trial numbers were

randomized to determine the order in which to test each chemical and each

concentration. The molarity and chemical of the solution used for each trial was

randomized to minimize the effect of lurking variables. Repetition was used in the

experiment to determine if the data from the same solutions had trends. Forty

trials were carried out, with four trials from each concentration of each solution,

and four control trials were carried out. There were an equal number of trials from

each concentration of each solution. The repetition of data resulted in less varied

results, according to the Law of Large Numbers.

In order to determine if there was in fact a difference in the mean

temperature changes for each of the concentrations, three Analysis of Variance

(ANOVA) tests were used. These tests were appropriate because the means of

three or more populations, in this case concentrations, were compared to one

another in each test. The tests were valid to use because of the ANOVA Rule of

Thumb: it is okay to use the test when the largest sample standard deviation is

no more than twice as large as the smallest standard deviation. For each test,

two times the smallest sample standard deviation was in fact larger than the

largest sample standard deviation, so all three tests would be valid.

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Figure 9. Comparative Boxplots of Solutions at 3 M

Figure 9 above shows all of the data for 3 M solutions graphed as different

boxplots. Glycerin has the highest spread among all of the different groups. The

upper and lower quartiles for that specific group are larger than any other group.

The data for 3 M ethylene glycol was most normally distributed.

The medians of all groups are very close to each other. The median of

propylene glycol is the largest at 23.4°C and the median of ethylene glycol is the

smallest at 22.9°C. Between the smallest and largest, there is only a difference of

0.5°C. This could indicate that there is not much of a difference in how the

different solutions affected the change in temperature. Although the boxplots

show similar trends in the data across all different groups, the ANOVA test was

used to see if there was a statistically significant difference among the obstacles.

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Figure 10 above shows all of the data for 3 M solutions graphed as

different boxplots. Glycerin and ethylene glycol both have a large amount of

spread. The upper quartile for ethylene glycol is fairly large compared to the

other groups. The data for 6 M glycerin, however, was most normally distributed

despite the spread.

The medians of all groups are again very close to each other. The median

of ethylene glycol is the largest at 23.4°C and the median of propylene glycol is

the smallest at 21.7°C. Between the smallest and largest, there is only a

difference of 1.7°C. Although this difference in temperature change is larger than

that of the 3 M solutions, this could still indicate that there is not much of a

difference in how the different solutions affected the change in temperature.

Although the boxplots show similar trends in the data across all different groups,

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the ANOVA test was used to see if there was a statistically significant difference

among the obstacles.


Figure 11 above shows all of the data for 9 M solutions graphed as

different boxplots. Ethylene glycol had the largest amount of spread but was also

the most normally distributed data among the other groups.

The medians of all groups are again very close to each other, although the

median for 9M glycerin is quite a bit higher in this grouping of solutions than it

had been in the others. The median of glycerin is the largest at 25.5°C and the

median of propylene glycol is the smallest at 21.8°C. Between the smallest and

largest, there is only a difference of 3.7°C. Because this difference is larger than

the other two concentrations, this could indicate that there may be a difference in

how the different solutions affected the change in temperature. To be sure,

28

Burgin – Drylie

another ANOVA test was used to see if there was a statistically significant

difference among the obstacles.

Figure 12. Boxplot of Control Data

Figure 12 above shows a boxplot of data taken during the trials using a

control of distilled water. The median of the control data was 24.75°C. The data

appears to be relatively normally distributed. The control was used to ensure that

other trials were being done correctly.

29

Burgin – Drylie

Table 6Table of Means, Sample Sizes, and Sample Standard Deviations

Chemical x̅ (°C) n s

3 MEthylene Glycol 22.8 4 1.617Propylene Glycol 23.9 4 1.605Glycerin 22.9 4 1.948



Table 6 above shows each chemical and concentration as well as its

sample mean, x̄, sample size, n, and sample standard deviation, s. This table

was used for easy reference while performing the three ANOVA tests.

Hypotheses for 3 M Solutions:

Ho: µeth3M = µprop3M = µglyc3M

Ha: Not all µeth3M, µprop3M, µglyc3M are equal







The null hypothesis of each test is that all sample means for all three

sample groups are equal to each other and that there is no difference between

solutions. The alternative hypothesis is that not all sample means are equal. This

would signify that there was a difference in how the different chemicals affected

the change in temperature of the solution.

30

Burgin – Drylie

Assumptions:

i independent simple random samples

normal distribution in each population

same unknown standard deviation, σ, among sample groups

Most assumptions for the statistical test were met. Each sample i, where i is

any one of the chemicals, was randomly assigned to a trial. Because each trial

took 20 minutes to complete, the researchers were only able to complete 4 of

each sample with the time and resources available, so there is no way of

knowing if they were normally distributed. In each of the groups, standard

deviation, σ, was unknown. Even though one of the assumptions may not have

been met, the ANOVA tests were carried out anyway.

The F statistic of the test is the proportion of the variation among sample

means between each population to the variation among individuals in all the

samples within each population. In other words, the F statistic is the mean

square group, MSG, divided by the mean square error, MSE.

F= MSGMSE

Before this value could be determined, the weighted mean x̄ had to be found.

This is found by multiplying the sample size for each population by the

mean for each population, adding them together, and dividing by N, the total

number of trials in all samples combined. Refer to Appendix B for the formula

and calculations. After all values were input into the formula, the value of x̄ for 3

M solutions was found to be 23.225°C, 6 M solutions was found to be 22.958°C,

and 9 M solutions was found to be 23.583°C.

31

Burgin – Drylie

Next, the mean square group, MSG, had to be calculated. This formula

takes the sample size of each population, multiplies it by the difference in sample

mean and weighted mean squared, adds them all together, and divides by one

less than I, the number of populations. Refer to Appendix B for the formula and

calculations. The value of 3 M solutions was found to be 1.480, 6 M solutions

was found to be 4.643, and 9 M solutions was found to be 16.191.

Finally, the mean square error, MSE, was calculated. This formula

uses the sample size of each population minus one and multiplies it by the

squared sample standard deviation. This is done for each population and they

are added together. Then the entire thing is divided by N – I, the total number of

populations subtracted from the total number of samples. Refer to Appendix B for

the formula and calculations. The value of 3 M solutions was found to be 2.996, 6

M solutions was found to be 6.756, and 9 M solutions was found to be 1.957.

Now that MSG and MSE had been determined for each of the tests, the F

statistic could be found. The F statistic is found by dividing MSG by MSE. See

Appendix B for the actual calculations.

The F statistic for the 3 M solutions was 0.494. This corresponds to a p-value

of 0.626. Because of this, it was concluded that the null hypothesis failed to be

rejected at α=0.05 significance level because the p-value is greater than the

alpha level. There is no significant evidence to suggest that the different

chemicals for 3 M solutions had an effect on the amount the temperature

changed. The p-value states that there is about a 62.6% chance that results this

32

Burgin – Drylie

extreme were attained by chance alone if the null hypothesis was assumed to be

true.


of 0.527. Because of this, it was concluded that the null hypothesis failed to be

rejected at α=0.05 significance level because the p-value is greater than the

alpha level. There is no significant evidence to suggest that the different

chemicals for 6 M solutions had an effect on the amount the temperature

changed. The p-value states that there is about a 52.7% chance that results this

extreme were attained by chance alone if the null hypothesis was assumed to be

true.


of 0.009. Because of this, it was concluded that the null hypothesis was rejected

at α=0.05 significance level because the p-value is smaller than the alpha level.

There is significant evidence to suggest that the different chemicals for 9 M

solutions had an effect on the amount the temperature changed. The p-value

states that there is about a 0.900% chance that results this extreme were

attained by chance alone if the null hypothesis was assumed to be true.

There was no significant difference in temperature change for 3 M and 6 M

solutions, which means that glycerin was just as effective as ethylene and

propylene glycol as antifreeze. However, there was a difference in temperature

change in the 9 M solutions, which means that 9 M glycerin is not as effective as

9 M solutions of the other chemicals.

33

Burgin – Drylie

Conclusion

The purpose of this experiment was to determine if glycerin is an effective

antifreeze by comparing the change in temperature in various concentrations of

glycerin solutions in an ice bath to the changes in temperature in various

concentrations of solutions made with commercially-used antifreezes. After

researching antifreeze and how it worked, an experiment was designed to

compare glycerin, ethylene glycol, and propylene glycol solutions of 3 M, 6 M,

and 9 M concentrations. Although the most common concentration of antifreeze

used in cars is a 50% solution of ethylene glycol, percent concentrations could

not be used in the experiment because the true molar concentrations of the

chemicals needed to be the same for the experiment to be valid.

The original hypothesis was that there would be no statistical difference

between the mean temperature depression, the changes in temperatures of the

solutions, and glycerin will therefore be effective antifreeze. After carrying out the

experiment and running ANOVA tests on the results, the hypothesis was

accepted because two of the three ANOVA tests that were carried out directly

support the hypothesis. The results of the third ANOVA test did not support the

hypothesis, but the results may be attributed to design flaws that occurred in the

experiment such as testing under non-ideal conditions.

A total of 40 randomized trials were carried out in the experiment,

including four control trials in which distilled water was used instead of a

concentrated solution. One solution with a designated concentration was used

per trial and placed into a test tube that was submerged in an ice bath. Salt was

34

Burgin – Drylie

added to maximize temperature depression of the ice bath by depressing the

freezing point of the ice, and the temperature of the solution was recorded with a

LabQuest temperature probe for 20 minutes.

When the experiment was completed, the data was analyzed using three

ANOVA tests, one for each concentration. The ANOVA tests were used to

determine if there was a difference in the mean temperature changes for each of

the concentrations. For the 3 M solutions, the test resulted in a p-value of 0.626.

This means that the null hypothesis failed to be rejected at the alpha level α,

0.05, and there was no difference in temperature change between different

solutions at 3 M. In regards to the problem, this means that 3 M glycerin is as

effective an antifreeze as the standard antifreeze chemicals, ethylene and

propylene glycol.

For the 6 M solutions, the test resulted in a p-value of 0.527. This means

that the null hypothesis failed to be rejected at the alpha level α, 0.05, and there

was no difference in temperature change between different solutions at 6 M. In

regards to the problem, this means that 6 M glycerin is an effective an antifreeze,

like the standard antifreeze chemicals, ethylene and propylene glycol.

For the 9 M solutions, the test resulted in a p-value of 0.009. This means

that the null hypothesis was rejected at the alpha level α, 0.05, and there was a

difference in temperature change between different solutions at 9 M. In regards

to the problem, this means that 9 M glycerin was not as effective an antifreeze as

the standard antifreeze chemicals, ethylene and propylene glycol.

35

Burgin – Drylie

The results of this experiment for the 3 M and 6 M solutions in which there

was no statistical difference in the mean change in temperature were supported

scientifically. Freezing point depression is a colligative property. When a

dissolvable substance, known as the solute, is added to water, ions are

introduced to the water that disrupt the placement of the molecules of water and

the formation of the crystalline structure of ice is impeded. The water molecules

are forced to move farther apart from each other, and more energy must be

removed before the molecules slow down enough to form bonds and solidify.

Because freezing point depression is a colligative property, it depends not on the

identity of the solute, but of the concentration of the solution. Thus, the number of

ions added is what matters, not what type of ions are added. Since each ANOVA

test compared the means of each chemical at the same molarity, each of the

solutions used in each group had the same ratio of solute to solvent on an atomic

level. The solutions therefore all had the same concentration of ions and there

should have been no difference amongst the results from each antifreeze used.

These results are supported by past findings related to freezing point

depression. In a lab that was written by Adrienne Oxley at Columbia College

discussed colligative properties of water and used the freezing point to find the

concentration of the solute, regardless of the identity of the dissolved substance

(Oxley). In a different lab performed at North Carolina State University, the

freezing point was predicted given the concentration of the solute (“Lab 3”).

These labs enforce that freezing point depression does not depend on the

identity of the solute, but rather on the concentration of said solute, because in

36

Burgin – Drylie

each of these labs, the concentration of the solute was either used or found, but

its identity was not a factor in the results achieved. Since freezing point

depression is colligative, the identity of the solute did not matter for these labs,

assuming the concentration of ions in the solution was constant throughout.

The discrepancy between the results of this experiment and the colligative

property that occurred for the 9 M solutions could have been due to design flaws

and human error. Due to inadequate resources, many flaws occurred with the

experiment’s set up and trials. Perhaps the largest design flaw that occurred was

that the chemical solutions could not reach freezing point with the lab equipment

available, so the change in temperature was used instead. The statistical test

was run using the change in temperature, but there is no way to know if the same

results would have been gleaned from the experiment if the temperatures of

solutions were lowered all the way to freezing point.

An additional design flaw was that certain aspects of the experiment were

hard to control consistently. The times at which ice, water, and salt were added,

for instance, were often early or late because multiple trials were run at the same

time with the same requirements. If the salt was added to the ice bath at a later

time, the salt may not have lowered the temperature of the bath by the same

amount in each trial, and the temperature that the molecules in the solution were

exposed to may have varied from trial to trial. The temperature of water added

was also hard to control, because the earlier trials had warmer water that had

been cooling in freezer for very long. The temperature of the water that was

added to the ice bath may have affected the depression of freezing point

37

Burgin – Drylie

because when the temperature of the water in the ice bath was lower, the

solution was given more of an opportunity to freeze as the molecules were at a

lower temperature and thus, lower energy. These lurking variables could not be

controlled, and the data obtained was therefore confounded.

The design flaws in the experiment are likely what led to the results of the

9 M ANOVA test that were not supported scientifically. Had the design errors not

occurred, it is possible that the 9 M solutions would also have been proven to

have no statistical difference and all of the antifreezes would have had the same

effectiveness. Testing whether or not 9 M solutions of the chemicals would be

effective could be something tested under ideal circumstances in further

research.

If the experiment were to be repeated under ideal circumstances, the

solutions would reach freezing point, and the freezing point and amount of time

passed before it reached freezing would be recorded. Additionally, the water

added would have been a more consistent temperature, and fewer trials would

be run at once, so that the ice, water, and salt could be added at the right time.

For further research, glycerin could be tested as antifreeze in an engine.

Since its effectiveness at depressing the freezing point has been proven, it

should hypothetically be capable of functioning as antifreeze. It must be tested in

a functioning engine, however, to ensure that there are no problems with its

performance in automobiles before people can start switching their ethylene

glycol-based antifreeze for glycerin.

38

Burgin – Drylie

Another related experiment could be carried out to compare glycerin’s

effectiveness at elevating the boiling point of water. This would be a dangerous

experiment that could only be carried out with special lab equipment, but the

results could further scientific confidence in glycerin as an alternative to ethylene

glycol or propylene glycol.

The results of this experiment, along with the results of possible future

research can be used to employ glycerin as safer, greener antifreeze. Ethylene

glycol is a toxic chemical that should not be introduced to the environment

("Ethylene Glycol: Environmental Aspects"). Propylene glycol is safer for

humans, but can still be hazardous to the environment in extreme conditions, and

is expensive to produce and purchase. Glycerin, however, is nontoxic to humans

and is not harmful to the environment. Furthermore, glycerin is a byproduct of

biodiesel production, and is therefore abundant in recent times. Switching to

glycerin as antifreeze would be safer for all who use antifreeze, and would be

friendlier to the environment as a whole. Its abundance makes it an affordable,

sensible choice for those looking to use safer antifreeze.

39

Burgin – Drylie

Acknowledgements

The researchers would like to express their sincerest thanks to the following

people for their continued support during the research process:

Mrs. Hilliard, for helping during experimentation and being all-around

supportive of the idea of the project.

Mr. Supal, for the tips he provided along the way.

The researchers would also like to extend their thanks to Mr. Darnell Jennings,

without whom they would lack knowledge of real-life applications of vehicle

engines and their components.

It is also important to mention the wonderful parents involved, who also provided

sufficient funding for the experiment:

Mr. and Mrs. Burgin

Mr. and Mrs. Drylie

Once again, to everybody involved in this entire process, the researchers

express their deepest thanks.

40

Burgin – Drylie

Appendix A

To carry out the experiment, three different concentrations of solutions

were made for each chemical. The concentrations used were 3 M, 6 M, and 9 M,

which were roughly derived from 25%, 50%, and 75% solutions of the chemicals.

Thirty mL of each solution were made so that three trials of 10 mL each could be

carried out. Eventually, the process was repeated to make an additional 30 mL of

solution and to run the final trial and redo trials as necessary.

The molarity of a solution can be found by calculating the moles of the

substance, and dividing it by the volume of the final solution according to the

following equation:

M=molL

in which volume is in liters. Each concentration of solution had to be made for

each of glycerin, ethylene glycol, and propylene glycol.

Calculations for Necessary Volume of Each Chemical:

Table 7Molecular Weight and Density of Each Chemical

Molecular Weight (g/mol) Density (g/mL)Ethylene Glycol 62 1.11Glycerin 92 1.26Propylene Glycol 76 1.04

Table 7 above shows values that were used in calculating the volume of

chemical needed to make each solutions: the molecular weight and the density of

each chemical.

41

Burgin – Drylie

M=molL

3= mol0.03

0.09=mol

0.09mol glycerin× 92g1molglycerin

=8.28 g

D=mV

1.26=8.28V

V =6.57mLglycerin

30−6.57=23.43mLwater

Figure 13. 3 M Glycerin

Figure 13 above shows the calculations used to find the amount of

glycerin and the amount of water needed to make 30 mL of the 3 M glycerin

solution. The desired molarity and the volume were substituted in for M and L in

the equation, and the moles were found to be 0.09.

This was multiplied by the molar mass of glycerin, 92 g, to find the grams

of glycerin needed. Since glycerin is a liquid, the liquid volume of glycerin was

found using the density of glycerin, 1.26 g/mL. The volume of glycerin required

was found to be 6.54 mL.

Since the total volume of is 30 mL, the volume of glycerin was subtracted

from 30 to find the necessary volume of water, 23.43 mL.

M=molL

6= mol0.03

0.18=mol

0.18mol glycerin× 92 g1molglycerin

=16.56 g

D=mV

1.26=16.56V

V=13.14 mLglycerin

30−13.14=16.86 mLwater


42

Burgin – Drylie

Figure 14 above shows the calculations used to find the volume of glycerin

needed to make 30 mL of the 6 M glycerin solution.

M=molL

9= mol0.03

0.27=mol

0.27mol glycerin× 92 g1mol glycerin

=24.84 g

D=mV

1.26=24.84V

V =19.71mLglycerin

30−19.71=10.26mLwater


Figure 15 above shows the calculations used to find the volume of glycerin

needed to make 30 mL of the 9 M glycerin solution.

M=molL

3= mol0.03

0.09=mol

0.09molethylene glycol× 62g1molethylene glycol

=5.58g

D=mV

1.11=5.58V

V=5.03mLethylene glycol

30−5.03=24.97mLwater

Figure 16. 3 M Ethylene Glycol

Figure 16 above shows the calculations used to find the volume of

ethylene glycol needed to make 30 mL of the 3 M ethylene glycol solution.

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Burgin – Drylie

M=molL

6= mol0.03

0.18=mol

0.18molethylene glycol× 62g1mol ethylene glycol

=11.16 g

D=mV

1.11=11.16V

V =10.05mLethylene glycol

30−10.05=19.95mLwater




M=molL

9= mol0.03

0.27=mol

0.27mol ethylene glycol× 62g1mol ethylene glycol

=16.74 g

D=mV

1.11=16.74V

V =15.08mLethylene glycol

30−15.08=14.92mLwater




M=molL

3= mol0.03

0.09=mol

0.09mol propylene glycol× 76 g1mol propylene glycol

=6.84 g

D=mV

1.04=6.84V

V=6.58mL propylene glycol

30−6.58=23.42mLwater

Figure 19. 3 M Propylene Glycol

44

Burgin – Drylie


ethylene glycol needed to make 30 mL of the 3 M propylene glycol solution.

M=molL

6= mol0.03

0.18=mol


=13.68g

D=mV

1.04=13.68V

V =13.15mL propylene glycol

30−13.15=16.85mLwater




M=molL

9= mol0.03

0.27=mol


=20.52g

D=mV

1.04=20.52V

V=19.73mL propylene gl ycol

30−19.73=10.27mLwater




45

Burgin – Drylie

Procedures for Making Solutions:

Materials:

50 mL Beaker (9)10 mL Graduated Cylinder (2)Stirring RodDistilled WaterGlycerin

Ethylene GlycolPropylene GlycolTapeMarkerPlastic Wrap

Procedures:

1. Use the graduated cylinder to measure the correct amount of the chemical

to make the desired solution.

2. Put the chemical into one of the 50 mL beakers.

3. Use the second graduated cylinder to measure the necessary distilled

water.

4. Pour the distilled water into the beaker with the chemical.

5. Use the stirring rod to mix the chemical and the distilled water to form the

solution.

6. Cover the beaker with plastic wrap.

7. Use the tape and marker to label the beaker.

8. Repeat procedures to make each solution.

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Burgin – Drylie

Appendix B

Calculations for the ANOVA Test for 3 M Solutions:

An ANOVA test was used to determine if there was a significant difference

between chemicals. All calculations for this test are shown here.

x̄=neth3M x̄eth3M+n¿ 3M x̄¿ 3M+nglyc3M x̄glyc3 M

N

Figure 22. Formula to find Weighted Mean

Figure 22 shows the formula used to find the weighted mean x̄ for the

experiment. This is found by multiplying the sample size for each population, n,

by the mean for each population, x̄, adding this value from each population

together, and dividing by N, the total number of trials in all samples combined.

x̄=4 (22.825)+4 (23.925)+4 (22.925)12

=23.225

Figure 23. Sample Equation Used to find Weighted Mean

Figure 23 above shows the formula to find the weighted mean x̄ when the

correct values are input. All sample sizes, n, consisted of 4 trials. The samples

means for each population were multiplied by n, and divided by 12, the total

number of trials. The value was found to be 23.225.

MSG=neth3 M ( x̄eth3M− x̄ )2+n¿3 M ( x̄¿ 3M− x̄ )2+nglyc 3M ( x̄glyc 3M− x̄ )2

I−1

Figure 24. Formula to find MSG

Next, the mean square group, MSG, had to be calculated. The formula for

this is shown in Figure 24 above. This formula takes the sample size of each

population, multiplies it by the difference in sample mean and weighted mean

47

Burgin – Drylie

squared, adds this value for each population together, and divides by one less

than I, the number of populations.

MSG=4(22.825−23.225)2+4 (23.925−23.225)2+4 (22.925−23.225)2

3−1=1.48

Figure 25. Sample Equation Used to find MSG

Figure 25 above shows the formula to find the mean square group, MSG,

when the correct values are input. All sample sizes, n, consisted of 4 trials. The

weighted mean x̄ was subtracted from each sample mean for each population,

squared, and multiplied by n, then divided by 2, the total number of materials

minus one. The value was found to be 1.48.

MSE=(neth3M−1 ) seth3 M

2+ (n¿3 M−1 ) s¿3 M2+ (nglyc 3M−1 ) sglyc3 M

2

N−I

Figure 26. Formula to find MSE

Finally, the mean square error, MSE, was calculated. The formula to find

MSE is shown in Figure 26 above. This formula uses the sample size of each

population minus one and multiplies it by the squared sample standard deviation.

This is done for each population and they are added together. Then the

numerator is divided by N – I, the total number of populations subtracted from the

total number of samples.

MSE=(4−1 ) 1.617352+ (4−1 )1.604942+(4−1 ) 1.948292

12−3=2.99583

Figure 27. Sample Equation Used to find MSE

Figure 27 above shows the formula to find the mean square error, MSE,

when the correct values are input into the formula. All sample sizes, n, consisted

of 4 trials, so n-1 was 3 for each population. This value was then multiplied by the

48

Burgin – Drylie

sample standard deviation squared and each population was added together.

Then it was divided by N-I, or 12-3, the total number of trials minus the number of

populations. The value was found to be 2.99583.

Now that MSG and MSE had been determined, the F statistic could be

found. The F statistic is found by dividing MSG by MSE.

F= MSGMSE

= 1.482.99583

=0.49402

After dividing MSG by MSE, the F statistic of the test was found to be 0.49402.

To calculate the p-value, the degrees of freedom had to be determined as

well. This value was calculated by dividing I-1 by N-I.

df = I−1N−I

= 3−112−3

=29

The degrees of freedom allowed for one to find the general interval in which the

p-value would fall. Using technology, the specific p-value was found to be

0.625792.

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Burgin – Drylie




x̄=neth6 M x̄eth6M+n¿ 6M x̄¿6M+nglyc6 M x̄ glyc6M

N






x̄=4 (24.075)+4 (21.925)+4 (22.875)12

=22.9583






MSG=neth6 M ( x̄eth6M− x̄)2+n¿6 M ( x̄¿6 M− x̄)2+nglyc6 M ( x̄glyc6 M− x̄)2

I−1





50

Burgin – Drylie



MSG=4(24.075−22.9583)2+4 (21.925−22.9583)2+4 (22.875−22.9583)2

3−1=4.64333







MSE=(neth6M−1 ) seth6M

2+(n¿ 6M−1 ) s¿ 6M2+(nglyc6 M−1 ) sglyc 6M

2

N−I








MSE=(4−1 ) 3.226322+( 4−1 )2.058112+ (4−1 )2.371182

12−3=6.75582




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Burgin – Drylie







F= MSGMSE

=4.643336.75582

=0.687308




df = I−1N−I

= 3−112−3

=29



0.527494.

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Burgin – Drylie




x̄=neth9 M x̄eth9M+n¿ 9M x̄¿9M+nglyc 9M x̄ glyc9M

N






x̄=4 (22.575)+4 (22.275)+4 (25.9)12

=23.5833






MSG=neth 9M ( x̄eth9M− x̄)2+n¿ 9M ( x̄¿9 M− x̄)2+nglyc9 M ( x̄glyc9 M− x̄)2

I−1


53

Burgin – Drylie






MSG=4(22.575−23.5833)2+4 (22.275−23.5833)2+4 (25.9−23.5833)2

3−1=16.1908







MSE=(neth9M−1 ) seth9M

2+(n¿ 9M−1 ) s¿ 9M2+(nglyc9 M−1 ) sglyc 9M

2

N−I








MSE=(4−1 ) 1.75952+ (4−1 )1.255322+ ( 4−1 )1.095452

12−3=1.95723

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Burgin – Drylie










F= MSGMSE

=16.19081.95723

=8.27232




df = I−1N−I

= 3−112−3

=29



0.009146.

55

Burgin – Drylie

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emmaburgin.weebly.com · web viewone such freezing point depression experiment was published by a...

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