Phase_Changes_v7b.docx
PhaseChangesofSolutions
An observation of temperature changes as heat is added to ice water and the effect of a solute on those
changes.
1
1.1
OBJECTIVES
EXPERIMENTAL GOAL
To record the change in temperature of water as heat is added to a mixture of water and ice.
1.2
PREREQUISITE SKILLS AND KNOWLEDGE
Students should be able to construct a simple VI in LabVIEW.
1.3
RESEARCH SKILLS
After this lab, students will have had practice in:
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1.4
following laboratory protocols
using a laboratory notebook
recording detailed software instructions into a laboratory notebook
using LabVIEW to control and collect data from a sensor
programming
propagating error
using Excel to propagate error
using a temperature probe to measure temperature
using a balance
measuring mass by difference
using a hot plate
making molal solutions
using R and RStudio to graphically analyze data
LEARNING OBJECTIVES
After this lab, students will be able to:
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Describe and explain the shape of a water heating curve
Describe the effect on melting point and boiling point by solutes added to the water
2
2.1
PRE-EXPERIMENT
MEASURING TEMPERATURE
The Celsius scale is named after the Swedish astronomer Anders Celsius, who first proposed a
temperature scale based on the freezing and boiling points of water.* Celsius used the term degrees
*
Read more on Wikipedia: https://en.wikipedia.org/wiki/Anders_Celsius and
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centigrade to describe the units of his scale, to indicate the one hundred steps from boiling to freezing.
The temperature scale is still sometimes referred to as centigrade.
2.1.1
Thermometers and Thermisters
Temperature is commonly measured with a mechanical device (e.g., a thermometer) or an electronic
device (e.g., a thermistor).
A typical thermometer contains a liquid such as mercury or alcohol that expands in a predictable way
when its temperature increases. Therefore, a column of this liquid will change its height in a predictable
way when it comes into contact with a substance of a different temperature.
A thermistor is an electronic component whose resistance varies with temperature. There are two different
kinds of thermistor: a positive temperature coefficient (PTC) thermistor shows an increase in resistance
with increasing temperature, while a negative temperature coefficient (NTC) thermistor shows a decrease
in resistance with increasing temperature.
Recall that the Vernier temperature sensor shows a change in the raw voltage when there is a change in
temperature. If the voltage from a temperature sensor goes up with increasing temperature, is the sensor
NTC or PTC? (Hint: Remember Ohm’s law.)
2.2
MOLALITY
Thermodynamic calculations involving the concentration of solute will often use the concentration unit of
molality instead of molarity. You will soon understand why this unit is used. Molality defines the
concentration of solute in a solution as the number of moles of solute per kilogram of solvent.
How is this concentration unit different from molarity?
The units of molality are mol/kg. Sometimes you may see the units m or molal used to indicate molality,
but these units are almost universally considered obsolete.
2.2.1
Example Molality Calculation
The dry mass of a 200 mL beaker is 143.737 g. DI water is added to bring the mass to 244.493 g, and then
sodium chloride is added to bring the mass up to 250.416 g. What is the molality of the solution?
The mass of the water is 244.493 – 143.737 g = (100.756 g)(1 kg/1000 g) = 0.100756 kg
The mass of the salt is 250.416 – 244.493 g = 5.923 g. This amount is (5.923 g)/(58.44 g/mol) = 0.10135
mol.
Thus,
themolality
0.10135mol
0.100756kg
1.0059mol/kg
The number of significant figures is only four, however. (Why?) So the answer is rounded to 1.006
mol/kg.
2.2.1
Propagating the Error in the Calculated Molality
Below are the error propagation formulas for multiplication and division.
(1)
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Phase Changes of Solutions |3
(2)
These equations can be rewritten to isolate the error on the left:
(3)
(4)
Compare equations (3) and (4). What parts are identical and what parts are different?
2.2.1.1 Example Error Propagation
For each mass measurement, assume the uncertainty is 0.002 g = 0.000 002 kg.†
Thus the error in the solute is simply 0.002 g.
To propagate the error in the mass of the water-ice slurry, use the addition and subtraction formula you
used last time
(5)
To propagate the error in the molality, use equation (2) or (4), but substitute the error for the solute for x
and the propagated error for the mass of the water-ice slurry for y.
Plugging in the values given in the example above, the calculations will look like this:
0.002
0.002
0.003
The error in the molality‡ is
(6)
1.0059
0.002
5.932
1.0059
0.000337
1.0059
0.000338
0.003
100.759
0.00002977
0.00034
≅ 0.0003
Notice you do not have to convert the masses inside the square-root from grams to kilograms.
Why don’t you?
†
Note the space between the first three zeros and the following digits. The space is left to indicate multiples of 1000.
This value could also be written 2 x 10-6 kg.
‡
The molar mass of the salt is assumed to be a constant which does not affect the error in the measured molality.
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2.2.2
Use Excel to Propagate Error
If you are going to make several of these calculations, or even one, Excel can make it easier to keep track
of numbers. There are many ways to set up your spreadsheet. One example looks like this:
The calculation of the error in the mass of ice-water slurry is shown below.
Compare this Excel function to Equation (5) above.
To calculate the error in the mass of ice water in kilograms (kg), divide by 1000, just as you would to
convert the mass from grams to kilograms. In a similar way, you can convert the error in the mass of salt
to an error in the moles of salt by dividing the error by the molar mass.
Finally, to find the error in the molality, use the expression below.
Compare this expression to Equations (4) and (6) above.
Make sure you can reproduce the above calculations in your own Excel workbook. When you are done,
replace the sample data above with the sample sucrose data below, and use it to answer the questions in
the Pre-Experiment Quiz. The molar mass of sucrose is 342.0 g/mol.
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Phase Changes of Solutions |5
DO NOT remove the script that contains calculations. These start with an equals (=) sign when you view
them in the fx line above the sheet. When you remove the data, some equations may produce errors, but
don’t worry about that. The errors will go away when you insert your own data. When you are satisfied,
save the workbook and email it to yourself to use in lab.
2.3
PREPARE LAB NOTEBOOK
Read ahead in the lab manual for this experiment, so that you can prepare your lab notebook. Prepare an
Excel workbook in which to enter and analyze your data, as described in the lab manual. Write a plan for
how to schedule your work so that you can finish the experiment and data analysis within the allotted
time.
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3
LABORATORY MANUAL
In this lab, you will collect a water heating curve like the one you collected in the previous lab, except
that you will dissolve either sucrose or calcium chloride in the water before starting to heat it.
3.1
MATERIALS CHECK OFF LIST
Each small group of (2-3) students will have:
Laptop computer with LabVIEW and RStudio
Vernier Sensor DAQ
Vernier Temperature probe
200 mL beaker (tall form)
200 – 250 mL beaker
Magnetic stir bar
Stirring hot plate
wash bottle with deionized water
2 large weighing boats
silicone pad
Each large group of 1-2 small groups will share one of:
Jar of sucrose
Jar of calcium chloride, CaCl2
The entire class will have access to
Ice
2 milligram balances with 400 g maximum
3.2
SAFETY AND WASTE DISPOSAL PROTOCOLS
In addition to your lab coat, goggles, long pants, and closed-toe shoes must be worn for this experiment.
Be careful to not come in contact with the hot plate while it is on.
When cooling down the beaker, there is danger of thermal shock cracking the glass. The temperature of a
hot beaker or flask should be lowered slowly in a controlled manner to minimize the risk. Students should
not sit with their laps directly underneath the hot plate.
Do not take the hot flask or beaker off the hotplate and place it directly on the table. The rapid change in
temperature could crack the glass. If you must take the beaker off the hotplate, place it onto a silicone
pad, or a stack of paper towels.
3.3
EXPERIMENTAL PROCEDURE
As you complete this procedure, be sure to record your actions in your lab notebook.
3.3.1
Using the Temperature-Sensing VI
Open your VI from the last post-lab for use in the following tasks.
Q1. Hold the temperature probe in your hand, while the program is running, and observe the change
in the voltage reading. Which type of thermistor is this, PTC or NTC?
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3.3.2
Prepare the Materials for the Solutions Heating Curve
You will be assigned a molality and a solute to test. Using the mass of water from the previous heating
curve as a guide, calculate the mass of solute you will need to add to your ice-water slurry in order to
achieve the assigned molality.
Q2. What is your assigned molality?
Q3. What mass of solute will you add to your slurry? Show your calculation.
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Measure out the calculated mass of solute into a large weighing boat.
Mass the (unused) 200 mL beaker with the stir bar as you did last lab. Record this mass.
Measure about 100.00 g of ice into the beaker.
Add water from the DI water dispenser as you did before. Do not add too much. Remember to
mass the beaker again in order to find the mass of water and ice by difference.
Replace the beaker onto the center of the cool hotplate. (Make sure the hotplate is cool before
putting the beaker onto it.)
Start the stirrer.
Lower the temperature probe into the slurry. For best results, the tip should be about midpoint
between the stir bar and the top of the slurry.
Start data acquisition by starting your VI,
If the temperature is dropping, wait for it to stabilize (flat line) before turning on the hotplate.
9. Turn on hot plate.
10. Add the already massed solute.
Collect a temperature reading in your lab notebook once every two to five minutes. Record the actual time
the reading is recorded.
As you collect time and temperature points, record also your observations of the state of the water.
Q4. At what time and temperature point did you notice that all the ice has melted?
Q5. At what time and temperature point did you notice that the water started to boil? This implies a
“rolling” boil is observed and not just bubbling.
Collect time and temperature points until your solution has been boiling for five minutes.
Turn off the hot plate and let your water cool before moving the beaker.
3.4
3.4.1
ANALYSIS
Enter Data into Excel
You will use Excel to manipulate the data you collected in both the previous lab and this lab. You will use
R to graph it.
1. Open your lab notebook to the water time and temperature data you collected.
2. Create three column headings in Excel: actual, elapsed, and temperature. (Do not leave a space in
any of your headings! Do not use parentheses.)
3. Enter your actual times in the first column.
4. Enter the elapsed time in the second column. If you want, you can Google “elapsed time Excel” to
learn how to use Excel to calculate the elapsed time,§ otherwise, you can calculate and enter the
elapsed time by hand.
§
If you do use Excel, you can use the custom format [m] to show only minutes in the elapsed time column.
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5. Enter the measured temperatures into the appropriate spots in the last column.
When you import your data into RStudio, highlight only the columns with headings elapsed and
temperature.
3.4.2
Plot your Data
3.4.3
Analyze the Graph that Depicts the Heating of Deionized Water
Use RStudio (hint: you can re-use your Linear_Fit script) to create a publishable plot** of your heating
curves, with Time in minutes on the independent axis and Temperature in degrees Celsius on the
dependent axis.
Q6. Use the snipping tool (or RStudio’s copy to clipboard feature) to take a snip of your plot and
paste it here.
Consider the shape of the heating curve. Why does the temperature change rapidly in some sections, but
very slowly in other sections? How does the added heat increase the temperature? Where does the heat go
when the temperature is not changing very much?
Q7. At which temperatures was the slope of the plot closer to flat?
Melting and boiling points are usually defined as the places on the heating curve where the temperature
remains relatively constant. At these temperatures, the two phases (solid and liquid, liquid and gas) exist
at equilibrium with each other.
Use Excel to calculate the standard deviation of the data points that you used to find the melting and
boiling temperatures. Use these values as the uncertainty in your melting point and boiling points.
Q8. What is the melting temperature of ice? Which data support your answer? Report the uncertainty
in this measurement.
Q9. What is the boiling temperature of water? Which data support your answer? Report the
uncertainty in this measurement.
Q10. Describe what you think happened to the added heat during each of the three segments of your
graph (the “Melting”, “Boiling” and “Heating” segments). In each segment, where did the heat
(energy) go? (What did it do?)
3.4.4
Analyze the Graph that Depicts the Heating of a Solution
Q11. Use the snipping tool to take a snip of your plot and paste it here.
Q12. Describe the shape of your plot. How does it differ from the heating curve of the DI water?
Q13. According to your data, what is the melting temperature of ice with your solute in it?
Q14. According to your data, what is the boiling temperature of your solution?
Subtract the melting temperature of the DI water from the melting temperature of your solution. This is
the melting point change. Propagate the uncertainty in the melting point change.
Q15. Report the melting point change with the propagated uncertainty. Report whether the change is
positive or negative.
**
A publishable plot has a title and axis titles with units.
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Phase Changes of Solutions |9
Subtract the boiling temperature of the DI water from the boiling temperature of your solution. This is the
boiling point change.
Q16. Report the boiling point change with the propagated uncertainty. Report whether the change is
positive or negative.
Q17. Use your Excel sheet to find the uncertainty in your calculated molality.
3.5
CLASS RESULTS
Be ready share the following data with the class:
1.
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4.
The solute name
The solute molality (actual, ± uncertainty)
The melting point change ± uncertainty
The boiling point change ± uncertainty
3.5.1
Analysis
Q18. Looking at just one of the solutes, what effect did concentration of the solute have on the change
in melting and boiling point?
Q19. Which solute had a greater effect on the melting or boiling point?
Q20. What properties of the solute could account for the difference in effect?
3.6
POST-LAB ASSIGNMENT
Work with your extended group to submit a one-page abstract in class, describing the experiment you just
completed. Include your figures in your abstract.
For details, refer to the Abstract Writing Guidelines posted in the Student Resources folder on e-Learning.
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