Intrinsic Viscosity of Polyvinyl Alcohol: Part B
Robert [email protected]
Office Hour: Thursday @ 9Beaupre 450
(or by appointment)
Adapted and modified from presentation by Cali Antolini1
Purpose:▪ Use viscosity data to determine the average molecular
weight of PVA ▪ Determine the percentage of head-to-head linkage▪ More error analysis practice
Purpose
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● Viscosity – frictional drag between layers of a liquid as itflows down a tube; “thickness”. (more viscous the liquid,longer to pass through tube)
● Specific Viscosity (ηsp):η, solution viscosity (units?)η0, viscosity of solvent (units?)
When will ηsp be zero?
Concepts
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• Intrinsic viscosity [η]:
▪ Solute’s contribution to the viscosity of the solution ▪ [η] is used to measure molecular weight of a soluble
polymer in a given solvent▪ [η] is the value of ηsp/c extrapolated to zero concentration
▪ By convention, the unit of c is g/(100mL)▪ The unit of [η] is (100 mL)/g
Concepts
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The PVA chains can bond in “head-to-tail” and “head-to-head” configurations.
Head-to-tail bond:
Head-to-head bond:
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Concepts
• Experimental Design:
▪ Compare the viscosity of PVA with and without head-to-head linkage.
▪ Head-to-head linkage is cleaved by periodate▪ Head-to-tail linkage remains intact
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Concepts
• Experimental Design:
▪ Compare the viscosity of PVA with and without head-to-head linkage.
▪ Head-to-head linkage is cleaved by periodate▪ Head-to-tail linkage remains intact
• What happens to the number of molecules after cleavage?
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Concepts
Start Time End Time
See page 320 of text book
Setup – Ostwald Viscometer
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Method:▪ Obtain viscosity data for different concentrations of
PVA▪ Use potassium periodate (KIO4) to cleave head-to-head
linkage and determine the viscosity of different concentrations of cleaved PVA (same dilutions as uncleaved PVA)
▪ Calculate the percentage of head-to-head coupling
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Method
Before starting:1. Record the concentration of the stock PVA and error2. Record error of all volumetric glassware
Cleaving Stock PVA:3. Obtain about 55mL of PVA in a beaker and place it on a hot plate with stir bar4. Add 0.25g KIO4 to the beaker and heat until clear (30 minutes, turn the heat knob to 5). Do not heat above 75°C, cool to room temp.
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Procedure
Preparing Un-cleaved PVA Solutions
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Procedure
Name Volume of Stock (PVA-U0) Final Volume
PVA-U1 15 mL 25 mL
PVA-U2 10 mL 25 mL
Name Volume of Cleaved Stock (PVA-C0) Final Volume
PVA-C1 15 mL 25 mL
PVA-C2 10 mL 25 mL
Preparing Cleaved PVA Solutions
Running the PVA solutions (show me results after each run!)5. Rinse viscometer 2x with water, determine viscosity of water 3x6. Rinse 2x with sample PVA, determine viscosity of stock PVA 3x7. Repeat steps 5 & 6 using the all PVA solutions (PVA-U1, PVA-U2, PVA-C0, PVA-C1, PVA-C2)
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Procedure
Cleaning Up:8. Rinse 3x with water, determine viscosity 3x. Show me results.9. Clean all glassware and properly dispose of chemical waste
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Procedure
▪ Handle the viscometer with great care as they are fragile and expensive.
▪ Wear lab coat and safety goggles during the whole lab.
▪ Dispose the waste in properly labeled waste bottle.▪ Make sure you wash your hands after the lab.
Precautions and Protocols
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● Make table of flow times for distilled water and polyvinyl alcohol solutions
● Calculate average flow time and average temperature for each concentration
● From distilled water data, find B—the apparatus constant
● Both η and ρ can be determined from tables in the syllabus packet (like you did last week)
Calculations
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▪ t = average time for species (seconds)
▪ ρ = density ( g cm-3), (assume ρ PVA = ρ water)
▪ B = apparatus constant
▪ η = viscosity (1 mP = 10-3 g·cm-1 ·s−1)
(1)
Calculations
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● Determine ηPVA and ηSP for both cleaved and uncleaved PVA solutions
● B was just calculated● ρ is from the table for water at the averaged
temperature of water ● η0 can be calculated using the average
temperature of water and viscosity table for water
Calculations
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• Extrapolate to c = 0 to obtain the value of intercept.
• One graph must be done by hand to prepare for in class lab report! All others must be done by excel.
Calculations● Determine concentrations of both the cleaved and uncleaved
PVA solutions using C1V1= C2V2.● Graph ηSP /[PVA] vs. [PVA] for both cleaved and uncleaved
○ Extrapolate the y-intercept to get the intrinsic viscosity
Random Errors and Total Differentials
● Given a function f(x,y), then the total differential of f is:
● Square and take the average of the above equation to get:
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● Using , you can derive ε(B). Show this derivation in the lab report.
● From ε(B), you can obtain,
● Evaluate the partial derivatives from above. You should be able to obtain:
Random Errors
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Calculations: Error Analysis
● Derive the equation for the propagation of errors for:
Hint find all partial derivatives in the following equation:
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Calculations: Error Analysis
● Derive the equation for the propagation of errors for:
Hint find all partial derivatives in the following equation:
● Show this derivation in your lab report.● This equation will be used to calculate ε(F) later
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● Determine ε(ηPVA) - using process from last week’s lab● ε(t) is found using ε(t)/t from last week and the average
flow time for each solution this week.● ε(B) is calculated in the same manner as ε(t), however, be
sure to use this week’s B value● ε(ρ) is the same as last week
● If you did not observe a temperature change above 0.5 ºC add 0.5 ºC to your lowest recorded temperature.
Calculations: Error Analysis
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Calculations: Error Analysis
● ε(η0) is found using the table in the lab manual.
● If you did not observe a temperature change above 0.5 ºC add 0.5 ºC to your lowest recorded temperature.
● ε(c) is obtained from as shown below:
● Errors are obtained from the stock solution flask and other volumetric glassware used.
▪ Get the intercept [η] and the range of error (R). ▪ R, max and min slopes MUST be done by hand for the hand drawn graph.
▪ See Pages 30-32 of CHM335 syllabus.
For graphs done in Excel, please use linear regression.Don’t forget to include equation, R-value, and error bars.
25Note: Graphical error analysis could be done either on original graph or separately.
W
Max
Min
Calculations: Error Analysis
• After obtaining [η] ± R/2, the viscosity average MW for cleaved and uncleaved PVA can be found through,
• Use Mv and M’v to determine Δ.
Calculations: Δ
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ResultsSummary of Calculations• Use η0 from the trial with the shortest time.• Show sample calculations for ηPVA, ηsp, ε(t), ε(c), ε(ρ),
ε(ηsp/c) and calculations for B, M, M’, and Δ.• Show equations for each ε(c) and all partials of ε(F)
Final Table:• Make a table with flow times of water and all solutions• Report values with errors and correct sig. figs.
– Errors are always 1 sig. fig.• Include values for ηPVA, ηsp, c, ηsp/c, [η]• Include all important values from calculations (errors) and
graphs
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Lab ReportUse pages 37-39 in the syllabus as reference for writing the full lab report. The lab report should include:
Title PageMy name is:My partner’s name(s):Date and section
Abstract: last thing to be written!Summary of completed lab (generally a sentence describing each section of the lab (including
results). No more than a paragraphIntroduction
Discussion of purposeTheory
Derive any key formulas used in experiment/data analysisDefine all symbols used in the lab in words
ProcedureAttach the procedure from your lab notebookNeeds to be signed by me!
Original DataAlso attached from your lab notebook and signed by me!
CalculationsProvide sample calculations by taking one from the original data to the final results
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Use pages 37-39 in the syllabus as reference for writing the full lab report. The lab report should include:
Error AnalysisDetermine and perform any necessary propagation of errors.Only one example of each kind of propagation needs to be shown.
Graphical analysisOne graph with error bars must be done using excelAll other graphs must be hand graphed
Final TableIncludes errors
Summary of dataSummarize the final results
Average intrinsic viscosityAverage molecular weightΔReport errors and use proper sig. figs.
ConclusionDiscuss
The significance of resultsThe frequency of head-to-head connectionsThe principal sources of error
Lab Report
• Make sure all PVA solutions go into the appropriate waste container
• After running PVA rinse the viscometers thoroughly!
• Examine the data as you collect it – are your results in agreement with the physical principles at work?
• If you are confused or have questions please come to my office hour or send an e-mail
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Reminders
• Show me the results of the water runs after the cleaning the viscometer
• Lab report: both electronic and physical copies
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DO NOT FORGET TO TURN IN YOUR LAB REPORTS
Reminders
