PartialSpecificVolumeOfYourOwnData
This experiment is sometimes run using sugar solutions and sometimes we get bold enough to try it with
actual polymers, such as sodium poly(styrene sulfonate). Use the data from your sugar or polymer
solutions to do the following:
1. Plot -1 vs. w using Origin or Excel or actual graph paper and pencil. Select the most revealing scale
possible. Plot only points and error bars, but do not draw a curve.
2. Print the plot and then determine v~2 and v~1 GRAPHICALLY (i.e., by hand) at two distinctly different
concentrations (if you measures sugar in water, try: w = 0.025 and w = 0.25; if you measured some
real polymer, choose different concentrations if you can—you may not be able to!). Estimate the
uncertainty and identify its primary source. (Component 2 = sugar or polymer ; component 1 =
water).
3. Replot the data using Origin, Excel or equivalent. This time, fit a smooth curve (or line if that is what
your error bars suggest) through the data. At the same two concentrations mentioned in Part 2,
determine v~2 and v~1 using the best fit data from the programs equations and information in the
densitometry HowTo on the website (http://macro.lsu.edu/howto). You probably want to turn on the
95% confidence lines in Origin—fun!
4. Origin will provide you with estimated uncertainties for each fitted parameter. (If you are new to
Origin, seek help.) Apply propagation of error principles (see, for example, the famous Bevington
book or our very own Data Handling PowerPoint presentation on the HowTo site) to estimate the
uncertainties (symbol  in v~2 and v~1 at each of the concentrations. Remember, for uncorrelated
 y 
 y 
errors, if y = y(x,u) then      x2     u2 . Show how you derived your uncertainties.
 x 
 u 
2
2
2
y
Compare them to the graphically estimated uncertainties.
5. Gather your data together as v~2 = XXX  YYY and V1 = UUU  WWW at each of the two
concentrations. Show both the graphical (manual) values and the computer values.