Partial Specific Density for HPC
Associated with this link are a few lab notebook pages from former student Derek Dorman. They
show the measurement of the partial specific volume of hydroxypropylcellulose (HPC) at 35oC,
which was an experiment we did in this class several years ago. The experiment was conducted
by first preparing a stock solution of HPC in water. The concentration is known both
volumetrically and by weight percent. Known volumes (and masses) of the stock solution are
placed in weighed vials. These are covered with weighed amounts of water. Triplicate density
measurements of density,  from the PAAR Densitometer
(http://macro.lsu.edu/howto/Densitometry.PDF ) appear on pages 22 and 23. Your job is to use
these data to compute the partial specific volume v~HPC in mL/g and the partial molar volume
VHPC in mL/mol at two specific weight/weight concentrations. You may assume a molar mass of
60,000 g/mol for this HPC.
 Plot -1 vs. w using Origin or Excel or actual graph paper and pencil. Select the most
revealing scale possible. Plot only points, not a curve.
 Determine v~2 and v~1 GRAPHICALLY (i.e., by hand) at w = 0.025 and w = 0.045. Estimate
the uncertainty and identify its primary source. (Component 2 = HPC; component 1 = water).
 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
determine v~2 and v~1 using the equations in the densitometry HowTo listed above.
 Origin will provide you with 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.
 y  2  y  2
  x     u . Show
 x 
 u 
2
2
Remember, for uncorrelated errors, if y = y(x,u) then  y2  

how you derived your uncertainties. Compare them to the graphically estimated
uncertainties.
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.