[cbc-chem1210] Exp 1 - eqn on page 8 and sig. fig.

[robert zellmer]

I'm getting questions about eqn 8 for the actual density of water
and s.f. in the calculations.

The eqn on page 8 uses two numbers, -0.00030 and 1.0042. People
have asked if these are exact.  No they aren't.  Someone took temperature
and density data between 20 and 30 C and fit the data to a linear eqn.
In doing so the sig. fig. for these numbers were determined from the s.f.
for the temp and density used.  You need to use the s.f. in these numbers
and the s.f. for your temperature to determine the proper s.f. for the
actual density.  This can be rather tricky since you need to use the rules
for mult/div and add/subtr. in the same calculation (mult. rule first 
followed
by add. rule).  I can pretty much make assurances you won't get 1 or 1.0.
Just so all of you know, water has it's greatest density of 1.00000 g/mL at
4.0 Celsius. It's density is 1.0 g/mL (two s.f., 1 decimal place) from 0 
C to 100 C.

You need to report the proper number of s.f. in the table for all the 
numbers,
including the error and % error.  This applies even if you use Excel.

This is the same for your graphs.  The s.f. in your density and intercept
are determined by the s.f. in your mass and volume being plotted.  I will
say since doing a best-fit line averages out the error in your actual data
points, if you have enough data points you can usually gain one s.f. from
a graph.  For instance, with enough data points, if you had 3 s.f. for
the mass and 3 s.f. for the volume you could report 4 s.f. for the slope
and intercept.  Two or three data points is not enough to gain a s.f.  Why?
think about this from the perspective of plotting a best-fit line.  The 
purpose
of a best-fit line is to "average out" the error in the data points.  If 
you have
only two data points the best-fit line will go right through them and will
not average out the error in the data.  Adding one more (total of 3 data 
points)
isn't much better.  The more data points you have the safer it is to 
claim an
extra s.f. in the numbers from the best-fit line (slope, intercept).  
For our
purposes in lab we'll say you need at least four.

Dr. Zellmer
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