[CHM 371] Re: error analysis problem 4

[Andrew J. Pounds]

>
> Dr. Pounds,
>
> I am working on problem #4.  I have found the melting points and have 
> found all the residuals on excel.  I am stuck trying to find the error 
> for the molar mass of the unknown.  The molar mass of the unknown was 
> found to be 81.55 g/mol.  I'm not sure how the error of the melting 
> point relates to the error of the molar mass.  I also am not sure what 
> to do with all the residuals I found on excel.  Basically, I'm stuck 
> finding the error for this.
>
> Thanks,
>
>
You are not alone --- two others have asked about this so I am 
responding to everyone.

Think about it this way...

Delta T = T1 - T2

You get the values of T1 and T2 by graphing and finding the intersection 
of the two lines.  So at this point there should be 4 lines on your 
plot.   Each one of those lines has some error associated with it.  So 
for each of those lines you should find the error in the slope and the y 
intercept using the Regression feature inside the Excel Analysis 
Toolpack.  Remember -- from that information you get the error in the 
slope and the Y-intercept.   Now -- by looking at the lines that 
represent the maximum slope and the minimum slopes for your plot you can 
come up with error bounds for each temperature.

Error in Slope


So this will give you T1±err and the same sort of thing for T2±err in 
the case of the solution with the unknown solid.  Now -- once you have 
all this the trick is to write ONE equation that will give you the molar 
mass as a function of T1, T2, the mass of the paradichlorobenzene, and 
the mass of the unknown solid (Kf will also be in this equation).  Once 
you have that one equation you can take partials with respect to each of 
the variables and, using the big equation I gave you last week,  
determine the uncertainty in your mass.



-- 
Andrew J. Pounds, Ph.D.  (pounds at theochem.mercer.edu)
Associate Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627

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