April 03, 2020, 08:35:38 PM
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Topic: Propagating uncertainty for Activation Energy Lab Report  (Read 134 times)

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Offline potatohead

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Propagating uncertainty for Activation Energy Lab Report
« on: March 20, 2020, 06:09:03 PM »
Hello everyone, I'm wondering how I would calculate the uncertainty of my findings for a lab report.

I found the activation energy of the alka seltzer reaction in water (C₆H₈O₇+3NaHCO₃ → 3H₂O+3CO2+Na3C6H5O7)

The way I found it was to measure pressure change over time in a closed erlenmeyer flask, convert that to concentration (using ideal gas law), and take its inverse over time to graphically find the rate constant. Then, I took the natural log of the rate constant against the inverse of time (aka the Arrhenius equation) to give me Ea times r. I divided the slope of the graph by R to give me Ea. However, now I'm confused where to begin with apparatus uncertainty and how it factors into my calculations.

I have the uncertainty of the digital stopwatch, of the pressure probe, of the graduated cylinder used for measuring, of the electronic balance and the thermometer (the trials were done at various temperatures).

So where do I even begin with this? Sorry if my explanation is weird, but I can share my document with you if you are able to explain to me how I would start.



Offline MNIO

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Re: Propagating uncertainty for Activation Energy Lab Report
« Reply #1 on: March 21, 2020, 08:22:32 PM »
Can you provide the data you collected?  because
  (1) I don't believe you're using the correct rate equation
  (2) you're confusing "t" and "T".. (time vs Temp) in the arrhenius equation

and fyi.. we propagate errors by the following
  given the functions
      A ± ∆A
      B ± ∆B
  for addition / subtraction
     (A+B) = (A+B) ± √ [(∆A)² + (∆B)²]
     (A-B) = (A-B) ± √ [(∆A)² + (∆B)²]
  for multiplication / division
     (A*B) = (A*B) ± (A*B)*√ [(∆A/A)² + (∆B/B)²]
     (A/B) = (A/B) ± (A/B)*√ [(∆A/A)² + (∆B/B)²]
  for a GENERAL equation,
     For any given function, Z = f(x)
     the error in Z.. i.e.. ∆Z = f'(x) * dx
  in other words.. for log functions
     Z = ln(x)
   ∆Z = (d (ln(x)) / dx) * ∆x = (1/x) * ∆x = ∆x / x



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