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/sci/ - Science & Math

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1118835 No.1118835 [Reply] [Original]

Dear /sci/,

I have a question about error analysis. In this experiment I took like 30 values of conductivity and calculated the rate constant from them using the concentration as an intermediate step. Now how I am supposed to calculate the error of the rate constant?

Just calculate the average value and then the standart derivition? But wouldn't that be disregarding the error of the conductivity and the concentration? Or should I use error propogation using average values for the concentration / conductivity?

Note: This is the formula for the rate constant:
<span class="math">k = \frac{1}{a-b}\ln\frac{(a-x)b}{(b-x)a}\frac{1}{t}[/spoiler]

>> No.1118851

You have two alternatives.

Progate error on the averages, or doing a nonlinear fit.

>> No.1118933

>>1118851

Thanks, I think I've got.

>> No.1119541

Sorry to bother you again but somehow I ended up with some huge eror.

<span class="math">a=3,18\pm0,1*10^{-2} \frac{mol}{L}[/spoiler]
<span class="math">b=4,81\pm0,11*10^{-2} \frac{mol}{L}[/spoiler]
<span class="math">\bar{x}=2,58\pm0,1*10^{-2} \frac{mol}{L}[/spoiler]
<span class="math">\bar{k}=9,67\pm1,34*10^{-2} \frac{L}{mol*s}[/spoiler]
<span class="math">T_1=293,6K[/spoiler]
<span class="math">T_2=303K[/spoiler]

With <span class="math">A=ke^{\frac{Ea}{RT}}=const.[/spoiler] and the formula from the opening post I end up at:

<span class="math">Ea=67.1 \pm 28.5 \frac{kJ{mol}[/spoiler]
and finally <span class="math">A=8.39*10^{10}\pm 9.95*10^{11}[/spoiler]

Is this actually possible or did I (as I think) fuck up somewhere? I tried calculating <span class="math">\Delta A[/spoiler] again and again but it ends up this huge due to the large <span class="math">\Delta Ea[/spoiler]

>> No.1119544

>>1119541
That one is: <span class="math">Ea=67.1 \pm 28.5 \frac{kJ}{mol}[/spoiler]

>> No.1119922

Sorry, I don't quite get what the setup is. Which variables did you measure? What do T_1 and T_2 correspond to, and what are their uncertainties?

>> No.1119956

I did a similar experiment recently. Basically conductivity measurements are used to monitor the rate/exent of a reaction, at two different temperatures T1 and T2 to find the activation energy from the Arrhenius equation.

I didn't bother doing a full error propagation, since I'd solved a load of simultaneous equations. I just added up the relative errors of each measured quantity used and said that's the percentage error for the final value.

>> No.1120000

if you have 30 independet measurements of k, then you're all set arent you?

If you have one value of k with a shitload of measurement of other stuff, then yeah, error propagate.

Just put the formula in mathematica and have it do the derivatives for you, you probably fucked them up

>> No.1120076
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1120076

This is what it looks like, also it's the first experiment I did and therefore this is my first time doing this error calculation stuff. THe assigment says: Calculate the error of Ea and A while considering the error of all parameters.

>>1119922
Uncertainities are <span class="math">\pm0.5K[/spoiler].

>>1120000
I don't have mathematica but I used my calculator to form the derivites (voyage 2000). I don't see any erros there.

>> No.1120090

>>1120076

Oh yeah, that was the one for 30 degrees C. I did another one for 20 but we didn't pay enough attention so ended up starting the experiment at 20.6°C.