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### Topic: Error propagation involving natural logarithms  (Read 316 times)

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#### daaniiell14

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• Mole Snacks: +0/-0 ##### Error propagation involving natural logarithms
« on: February 18, 2020, 01:11:56 PM »
In our kinetics lab we are plotting $$ln\frac{ A_{inf}-A }{ A_{inf} }$$ against -kt, i.e solving an pseudo first order reacting to find a rate constant. The problem however is finding out how the different errors (uncertainties) of the stuff in the ln term get translated to uncertainties in the y axis when i plot these.

I have tried using the error propagation rules to first solve for the numerator and then the entire paranthesis. The uncertainties is for A(inf)=0,008328 and A=0,05 and A(inf)=2,082 is just another constant so the only variable is A.

Trying to use the natural logarithm error propagation law then just causes chaos because my A is in the denominator which means that with higher Absorbance values for some reason my error gets larger and larger even though logically it should be the opposite since an error in 0,05 impacts A=0.1 more than A=2.0?

#### Corribus

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• Gender: • A lover of spectroscopy and chocolate. ##### Re: Error propagation involving natural logarithms
« Reply #1 on: February 18, 2020, 05:48:38 PM »
Are your two terms linked as independent pairs? I.e., do you obtain A and Ainf values for three independent experiments? If that's the case I would just calculate three values by your equation and taken the std. deviation of the mean as your over all error.

I'm no statistician but I only use error propagation if the measurements/values are decoupled from each other.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### Enthalpy ##### Re: Error propagation involving natural logarithms
« Reply #2 on: February 19, 2020, 02:53:37 PM »
A relative error in a logarithm propagates as an absolute error. That's tricky. That is, 1% error in a log becomes 0.01 error, whether the 1% accuracy is on camels or on koalas.

This implies that the result of a log has usually no unit. And for instance, a relative error on a pH has no meaning.