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### AuthorTopic: How to calculate the percentage error in change in pH?  (Read 303 times) !function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0];if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src="https://platform.twitter.com/widgets.js";fjs.parentNode.insertBefore(js,fjs);}}(document,"script","twitter-wjs"); (function() {var po = document.createElement("script"); po.type = "text/javascript"; po.async = true;po.src = "https://apis.google.com/js/plusone.js";var s = document.getElementsByTagName("script")[0]; s.parentNode.insertBefore(po, s);})();

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#### marimelida

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##### How to calculate the percentage error in change in pH?
« on: January 26, 2019, 02:53:27 AM »

In my experiment, I added HCl(aq) into a buffer solution until there was a pH change of 1 pH unit. The pH meter has an uncertainty of +/- 0.2. I was wondering how I would calculate the percentage uncertainty of the solution facing a pH change of 1 unit.

I did it by calculating Change in pH = 7.2 +/- 0.2  -  6.2 +/- 0.2  = 1 +/- 0.4

but the percentage uncertainty is then 40%, is this correct? It's just such a large amount
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#### mjc123

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##### Re: How to calculate the percentage error in change in pH?
« Reply #1 on: January 28, 2019, 01:14:22 AM »

Assuming the error is random, not systematic, variances not errors are additive. Thus the variance of the sum (or difference) of two measurements is 0.22 + 0.22, and the error of the sum is the square root of that.
Rule of thumb: error of the sum or difference between 2 measurements with the same error is sqrt(2)*error of one measurement.
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#### Enthalpy

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##### Re: How to calculate the percentage error in change in pH?
« Reply #2 on: January 28, 2019, 02:24:02 AM »

Beware pH are logarithms! Percentages of logarithms are most often meaningless.

That is, an absolute change in a logarithm, for instance a change of 0.2 in the pH, is already a relative (percentage) change in the H+ concentration.

Consistently, you could also have 0.2 uncertainty on a pH of zero.
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