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### AuthorTopic: Help with differentiating integrated first - order rate equation  (Read 422 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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#### elnino2206

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##### Help with differentiating integrated first - order rate equation
« on: June 16, 2017, 07:23:29 AM »

I understand how to integrate d[A]/dT = k[A] to form the integrated first - order rate equation: [A] = [A]0 * exp(-kt).

However to 'check' this by differentiating d[A]/dT to form k[A], I am having trouble.  So far I reach d[A]/dT = [A]0*-k*exp(-kt).  Please may someone point me in the right direction?
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#### mjc123

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##### Re: Help with differentiating integrated first - order rate equation
« Reply #1 on: June 18, 2017, 10:33:39 PM »

Your rate equation should be d[A]/dt = -k[A] to give the quoted integral equation for [A]. This is the first order rate law. d[A]/dt = k[A] would be an autocatalytic reaction.
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