The rate of a first-order reaction is followed by spectroscopy,
m...

Question

The rate of a first-order reaction is followed by spectroscopy,
monitoring the absorbance of a colored reactant at 520 nm.
The reaction occurs in a 1.00-cm sample cell, and the only
colored species in the reaction has an extinction coefficient
of 5.60 * 103 M-1 cm-1 at 520 nm. (c) Calculate the half-life of the reaction.

Accepted Answer

Hey everyone. So today we're being asked to find the half life of a first order reaction that was observed using spectral spectroscopy. So there's a lot of stuff and a lot of data that is given in this question but we're actually being misled because there's only a couple of key things that we really need to take note of. So first of all we're being asked what is the half life of the reaction? And we're also given the decay rate as well as what type of reaction it is. And this is actually all we need because as we can recall, the half life for a first order reaction can be described with the constant. The natural log of two divided by K where K. Is the decay rate. Great. So simplifying this, we get that the natural log of two divided by 3.89 times 10 to the negative four seconds to the negative one gives us a final answer of 81.49 seconds, 1781.49 seconds. However, we would like our answer to be in minutes. And if we want to do this, we can also just take this 0.49, we have seconds and remember that for every one minute one minute We have 60 seconds. So our seconds will cancel out and we will be left with a final answer of 29.7 minutes. Therefore the half life for this reaction will be 29.7 minutes. I hope this helps. And I look forward to seeing you all in the next one.

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