How to find the original concentration?

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Posted on : 21-02-2014 | By : My Study Coach | In : Improve Your Concentration
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The half-life of a first order reaction is 57.4 s. What was the original concentration, in mol/L, if after 2.7 minutes, the concentration of reactant is 0.0742 mol/L?

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Comments (1)

So in a first order reaction there are two equations you need to know to find the original concentration:

Integrated rate law: [At]=[A0]e^-kt
Half-Life: t1/2=ln2/k

First you will solve for k by inputting the half-life 57.4s into the equation. Using basic algebra k comes out to be about .012.

Now, you will take the k value found about and insert into into the integrated rate law, with the time elapsed in converted to sec…it should resemble the following
.0742=AOe^-.012*162
Solving for AO (initial concentration of A)= .5247 mol/L

So you ask…is this correct. Well there is always a way to check your answers. On a basic level 57.4 sec half-life and 2.7 min elapsed looks to be almost 3 half-lives. If you know this conceptually you can check yourself on a test. Every half-life takes one-half of the original concentration…1/2 three times equals 1/8. So the answer should be a little under 8 times the concentration, and it is since the third half life would be .5936 mol/L. Finally if this isn’t clear cut close to one side of the other go inbetween the two half-lives so you have a range that your math could come in.

Hope that helps.

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