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The half-life of a reaction of compound $A$ to give compounds $D$ and $E$ is 8.50 min when the initial concentration of $A$ is $0.150 \mathrm{~mol} / \mathrm{~L}$. How long will it take for the concentration to drop to $0.0300 \mathrm{~mol} / \mathrm{~L}$ if the reaction is (a) first order with respect to $A$ or (b) second order with respect to $A ?$
A. 19.75 minutesB. 34 minutes
Chemistry 102
Chapter 12
Kinetics
Drexel University
University of Kentucky
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University of Toronto
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love one, This is Ricky. And today we're working on problem number 42 and we have to calculate e time. It will take for concentration to drop 2.3 miles a Moler into scenarios if the reactions for a shorter with respect to a or second order with respect to pay. So we have an equation A mix tape, D plus e. Yeah, we haven't a knot, um, of 0.15 Mueller, we have a final concentration of points. 300 Molin. And so if we go through scenario A where I am isn't one. We have 1/2 life formula of equals. One have of 0.6 93 over. Okay. And we are going to solve for Kay. So K is equal to 693 over there have. All right, so we Hi. We also know that the half life is equal to 8.5 minutes. So if we plug this into our formula, we get where 815 Her minute is our great constant. Now, let's put this into the integrated rate law for a for a first order equation. So we have natural log A. It's equal to negative. Katie plus national log The nonce rearranged to solve for T C T is equal to natural log of a knot minus natural of a all over K. Now we can plug plug in our initial plug in her final conflict in our okay value when we get that time is equal to 1928 minutes. All right, Now we have to do the same thing when this is a second order reaction. Okay, so let's solve for our you're a very constant. So we have won over K. Time's a knot is equal to you. Are half life equation rearranged to sulfur case okay is equal to, um K is equal to one over half life times a knot. If we plug and chug, we get that K is equal to 0.784 Her Moeller per minutes is equal to K. Now, what we want to do is plug into the integrated rate law and then solve for tea. So we got one over a people to katie plus one over a knot rearranged the sulfur T so t is equal to t is equal to one over a minus one over a knots. In this entire quantity is divided by K. We plug in shock when we get that T is equal to 34 minutes. So I hope this video was helpful.
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