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Question 15 of 26After 62.0 min, 18.0%0 of compound has decomposed: Wlut the half-life of this reaction assuming first-order kinetics?41/2...

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Question 15 of 26After 62.0 min, 18.0%0 of compound has decomposed: Wlut the half-life of this reaction assuming first-order kinetics?41/2

Question 15 of 26 After 62.0 min, 18.0%0 of compound has decomposed: Wlut the half-life of this reaction assuming first-order kinetics? 41/2



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Question 15 of 26 After 62.0 min, 18.0%0 of compound has decomposed: Wlut
the half-life of this reaction assuming first-order kinetics? 41/2

So we know that 75% of our total decomposes in 60 minutes. We need to figure out how Maney half lives have occurred in those 60 minutes. So I always like to pretend that if we start with 100 Adams after, ah, 1/2 life, it's gonna be 50. After another half life, it's gonna be 25. And so in this case is telling us that 75% of our total has decomposed meaning we have 25% left, so 25% left of 100. Adams is gonna be 25. So right after that, we know that you've gone through 2/2 lives in order to decompose 75%. So to half lives equals 75% decomposition. So if 2/2 lives occur in 60 minutes equal 60 that means 1/2 life is just gonna be half a 60. And that's 30

Just a pretty easy question. Once you understand the tools they need to first will know that the half life is equal to the natural log of to over K. Now, this could be derived from the integrate ray laws, but for a first order decay. But it's best if you just know this. You're gonna use it pretty commonly. And so we're told that K is equal to 6.7 time sensitive you for it in verse seconds. And so, putting that together, you'll find half life is equal to a 17 point 24 seconds. Now, this is one of those ah, actually part may. Um, not seconds. You'll find it. That's minutes. I actually I got the answer. But then find mystics Arrest to fight it a minute. But in a 17.24 minutes. Now this question is one of those nice little circumstances work. It's asking what it's gonna drop to 6.25%. And so let's work. Walk through what happens. So if we start 100% we go through 1/2 life, we'll go to 50% another one 25 than 12.5 and then 6.25 So what we're seeing is that we have 1/2 life, 2/2 lives, 3/2 lives, 4/2 lives. And so this is on those nice areas where they're hitting, hitting it right on the half life. So you can just take the 17.24 most by by four, you'll get 69 minutes, and that's our answer.

Okay, so here we're using the radio activity equation for the book. Our rate at Time T is equal to initial. Our rates are not time for you to the minus lambda T you rearrange the equation, get months like the tea eagles. Natural log of arbor or not. Uh, so Lambda we know from the book is log of two over tea, half up for half life time. So that's what we want to find here. So you rearrange that equation yet t happens. Negative. Lambda. Two times t time over the log of the space you are for or not, which is 3 20 over 12 baby. Just ah, corner and time is 2.6 hours. Uh, for this to go down by four times and so you see, the half life is 1.8 out.

Reactant which have been worded into products. The provided hypothetical first order reaction is shown here. We are provided with the half life. The final concentration, The concentration of reactant at time. three seconds can be expressed as natural law, concentration of reactant at time T equals negative. Katie Press. Natural Law Had concentration at zero time. This is a question one. The real constant and half lifetime In the first order reaction can be expressed as K equals 0.693 divided play. Do you have? This is the second Equation. We substitute equation number two We substitute the values in equation number two K equals 0.693 Divided by 2.3 10 raised to power to. And the constant turns out to be 0.30 10 day step 1 -2 Second and work. We substitute this value into equation one. So they are Natural Law 3.75. 10 ways to power -3 divided by 4.32. 10 ways to power negative too equals negative 0.30 10 days to power negative too. D No solving negative 2.44 equals negative. 0.30 10 ways to govern negative too. And the time equals 2.44 Divided by 0.30 10 day super negative two. And the time required turns out to be a point 13 10 days to powers too. Seconds


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