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### Topic: Decomposition and half-life  (Read 9114 times)

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#### sweetdaisy186

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##### Decomposition and half-life
« on: July 22, 2005, 09:12:18 PM »
What is the final concentration for the decomposition of 0.45 M X after 1.6 hours if the half-life is 35.0 minutes and the rate law is rate = k[X]2?

So, here is my theory. After 35 minutes, it would be .225MX
After 1.6 hours, it would be .196 MX

We know that 1.6 hours is equal to 96 minutes

And it we know that 105 minutes needed to reach half life.

Am I on the right track? Or am I making this way harder than it needs to be?

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##### Re:Decomposition and half-life
« Reply #1 on: July 23, 2005, 01:01:11 AM »
How did you come to the conclusion that half-life is reached after 105 minutes??
The only stupid question is a question not asked.

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##### Re:Decomposition and half-life
« Reply #2 on: July 23, 2005, 03:49:41 AM »
k= 0.693/ t1/2
= 0.693/35min
=0.0198min-1

ln [x ]t / [x ]0 = -kt = ?

[x ]t / [x ]0=e?= fraction remaining

(0.45mol)(fraction remaining)=?.??mol

I havnt included answers to the equation cause it will do you no good to just rote learn this problem,understand the equation and youl find it as easy as 1+1 :bigwink:
hope ive helped and not confused you with my rough explaination!

cheers,

The only stupid question is a question not asked.

#### xiankai

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##### Re:Decomposition and half-life
« Reply #3 on: July 23, 2005, 09:12:05 AM »
in that case, where did 0.693 jump out from?
one learns best by teaching

#### Donaldson Tan

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##### Re:Decomposition and half-life
« Reply #4 on: July 23, 2005, 10:58:30 AM »
ln 2 = 0.693
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### xiankai

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##### Re:Decomposition and half-life
« Reply #5 on: July 23, 2005, 08:23:01 PM »
i get it... thanks.
one learns best by teaching

#### sweetdaisy186

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##### Re:Decomposition and half-life
« Reply #6 on: July 23, 2005, 10:25:06 PM »
Hmmm, I like that you didn't tell me word for word. I learn better that way. BTW, what does rote mean?

I think I might have messed up my question because I meant to say that the Rate law = k[ x ] 2

So, I would use the T1/2 = 1/k[A]0 right? Apparently, the X and the [ ] make a dot. So then I got that k=.06349. And then I thought that I could plug it into the 1/[At =kt + 1/[A0 and when I did that I got .074 M. That seems sort of small if you ask me. My math was (0.06349*96) + (1/0.45)

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##### Re:Decomposition and half-life
« Reply #7 on: July 24, 2005, 01:56:31 AM »
You have showed an honest attempt at the question so ive done the working with answers. If anyone thinks ive made a mistake with my working please point this person in the right direction. ( rote learning is just memorization without understanding the problem)

k= 0.693/ t1/2
= 0.693/35min
=0.0198min-1

ln [x ]t / [x ]0 = -kt = -(0.0198mins-1)(96mins)= -1.9008

[x ]t / [x ]0=e-1.9008= 0.15

(0.45mol)(0.15)= 0.0675mol

cheers,

The only stupid question is a question not asked.

#### sweetdaisy186

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##### Re:Decomposition and half-life
« Reply #8 on: July 24, 2005, 11:19:18 PM »
Hmmm, I understand your work, but I don't understand why this is a first order reaction and not a second order. Thanks for showing me your work!!

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##### Re:Decomposition and half-life
« Reply #9 on: July 25, 2005, 05:42:19 AM »
I didnt realise that you had typed k=
• 2
Sorry :blush: your right it is a second order reaction

im workin on it and will post somthing in an hour or so.

cheers,

The only stupid question is a question not asked.

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##### Re:Decomposition and half-life
« Reply #10 on: July 25, 2005, 09:59:32 AM »
Ok youve got my brain workin overtome on this so here goes,

[x ]t= [x ]o / 1+[x ]okt

your right to use: t½ = 1 / k [A ]o, k=0.06349L/mol*min

therefore:

[x ]t=0.45M / 1+0.45*0.06349*96min

=0.45/3.742768

=0.12M (after 96 mins)

Ive also just read that the length of half-life increases as concentration decreases in a second order reaction,so 70 and 105 mins (respectivly) arn't  2nd and 3rd half-lives.

I really hope this is right as my brain hurts from trying to figure it out!
thanks for the challenge,