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Half life First order reaction

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samera12

Senior Member

samera12

Joined: 09 November 2005

Posts: 775

Posted: 03 March 2010 at 8:58pm | IP Logged
Hi, I was wondering if anyone could help me out with this question. I cant seem to get the answer right.

The first-order reaction has a half-life of 144 min. How long will it take for a sample of acctoacctic acid to be 65% decomposed?

Answer is : 218min

Thanks
samera


Edited by samera143 - 03 March 2010 at 8:59pm

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akhl

IF-Rockerz

akhl

Joined: 30 March 2007

Posts: 5223

Posted: 04 March 2010 at 6:37am | IP Logged
Let initial amount = No
Amount after the decomposition = N
There is 65% decomposition. Therefore 100-65 = 35 % remains
 
N = 35% of No
Or N = 0.35 No
t = (1/lambda) * ln(No/N)
But lambda = 0.693/T1/2
Therefore t = (T1/2 / 0.693) * ln (No/N)
t = (144 / 0.693) * ln(1/0.35)
t = 218 min
Ans: 218 min
 
Let me know if you need any further clarification.
 
Tips:
For first order reaction, remeber the following formulas:-
 
N = No * e^(-lambda * t)
lambda = 0.693 / (t1/2)
t = (1/lambda) * ln(No/N)
 
Here No = initial amount
N = amount after time t
lambda = rate constant
t1/2 = half life i.e. the time after which N = half of No
 
 


Edited by akhl - 04 March 2010 at 7:22am

samera12

Senior Member

samera12

Joined: 09 November 2005

Posts: 775

Posted: 04 March 2010 at 10:30pm | IP Logged
Thankss alottttt!! Its well explained..Smile

akhl

IF-Rockerz

akhl

Joined: 30 March 2007

Posts: 5223

Posted: 05 March 2010 at 1:21am | IP Logged
Glad to be of help. Let me know if you need any further help in Physics, Chemistry, Mathematics,

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