Rate of first order reaction is 0.04 at 10 mins and 0.03 at 20 minutes after intiation. Find the half life period of the reaction
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Rate of reaction in 1st order reaction is proportional to concentration. This is taught in #2 | Rate Constant
Therefore, using the formula for 1st reaction taught in #7 | Different Order of Reactions to calculate k, we will get k = 2.303/(t2 - t1) * log{(0.04 * k)/(0.03 * k)}
t2 - t1 = (20 -10) seconds = 10 seconds. Also, k in the log portion will cancel out.
so, finally we get, k = 2.303/10*log(4/3)
Now use the formula showing relation between t1/2 & k (t1/2 = 0.693/k ) in #7 | Different Order of Reactions to calculate t1/2
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