the gaseous reaction A2---> 2a is first order in A2 .after 12.3 minutes 65% of A2 remains undecomposed . how long will it take to decompose 90% of A2 ?what is the half life of the reaction?

Dear Student,

As this is a 1st order reaction,
So, ​ln A = -kt + ln A
i.e. ln (0.65) = - (k) (738​ s) + ln 1.00        [65% means 0.65 if total conc. initially was 1 i.e. Ao = 1,   12.3 min = 738 s]
or,  k = 0.000584010​ s-1.

Now, to decompose 90% means 10% remains. So, putting this in equation,
ln A = -kt + ln Ao
ln 0.100 = - (​ 0.000584010​ s-1) (t) + ln 1.00

t = 3943 s  i.e. almost 66 minutes.

Half life of reaction = 0.693k=0.6930.000584010=1187 s ie. almost 20minutes.


Regards

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