Thermal decomposition of a compound is of first order. If 50 % of a sample of the compound is decomposed in 120 minutes how long will it take for 90 % of the compound to decompose?

Question

Thermal decomposition of a compound is of first order. If 50 % of a sample of the compound is decomposed in 120 minutes how long will it take for 90 % of the compound to decompose? (A) 399 min (B) 410 min (C) 250 min (D) 120 min

Tardigrade Admin · Accepted Answer

First calculate the values of K K=(0.693/T12)=(0.693/120)=5.77×10-3 min-1 Now we know that for a first order reaction K=(2.303/t)log((a/a-x)) Here the initial concentration a = 100 and n = 90 ∴ 5.77×10-3=(2.303/t)log (100/100-90) t=(2.303/5.77×10-3)log ((a/a-x)) Solving, t = 399 minute

Q. Thermal decomposition of a compound is of first order. If 50% of a sample of the compound is decomposed in 120 minutes how long will it take for 90% of the compound to decompose?

399 min

410 min

250 min

120 min

First calculate the values of K K=T120.693​=1200.693​=5.77×10−3min−1 Now we know that for a first order reaction K=t2.303​log(a−xa​) Here the initial concentration a=100 and n=90 ∴5.77×10−3=t2.303​log100−90100​ t=5.77×10−32.303​log(a−xa​) Solving, t=399 minute

Q. Thermal decomposition of a compound is of first order. If $50%$ of a sample of the compound is decomposed in $120$ minutes how long will it take for $90%$ of the compound to decompose?