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?

First calculate the values of K K=0.693T1/2=0.693120=5.77×10−3min⁡−1Now we know that for a first order reactionK=2.303tlog⁡(aa−x)Here the initial concentration a = 100 and  x  = 90∴ 5.77×10−3=2.303tlog⁡100100−90t=2.3035.77×10−3log⁡(10010)Solving, t = 399 minute