The thermal decomposition of a compound is of first order. If `50%` of a sample of the compound is decomposed in 120 minutes, how long it take for `90%` of the compounds to decompose.

Explanation

Step I: Calculation of rate constant: (k)
`k=(0.693)/t_(1//2)=0.693/(120 "min")`
Step II: Calculation of time for 90 percent decomposition
`a=100%, (a-x)= 10%, k=0.693//120 min^(-1)`
`t=(2.303)/(k) log a/(a-x) = (2.303)/(0.693/120 min^(-1)) log 100/10`
`=(2.303 xx 120)/(0.693) = 389.79 min`.