The reaction given below is observed to be first order with rate constant `7.8xx10^(-3)" sec"^(-1)`. Calculate the time required for the total pressure in a system containing A at an initial pressure of 0.1 atm to rise to 0.145 atm and also find the total pressure after 100sec.
`2 A(g) rarr 4B (g) + C(g)`

Explanation

`{:(,,2A_((g)),,to,,4B_((g)),,+,,C_((g))),("Initial",,P_(0),,,,0,,,,0),("At time t",,P_(0)-P.,,,,2P.,,,,P.//2):}`
`P_("total")=P_(0)-P.+2P.+P.//2=P_(0)+(3P.)/(2)`
`P.=(2)/(3)(0.145-0.1)=0.03atm`
`k=(2.303)/(t)log.(P_(0))/(P_(0)-P.)`
`t=(2.303)/(7.48xx10^(-3))log((0.1)/(0.07))=47.7sec`
Also, `k=(2.303)/(t)log((0.1)/(0.1-P.))`
`7.48xx10^(-3)=(2.303)/(100)log((0.1)/(0.1-P.))`
`0.1-P.=0.047`
`P.=0.053`
`P_("total")=0.1+(3)/(2)(0.053)~~0.180atm`.