`A(g)overset(Delta)rarrP(g)+Q(g)+R(g),` follows first order kinetics with a half-life of 69.3 s at `500^(@)C.` Starting from the gas A enclosed in a container at `500^(@)C` and at a pressure of 0.4 atm, the total pressure of the system after 230 s will be

Options

A. 1.15 atm
B. 1.32 atm
C. 1.22 atm
D. 1.12 atm

Answer

D

Explanation

`A(g)rarrP(g)+Q(g)+R(g)`
`{:(At " t"=0,0."4atm",0,0,0),(At" time "t,(0.4-x),x,x,x):}`
`p_(t)=(0.4-x)+x+x+x=0.4+2x`
`orx=(p_(t)-0.4)/(2)`
`thereforep_(A)=p_(0)-x=p_(0)-(p_(t)-0.4)/(2)`
`=(2xx0.4-p_(t)+0.4)/(2)=(1.2-p_(t))/(2)`
`k=(2.303)/(t)"log"((p_(0))/(p_(A)))`
`(0.693)/(t_(1//2))=(2.303)/(230)"log"((0.4xx2)/(1.2-p_(t)))`
`(0.693)/(69.3)=(2.303)/(230)"log"((0.8)/(1.2-p_(t)))`
`"log"((0.8)/(1.2-p_(t)))=(0.693xx230)/(69.3xx2.303)=0.9987`
`(0.8)/(1.2-p_(t))=Antilog(0.9987)=10`
`therefore" " 12-10p_(t)=0.8orp_(t)=1.12" atm"`