The following data were obtained during the first order thermal decomposition of `N_(2)O_(5)(g)` at constant volume: `2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)`
`{:("SI.No","Time(s)","Pressure (atm)"),(1.,0,0.5),(2.,100,0.512):}`
Calculate the rate constant.

Explanation

`" "2N_(2)O_(5)(g)rarr2N_(2)O_(4)(g)+O_(2)(g)`
`{:("Initial pressure"(P_(i))"at " t=0:,0.5"atm",0"atm",0"atm"),("Pressure" (P_(t))"at time t:",(0.5-2x)"atm",2x"atm",x"atm"):}`
`therefore P_(t)=p_(N_(2)O_(5))+p_(N_(2)O_(4))+p_(O_(2))=(0.5-2x)+2x+x=0.5+x`
`thereforex=p_(t)-0.5`
`therefore p_(N_(2)O_(5))=0.5-2x=0.5-2(P_(t)-0.5)=1.5-2P_(t)`
At t = 100s ` P_(t)=0.512"atm"`
`thereforep_(N_(2)O_(5))=0.5-2x=1.5-2xx0.512=0.476 "atm" `
`therefore k=(2.303)/(t)log.(P_(i))/(P_(t))=(2.303)/(100)log.(0.5)/(0.476)=4.92xx10^(-4)s^(-1)`