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)to 2N_(2)O_(4)(g) +O_(2)(g)`

Calculate the rate constnat.

Explanation

`2N_(2)O_(5)(g) to 2N_(2)O_(4)(g)+ O_(2)(g)`
`{:("At " t=0, 0.5" atm", 0 " atm", 0 " atm"),("At time " t, 0.5-2x " atm" , 2x" atm", x" atm"):}`
`p_(t) = p_(N_(2)O_(5)) + p_(N_(2)O_(4)) + p_(O_(2))`
= (0.5 -2x) + 2x +x =0.5 +x
`x = p_(t)-0.5`
`p_(N_(2)O_(5))= 0.5-2x =0.5-2(p_(1)-0.5) =1.5-2p_(1)`
`"At "t = 100s, p_(1) = 0.512 atm`
`p_(N_(2)O_(5))= 1.5-2 xx 0.512 = 0.476 "atm"`
`k = (2.303)/(t) "log" ("pi")/("pA")`
`k = (2.303)/(100s) "log" (0.5 " atm")/(0.476" atm")`
`k = (2.303)/(100s) xx 0.0216 = 4.98 xx 10^(-4)s^(-1)`