A container of `2` litre contain `4` moles of `N_(2)O_(5)`. On heating to `100^(@)C, N_(2)O_(5)` undergoes complete dissociation to `NO_(2)` and `O_(2)`. If rate constant for decomposition of `N_(2)O_(5)` is `6.2xx10^(-4) sec^(-1)`, select the correct statements:

Options

A. (a) The mole ratio before and after dissociation is `4:2`
B. (b) The time required to complete `40%` of reaction is `824 sec`
C. (c ) `t_(1//2)` of `N_(2)O_(5)` is `1117.7` sec and it is independent of temperature
D. (d) If volume of container is doubled, the rate of decomposition becomes half of the initial rate

Answer

b, c, d

Explanation

`{:(,N_(2)O_(5),rarr,2NO_(2),+,1/2O_(2)),("Initial mole",4,,0,,0),("After diss. mole",0,,8,,2):}`
`:.` Mole ratio`=4/10=2:5`
`t_(1//2)=0.693/K=0.693/(6.2xx10^(-4))=1117.7 sec`
But it depends upon temp. as `K` depends upon `T`.
`t_(40%)=2.303/(6.2xx10^(-4))"log"100/((100-40))`
`=824 sec`
Rate `r_(1)=K [N_(2)O_(5)]`, If `V` is double the concentration becomes half.
`:. r_(2)=Kxx1/2[N_(2)O_(5)]`
`:. r_(1)/r_(2)=2/1`