Some `PH_(3)` is introfuced into a flask at `600^(@)C` containing inert gas. `PH_(3)` decomposed to give `P_(4)(g)` and `H_(2)(g)`. The total pressure as a function of time is given below.
`|{:("Time (s)" " "0,60,120,oo),("Pressure (mm) (total) 262.4",272.9,275.53,276.4):}|`
Find the order and half life.

Explanation

`{:(,4PH_(3(g)),+,"Inert gas",rarr,P_(4(g)),+,6H_(2(g)),+,"Inert gas"),("At t=0,",P,,P',,,,0,,0),("At t=t," ,(P - A),,P',,A/P,,(6A)/(4),,P'),("At t=oo",0,,P',,P/4,,(6P)/(4),,P'):}`
At `t=0, P=262.40=P_(PH_(3))+P_(I.G)`
At `t=60, P=272.90=P_(PH_(3)("Left")) +P_(P_(4)(g))+P_(H_(2)(g))+P_(I.G)`
At `t=120, P=275.51=P_(PH_(3)("Left")) +P_(P_(4)(g))+P_(H_(2)(g))+P_(I.G)`
At `t=oo, P=276.40=P_(P_(4)(g))+P_(H_(2)(g))+P_(I.G)`
`:. P/4+(6P)/(4)+P'=276.40`
`:. 7P+4P'=(276.40)xx4 ...(1)`
Also at `t=0, P+P'=262.40 ...(2)`
`:. P=18.66 mm`
`P'=243.74 mm`
At `t=60, pressure =272.90=(P-A)+P'+A/4+(6A)/(4)`
`272.90=1866-A+243.74+(7A)/(4)`
`:. A=14.0 mm`
`:. K=2.303/t"log"([P_(PH_(3))]_(0))/([P_(PH_(3))]_(60))`
`=2.303/60"log"18.66/((18.66-14))`
`=2.31xx10^(-2) sec^(-1)`
At `t=120`,
pressure=`275.51=P-A'+P'+(A')/4+(6A')/4`
`275.51=18.66-A'+243.74+(7A')/4`
`:. A'=17.48 mm`
`:. K=2.303/120"log"18.66/((18.66-17.48))`
`=2.30xx10^(-2) sec^(-1)`
`:.` Reaction is of first order.