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) rarr P_(4)(g)+6H_(2)(g)`
or
`PH_(3)(g)rarr (1)/(4)P_(4)(g)+3H_(2)(g)`
`{:("Initial",a,,0,0),("Final",a-x,,(x)/(4),(3)/(2)x):}`
`P_(t) prop a-x + (x)/(4) + (3)/(2)x`
`P_(t) prop a+ (3)/(4)x`
(a) When `t = 0, a prop 262.4`
`a + (3)/(4)x prop 272.9`
`(3)/(4)x prop 279.9-262.4`
`x prop (4)/(3) xx 10.5 = (42)/(3) =14`
`k = (2.303)/(60) log.(262.4)/(262.4-14)`
`= (2.303)/(60)log.(262.4)/(248.4)`
`= (2.303)/(60)log.(1.056)`
`= (2.303)/(60) xx 0.0238 = 0.0009`
(b) For first order reaction
`t_(1//2) = (0.693)/(k) = (0.693)/(0.0009) = 770 s`