Arsine decomposes on heating according to the equation `2AsH_(3)(g) rarr 2As(s) + 3H_(2)(g)`. The decompoistion was studied at constant temperature and constant volume by measuring the total pressure at various intervals of time.
`|{:("Time (min)",0,5,7.5,10),("Total Pressure (atm)",1,1.09,1.13,1.16):}|`
Assume it to be a first order reaction, calculate the specific rate constant and half life of the reaction.

Explanation

`{:(,AsH_(3), rarr, As(s)+, (3)/(2)H_(2)(g)), ("Initial",1,,0,0),("Final",1-x,,0,(3)/(2)x):}`
(a) `1-x+(3)/(2)x prop 1.09 rArr x prop 0.18`
`:. k = (2.303)/(5) log.(1)/(1-0.18) = (2.303)/(5) xx 0.084`
`= 0.04 min^(-1)`
(b) `1-x+(3)/(2)x prop1.13 rArr x prop 0.26`
`k = (2.303)/(7.5)log.(1)/(1-0.26)`
`= (2.303)/(7.5)log.(1)/(0.74)`
`= (2.303)/(7.5) xx 0.1306 = 0.0401 min^(-1)`
( c) `-x+(3)/(2)x prop 1.16 rArr x prop 0.32`
`k = (2.303)/(10) log.(1)/(1-0.32)`
`= (2.303)/(10) log.(1)/(0.68)`
`= (2.303)/(10) xx 0.1676 = 0.039 min^(-1)`
Mean value of `k = (0.04 + 0.0401 + 0.039)/(3)`
`= 0.0397 min^(-1)`
`t_(1//2) = (0.693)/(k) = (0.693)/(0.0397) = 17.46 min`