`A_((g)) overset(Delta)to P_((g)) + "Q"_((g)) + R_((g))` , follows first order kinetics with a half life of 69.3 s at `500^(@)` C. Starting from the gas ‘A’ enclosed in a container at `500^(@) C` and at a pressure of 0.4 atm, the total pressure of the system after 230 s will be

Options

A. 1.15 atm
B. 1.32 atm
C. 1.22 atm
D. 1.12 atm

Answer

D

Explanation

(D) `t_(1//2) = 69.3 s`
`k=(0.693)/(t_(1//2))=(0.693)/(69.3)=0.01s^(-1)`
`t = (2.303)/(k) "log" ([R_(0)])/([R])`
`230= (2.303)/(0.01)"log"((0.4))/([R])`
or log `((0.4))/([R]) = (230xx0.01)/(2.303)=1`
or log `((0.4))/([R])` =1
or `(0.4)/([R]) =10" " ( because "log"10=1 `)
`:. [R] =(0.4)/(10)=0.04 `atm
`:. ` The pressure of gas A after 230 s = 0.04 atm Decrease in pressure of gas A in 230 s
`= 0.4-0.04 ` = 0.36 atm .
`:. A(g) overset(Delta)(rarr) P(g) +Q(g)+R(g)`
At t=0 0.4 atm . `" "0" "0" "0`
At
t=232 s 0.04 atm `" "` 0.36 atm 0.36 atm 0.36 atm Total pressure = 0.04 + 0.36 + 0.36 +0.36 = 1.12 atm.