`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

`t_(1//2)= 69.3s, t= 230s, a = 0.4 atm`
For first order reaction,
`k=(0.693)/(t_(1//2))=(0.693)/(69.3)=0.01s^(-1)`
`k=(2.303)/(t) log. (a)/(a-x)= (2.303)/(230)log. (0.4)/(0.4-x)`
`0.01= (2.303)/(230) log. (0.4)/(0.4-x)=0.01 log. (0.4)/(0.4-x)`
`(0.01)/(0.01)= log. (0.4)/(0.4-x) rArr 1 = log. (0.4)/(0.4-x)`
Antilog of `1= (0.4)/(0.4-x) rArr 10 = (0.4)/(0.4-x)`
`x=0.36`
For the given reaction,
`{:(" "A_((g))overset(Delta)rarrP_((g))+Q_((g))+R_((g))),("Initial 0.4 0 0 0" ),("Final 0.4-0.36 0.36 0.36 0.36"),():}`
Total pressure
`=(0.4-0.36)+(3xx0.36)=1.12` atm