The following data is obtained during the first order thermal decomposition of `2A_((g)) rarr B_((g))+C_((s))` at constant volume and temperature .

The rate constant in `min^(-1)` is :

Options

A. 0.0693
B. `6.93`
C. 0.00693
D. 69.3

Answer

A

Explanation

(A) `2A(g) rarr B(g)+C(s) `
At t =0 `" " P " " 0" " 0`
At t=10 mm `" " P-P " " p//2" "0`
after completion 0 (P)/(2)
The total pressure after 10 min
`= P-p +(p)/(2)`
`= P- (p)/(2)`
=300 mm Hg
The total pressure after completion
`=(P)/(2) = 200 mm Hg `
`:.` P=400
`:. [R_(0)]=400`
Now `P-(P)/(2)` = 300
or `400-(P)/(2)=300`
or `(P)/(2)=100`
or p=200
`:.` Pressure of A after 10 min
=P-p=400 -200 =200
`:. [R]= 200`
`k=(2.303)/(t) "log"([R]_(0))/([R])`
`= (2.303)/(10)"log" (400)/(200) =(2.303)/(10)"log"2`
`= (2.303)/(10)xx0.3010=0.0693 "min"^(-1)`