For the first order reaction `A(g) rarr 2B(g) + C(g)`, the initial pressure is `P_(A) = 90` mm Hg, the pressure after `10` minutes is found to be `180` mm Hg. The rate constant of the reaction is

Options

A. `1.15 xx 10^(-3) sec^(-1)`
B. `2.3 xx 10^(-3) sec^(-1)`
C. `3.45 xx 10^(-3) sec^(-1)`
D. `6 xx 10^(-3) sec^(-1)`

Answer

A

Explanation

`{:("The reaction is",A_((g)),rarr,B_((g)),+, C_((g))),("at t=0 pressure",PA,,0,,0),("Pressure after",P_(4)-x,,2x,,x),("10 minutes",,,,,):}`
Total pressure after `10` minutes, `P_(T) = P_(A) + P_(B) + P_( C)`
or, `P_(T) = (P_(A) - x) + 2x + x`
`= P_(A) + 2x = 180`
`because P_(A) = 90mm`
`90 + 2x = 180` or, `X = 45 mm`
`:. P_(A) - x = 90 - 45 = 45 mm`
Since, `kt = 2.303 "log"(P_(A))/(P_(A) - x)`
or, `k xx 10 = 2.303 "log"(90)/(90 - 45)`
`k xx 10 = 0.693`
or, `k(0.693)/(10) = 0.0693 "min"^(-1)`
`= (0.693)/(10 xx 60 sec) = 1.155 xx 10^(-3) sec^(-1)`