In a certain polluted atmosphere containing `O_(3)` at a steady-state concentration of `2.0 xx 10^(-8) mol L^(-1)`, the hourly Production of `O_(3)` by all sources was estimated as `7.2 xx 10^(-15) mol L^(-1)`. If only mechanism for the destruction of `O_(3)` is the second order reaction,
`2O_(3) rarr 3O_(2)`
Calculate the rate constant for the destruction reaction defined by the rate law for `-Delta[O_(3)]//Delta t`.

Explanation

At the steady state, the rate of destruction of `O_(3)` must be equal to the rate of tits generation, `7.2 xx 10^(-15) mol L^(-1) hr^(-1)`.
For the second order rate law:
`k = -(1)/([O_(3)]^(2)) (Delta[O_(3)])/(Delta t)`
`= (1)/((2.0 xx 10^(-8) M)^(2)) xx (7.2 xx 10^(-15)M hr^(-1))/(3600 s hr^(-1))`
`= 5 xx 10^(-3) L mol^(-1) s^(-1)`