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The reaction 2NO(2) rarr2NO+O(2) is seco...

The reaction `2NO_(2) rarr2NO+O_(2)` is second order respect to `NO_(2)`. If the intial concentration of `NO_(2)(g)` is `6.54 xx10^(-4) mol L^(-1)` and the intial reaction rate is `4.42 xx10^(-7) mol L^(-1) s^(-1)` what is the half life of the reaction.

A

`1.48 xx 10^(3)s`

B

`2.63 xx 10^(4)s`

C

`1.96 xx 10^(2)s`

D

`3.06 xx 10^(3)s`

Text Solution

Verified by Experts

Rate `= k[NO_(2)]^(2)`. To find the rate constant solve the rate law with the given data :
`k = (4.42 xx 10^(-7) mol L^(-1)s^(-1))/((6.54 xx 10^(-4) mol L^(-1))^(2)) = 1.03 L mol^(-1)s^(-1)`
The half-life of the system is found using the half-life equation for a second-order reaction.
`t_(1//2) = (1)/(k xx ("initial concentration of reactant")) = (1)/((1.03 L mol^(-1)s^(-1))(6.54 xx 10^(-4) mol L^(-1))) = 1.48 xx 10^(3)s`
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