The decomposition of nitrogen dioxide gas to nitrogen monoxide gas and molecular

Question

The decomposition of nitrogen dioxide gas to nitrogen monoxide gas and molecular oxygen gas is second-order in nitrogen dioxide. After a period of 2.7 times 10^3 s,the concentration of NO falls from an initial value of 2.8 times 10^-3 mol/L to a final value of 2.0 times 10^-3 mol/I.. What is the rate constant, k for the process? What is the half-life for the decomposition of chcmical A via a zero-order proccss if the rate constant is 5.0 times 106-2 M s^-1 at 25degreeC if an experiment is conductcd with [A]_0 = 2.3 times 10^-3 M?

Explanation / Answer

Ok, for the first part we have to use a the integrated second order rate law:

1/[A] = kt + 1/[Ao].... Being A final concetration, k the rate constant, t the time, Ao the initial concetration

1/(2x10-3) = k 2.7x103 + 1/(2.8x10-3)

1/(2x10-3) - 1/(2.8x10-3)= k 2.7x103

142.857/2.7x103=k

k=0.0529 M-1s-1

For second part: As we have a zero order reaction we have to use this equation:

[A] = -kt + [Ao] .... Same legends as above and also remember half-life is the time where half of the chemical reacts, so

[A] = -kt + [Ao]

1.15 x 10-3= -5.0x10-2 t1/2 + 2.3 x 10-3

1.15 x 10-3 - 2.3 x 10-3= -5.0x10-2 t1/2

-1.15 x 10-3/-5.0x10-2 =t1/2

t1/2=0.023 seconds

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