Question #191710

The decomposition of N2O5 follows first-order kinetics based on the reaction below.

2N2O5(g) O2(g) + 4NO2(g)

The rate constant of the reaction at 25ºC is 3.46 x 10-5 /s. How long (in seconds) would it take for an initial concentration of 0.050 M to decrease to 0.015 M? What is the half-life of the reaction?

Expert's answer

The reaction is

"2N_2O_5\\Rightarrow 4NO_2+O_2"

In question we have given that

Initial concentration"(C_0)" "=0.050" M

Final concentration"(C_t)" "=0.015" M

Rate constant(K) "=" "3.46\\times10^{-5}" per second

Now for the first order reaction:

"T=\\dfrac{2.303}{K}Log\\dfrac{C_0}{C_t}"

"T=\\dfrac{2.303}{3.46\\times10^{-5}}Log\\dfrac{0.050}{0.015}=3.46\\times10^4" seconds

Now half life period for the first order reaction"=\\dfrac{0.693}{K}"

"=\\dfrac{0.693}{3.46\\times10^{-5}}=2.00\\times10^{4}" second

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