Question

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? 

Answer 1

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