Question

N2O5 decomposes to form NO2 and O2 with first-order kinetics. The initial concentration of N2O5 is 3.0 M and the reaction runs for 3.5 minutes. If the rate constant, k, equals 5.89 × 10−3, what is the final concentration of N2O5?

Answer 1

Answer : The final concentration of $N_2O_5$ is, 2.9 M

Explanation :

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  = $5.89\times 10^{-3}\text{ min}^{-1}$

t = time passed by the sample  = 3.5 min

a = initial concentration of the reactant  = 3.0 M

a - x = concentration left after decay process = ?

Now put all the given values in above equation, we get

$3.5=\frac{2.303}{5.89\times 10^{-3}}\log\frac{3.0}{a-x}$

$a-x=2.9M$

Thus, the final concentration of $N_2O_5$ is, 2.9 M