Question

A student obtained the following data for the decomposition of nitramide in aqueous solution at 25 °C.

NH₂NO₂(aq)N₂O(g) + H₂O(l)

[NH2NO2], M	0.672	0.336	0.168	8.40×10-2
time, min	0	179	358	537

(1) What is the half-life for the reaction starting at t=0 min? min

What is the half-life for the reaction starting at t=179 min? min

Does the half-life increase, decrease or remain constant as the reaction proceeds? _________increasedecreaseremain constant

(2) Is the reaction zero, first, or second order? _______zerofirstsecond

(3) Based on these data, what is the rate constant for the reaction? min^-1

Answer 1

1. Given the data for decomposition of nitramide:

Initial Concentration = 0.672 M at t = 0 min

Final concentration = 0.336 M at t = 179 min

Half life is the time required for halving the initial or original concentration.

Thus half of initial concentration = 0.672/2 M

= 0.336 M

This is exactly same as the final concentration reached in 179 min (179 min-0 min).

Thus, half life of decomposition ofnitramide is 179 min.

As half life is a constant quantity or constant property of the substance. Thus, it will remain same at t= 0 and at t= 179 min and afterwards also.

It will remain constant throughout the course of reaction.

2. The reaction of decomposition of nitramide is first order. The rate is dependent on the initial concentration of only one reactant nitramide.

3. The rate constant for a first order reaction is related to half life as:

Rate constant k = 0.693/half life time

Substitute the value of half life

k = 0.693/179 min

k = 0.00387 min ^-1

^{​​​​​​}Therefore, rate constant for the reaction is 0.00387 min ^-1