Answer :
The order of reaction is, 0 (zero order reaction).
The value of rate constant is, 
Explanation :
Half life : It is defined as the time in which the concentration of a reactant is reduced to half of its original value.
The general expression of half-life for nth order is:
![t_{1/2}\propto \frac{1}{[A_o]^{n-1}}](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%5Cpropto%20%5Cfrac%7B1%7D%7B%5BA_o%5D%5E%7Bn-1%7D%7D)
or,
![\frac{t_{1/2}_1}{t_{1/2}_2}=\frac{[A_2]^{n-1}}{[A_1]^{n-1}}](https://tex.z-dn.net/?f=%5Cfrac%7Bt_%7B1%2F2%7D_1%7D%7Bt_%7B1%2F2%7D_2%7D%3D%5Cfrac%7B%5BA_2%5D%5E%7Bn-1%7D%7D%7B%5BA_1%5D%5E%7Bn-1%7D%7D)
or,
.............(1)
where,
= half-life of the reaction
n = order of reaction
[A] = concentration
As we are given:
Initial concentration of A = 0.229 M
Final concentration of A = 0.639 M
Initial half-life of the reaction = 29.5 s
Final half-life of the reaction = 82.3 s
Now put all the given values in the above formula 1, we get:


Thus, the order of reaction is, 0 (zero order reaction).
Now we have to determine the rate constant.
To calculate the rate constant for zero order the expression will be:
![t_{1/2}=\frac{[A_o]}{2k}](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%3D%5Cfrac%7B%5BA_o%5D%7D%7B2k%7D)
When,
= 29.5 s
= 0.229 M


Thus, the value of rate constant is, 