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 (1)/([A_o]^(n-1))](https://img.qammunity.org/2021/formulas/chemistry/college/c0ylcn3s9gtkl2og4wbqbj0qtgpg3foswe.png)
or,
![(t_(1/2)_1)/(t_(1/2)_2)=([A_2]^(n-1))/([A_1]^(n-1))](https://img.qammunity.org/2021/formulas/chemistry/college/p7n18i5ft7e4jvddjo8ao6y0gtmol54bxp.png)
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)=([A_o])/(2k)](https://img.qammunity.org/2021/formulas/chemistry/college/ltf2hgs1nz11xu3q7ywtfzptaays9qqdyb.png)
When,
= 29.5 s
= 0.229 M


Thus, the value of rate constant is,
