Calculate the Half-life of Iodine in Reaction Between Argon and Iodine

Question

The rate constant for the reaction is

I + I +Ar → I₂ + Ar

Is 0.59 ×10¹⁶ cm⁶ mol^-2s^-1 at 293K. What is the half-life of I if [I]₀  = 2×10^-5 molL^-1 and [Ar] = 5×10^-3 molL^-1?
 
Summary

The question belongs to Chemical Engineering and it is about the reaction between Iodine and Argon. The question is about calculating the half life of iodine.

Note: The solution is in handwritten format.