The gas phase decomposition of HI, HI(g) → 1/2H2(g) + 1/2I2(g)?
The gas phase decomposition of HI, HI(g) → 1/2H2(g) + 1/2I2(g) , has the rate equation, -∆ [HI] / ∆t = K[HI]2 where K=30.0 L/mol. min at 443°C. How much time does it take for the concentration of HI to drop from 0.010 mol/L to 0.0050 mol/L at 443°C?
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This is a second order reaction because the rate law is k[HI]^2. We can therefore use the integrated rate law equation for second order reactions to solve this problem:
1/[A] = kt + 1/[A]o, where [A] = [HI]= 0.005 mol/L, [A]o = [HI]o = 0.010 mol/L, and k = 30.0 L/mol min. Plug those numbers into the equation and solve for t, which will come out to 3.33 min.
Alternatively, you might notice that the question is basically asking for the half-life of the reaction, because it is asking you for the time it takes for the HI concentration to drop by 50%. We can thus use the simpler half-life equation for second-order reactions to solve this problem, which is t= 1/(k[A]o). Plugging k= 30 and [A]o = 0.010 into this equation gives you the same answer.