**Practice Problem 8**

Hydrogen iodide decomposes to give a mixture of hydrogen and iodine:

2 HI(*g*) H_{2}(*g*) + I_{2}(*g*)

Use the following data to determine whether the decomposition of HI in the gas phase is first order or second order in hydrogen iodide.

**Initial (HI) ( M)
Initial Instantaneous **

**
Rate of Reaction ( M/s) **

Trial 1: 1.0 x 10^{-2 }
4.0 x 10^{-6 }

Trial 2: 2.0 x 10^{-2 }
1.6 x 10^{-5 }

Trial 3: 3.0 x 10^{-2 }
3.6 x 10^{-5 }

**Solution**

We can start by comparing trials 1 and 2. When the initial concentration of HI is doubled, the initial rate of reaction increases by a factor of 4:

Now let's compare trials 1 and 3. When the initial concentration of HI is tripled, the initial rate increases by a factor of 9:

The rate of this reaction is proportional to the square of the HI concentration. The reaction is therefore second order in HI, as noted in a previous section:

Rate = *k*(HI)^{2}