Practice Problem 8

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

2 HI(g) H₂(g) + I₂(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