**Practice Problem 12**

Calculate the rate of decomposition of HI at 600°C.

**Solution**

We start with the following form of the Arrhenius equation:

We then pick any one of the three data points used in the preceding practice problem as
*T*_{1} and allow the value of *T*_{2} to be 873 K:

*T*_{1} = 573 K
*k*_{1} = 2.91 x
10-6 *M*/s

*T*_{2} = 873 K *k*_{2}
= ?

Substituting what we know about the system into the equation given above gives the following result:

We can simplify the right-hand side of this equation as follows:

We then take the antilog of both sides of the equation:

Solving for *k*_{2} gives the rate constant for this
reaction at 600°C:

*k*_{2} = 1.6 *M*/s

Increasing the temperature of the reaction from 573 K to 873 K therefore increases the rate constant for the reaction by a factor of almost a million.