Practice Problem 12
Calculate the rate of decomposition of HI at 600°C.
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 T1 and allow the value of T2 to be 873 K:
T1 = 573 K k1 = 2.91 x 10-6 M/s
T2 = 873 K k2 = ?
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 k2 gives the rate constant for this reaction at 600°C:
k2 = 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.