Practice Problem 12

Calculate the rate of decomposition of HI at 600C.


Solution

We start with the following form of the Arrhenius equation:

Ex22_12a.gif (1429 bytes)

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:

Ex22_12b.gif (1967 bytes)

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

Ex22_12c.gif (1429 bytes)

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

Ex22_12d.gif (1315 bytes)

Solving for k2 gives the rate constant for this reaction at 600C:

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.

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