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Calculation Involving a Change in TemperatureLet's examine the general rule of thumb regarding the rate constant doubling for a 10 ° C increase in temperature. Assume a pre-exponential factor of 5.0 x 1016 s-1. The ideal gas constant is 8.3145 J/mol K. Find the ratio of the two different rate constants for an activation energy of 147 kJ/mol and a change in temperature from 490 K to 500 K and 500 K to 510 K. Solution: A total of three temperatures are given at which to find the rate constants. We can insert these given values into Arrhenius' equation. We will calculate three rate constants, k1, k2, and k3 at 490 K, 500 K, and 510 K respectively. k1 = 5.0 x 1016*exp(-147,000/(8.3145*490)) = 10.689 s-1 k2 = 5.0 x 1016*exp(-147,000/(8.3145*500)) = 21.996 s-1 k3 = 5.0 x 1016*exp(-147,000/(8.3145*510)) = 44.001 s-1 Now let's look at the ratios of these rate constants. This is the increase in the rate constant by raising the temperature from 490 K to 500 K. This is the increase in the rate constant by raising the temperature from 500 K to 510 K. As you can see, the rate constant only doubles for a specific temperature change of 10 ° C.
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