Chemistry Rate Law question?

The hydrolysis of a tosylate derivitive of a naturally occuring organic terpene compound has an initial reaction rate of 6.15 x 10 ^-7 mol / (L X s) at 25°C. The reaction is temperature dependent and sees a tripling in rate for every 10 °C increase. What is the rate at :

a.) 15 °C

b.) 75 °C

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If the initial reaction rate was 6.15 x 10^-7 at 25 degrees Celsius, and the rate triples for every additional ten degrees, you would simply divide by three to get the rate for fifteen degrees Celsius, since this is ten degrees less:

6.15 x 10^-7 / 3 = 2.05 x 10^-7

To get the reaction rate for seventy five degrees Celsius, that is a difference of fifty degrees. That is five sets of ten, so we need five triplings of the initial reaction rate. If the reaction rate triples for every ten degrees of difference, that would be the same as multiplying the initial reaction rate times 243, because 3 x 3 x 3 x 3 x 3 = 243. So multiply 6.15 x 10^-7 times 243:

6.15 x 10^-7 x 243 = 1494.45 x 10^-7, or 1.495 x 10^-4

You would adjust the negative exponent by three decimal places, resulting in an answer of 1.495 x 10^-4. This is exactly what you would expect to see, if the reaction rate is temperature dependent, indicating a rise in the reaction rate as the temperature increased.

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