Rate of a chemical reaction: The temperature dependence of the rate of a certain chemical reaction in particular equipment is given by

grams/sec,

where R is the rate of the reaction and T is in degrees Celsius.
We can find Tmax, the temperature at which the rate is a maximum, by differentiating and setting the derivative to 0.

At Tmax, this expression equals 0:

From this, we get , or deg C.

This is the temperature at which the maximum rate occurs. To get the maximum rate, Rmax, itself, we can substitute into the equation for the rate:

Test Problem: Find the values of Tmax and Rmax for

Tmax Rmax
a) 15.8, 56000
b) 6.30, 5694
c) 3.98, 6872