Arrhenius equation

In attempting to quantify the increase of a reaction rate with temperature, Arrhenius compared observed increases in reaction rate with the temperature dependence of some possible causes.
The influence of temperature on the specific reaction rate is very large in that, at ordinary temperatures, the rate increases by 10 to 15 per cent for each one-degree rise in temperature. It cannot be assumed, therefore, that the increasing reaction velocity comes from the increasing frequency of collisions of the reacting molecules. According to the kinetic theory of gases, the velocity of the gas molecules changes only by about 1/6 per cent of its value for each one-degree rise in temperature and the frequency of collisions increases in the same ratio.
1) Use a formula for a typical molecular speed (average speed, root mean square speed, or most likely speed) to compute the percentage increase in speed for the following one-degree temperature increases:
a) 0°C to 1°C
b) 25°C to 26°C
c) 50°C to 51°C
Is Arrhenius's generalization about the velocities of gas molecules justified?

2) Using the equation we now call the Arrhenius equation for a reaction rate constant, compute the activation energy for a reaction if its rate constant increases
a) 10%
b) 15%
when the temperature is raised from 25°C to 26°C.

Reference

Svante Arrhenius, "On the Reaction Velocity of the Inversion of Cane Sugar by Acids," Zeitschrift für physikalische Chemie 4, 226ff (1889)
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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