# The rule of thumb that the rate of reaction doubles for a 10 degrees C increase in temperature...

## Question:

The rule of thumb that the rate of reaction doubles for a 10° C increase in temperature occurs only at a specific temperature for a given activation energy. Develop a relationship between the temperature and activation energy for which the rule holds. Ignore any variation of concentration with temperature.

## Logarithmic Form of the Arrhenius Law:

The Arrhenius Law states that the rate constant of a reaction is related to the frequency factor, activation energy, and temperature, where R is the universal gas constant (8.314 J / mol K).

{eq}\displaystyle \ln \dfrac{k_2}{k_1} = \dfrac{-E_{\text{a}}}{R} \left( \dfrac{1}{T_2} - \dfrac{1}{T_1} \right) \\ {/eq}

The equation above is the logarithmic form of the Arrhenius Law.

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Let the temperature be T. The rate constant ratio is 2 to account for the rate doubling. Isolating the activation energy, we get:

{eq}\ln 2 =... Arrhenius Acid: Definition & Examples

from

Chapter 16 / Lesson 2
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What is an Arrhenius acid? Learn the definition of Arrhenius acid and the aqueous acid equation according to the theory, then see Arrhenius acid examples.