# Solving Arrhenius Eqn: Double Reaction Rate at 10°C

• fk378
In summary, the conversation discusses a common rule of thumb for reaction rates and the derivation of this rule under certain conditions. The conversation also addresses the variables to plug into the equation and the value to solve for, which is Ea. The correct equation to use is also mentioned.
fk378

## Homework Statement

A common rule of thumb is that temperature 10 degrees C for many reactions will double the reaction rate. Derive under what conditions this is true.

## Homework Equations

ln(k) - ln(2k) = (-Ea/R) [(1/T1)-(1/T2)]

## The Attempt at a Solution

I know I have to start off by plugging in values for T1 and T2, but what exactly am I trying to solve for? My teacher said to solve for Ea, but that is the measure of kinetic energy needed for reaction...what do I solve for when looking for reaction rate?

Also, can I leave the rate constants in or should I plug in actual values for those as well?

I had the exact same question on a quiz, but instead we were given the room temperature. Indeed you do want to solve for Ea. You'll want to plug in values for ln k & temp. Think arbitrary values for what you want to plug in for the numbers, as long as they all relate to each other.

But what value of Ea am I looking for? If I'm plugging in all my values into that equation that I typed up there, of course I'll just get a value for Ea.
And why am I solving for Ea anyway? How will I know what the reaction rate is if I know Ea?

The equation you are using is incorrect.

Last edited by a moderator:
I'm using the same equation as that...I'm just changing the locations of the corresponding k1/T1 and k2/T2 values.

Nice derivation, Roco. Rewrite the expression and solve for Ea. Use "T1+10" in place of "T2".

## 1. What is the Arrhenius equation?

The Arrhenius equation is a mathematical formula that relates the rate of a chemical reaction to temperature. It was developed by Swedish chemist Svante Arrhenius in the late 19th century and is based on the concept that a higher temperature leads to a faster reaction rate.

## 2. How does the Arrhenius equation help in understanding reaction rates?

The Arrhenius equation allows scientists to calculate the activation energy of a reaction, which is the minimum amount of energy needed for a chemical reaction to occur. By knowing the activation energy, scientists can predict how temperature changes will affect the rate of a reaction.

## 3. What is a double reaction rate and how is it achieved?

A double reaction rate means that the rate of the chemical reaction has doubled compared to the original rate. This can be achieved by either doubling the temperature or by using a catalyst, which lowers the activation energy and allows the reaction to occur at a faster rate.

## 4. Why is 10°C used in the context of the Arrhenius equation?

10°C is often used in the context of the Arrhenius equation because it is a standard temperature that is close to room temperature and allows for easy comparison of reaction rates. Additionally, at 10°C, most chemical reactions are still relatively slow and can be easily measured and studied.

## 5. Can the Arrhenius equation be used for all types of chemical reactions?

No, the Arrhenius equation is most accurate for simple, one-step reactions. For more complex reactions with multiple steps and intermediate products, the equation may not accurately predict the rate of the reaction. Additionally, the Arrhenius equation is only applicable to reactions that are affected by temperature, so it cannot be used for all types of chemical reactions.

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