# Calcualting Activation Energy using Arrhenius equation and plot

In summary, the conversation discussed using the Arrhenius equation to plot a straight line graph and find the gradient to determine the activation energy. The units of the gradient were clarified to be 1/T, and the activation energy was determined to be 45937.6 Joules or J/mol.
This is part of a lab report so not sure if the template agrees with what I am asking but basically using the Arrhenius equation in the form of $ln(k)=ln(A)+(\frac{-E_a}{R})(\frac{1}{T})$ I plotted a straight line graph of ln(k) vs 1/T and found the gradient to be -5525.

Its the units that are confusing me so not sure if it is as straight forward as what I have done below.
$$gradient=\frac{-E_a}{R} \\ (gradient)(R)=-E_a \\ (-5525)(8.3145)=-E_a \\ -45937.6=-Ea \\ ∴ E_a=45937.6 Joules$$

any help is really appreciated, thanks.

Yes, you did it correctly. The E/RT is dimensionless, so the gradient has units of 1/T, and the activation energy is in J/mole.

Chet

Chestermiller said:
Yes, you did it correctly. The E/RT is dimensionless, so the gradient has units of 1/T, and the activation energy is in J/mole.

Chet

Right ok, thanks for clearing that up ie J/mol and not just J. Much appreciated, thanks :)

## 1. What is the Arrhenius equation and how is it used to calculate activation energy?

The Arrhenius equation is a mathematical expression that relates the rate of a chemical reaction to its temperature. It is used to calculate the activation energy, which is the minimum energy required for a reaction to occur. The equation is written as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

## 2. How do I plot the Arrhenius equation to determine the activation energy?

To plot the Arrhenius equation, you will need to rearrange the equation to the form of ln(k) = ln(A) - (Ea/R) * (1/T). Then, plot ln(k) as the y-axis and 1/T as the x-axis. The slope of the line will be equal to -Ea/R, allowing you to determine the activation energy.

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

The Arrhenius equation is primarily used for reactions that follow the Arrhenius behavior, which means they are thermally activated and have a single-step mechanism. Reactions that do not follow this behavior, such as catalyzed reactions, may require different equations to determine the activation energy.

## 4. What are the potential sources of error when using the Arrhenius equation to calculate activation energy?

Some potential sources of error when using the Arrhenius equation include inaccuracies in temperature measurements, uncertainties in the rate constant values, and assumptions made about the reaction mechanism. It is important to use precise and accurate data to minimize these errors.

## 5. Can the Arrhenius equation be used to predict the rate of a reaction at different temperatures?

Yes, the Arrhenius equation can be used to predict the rate of a reaction at different temperatures. By plugging in different values of temperature, the equation can provide a general idea of how the rate of the reaction will change. However, it is important to note that the equation assumes a constant activation energy, which may not always be the case for real reactions.

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