How to Find Activation Energy from a Graph

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Written By tony

Tony is a writer and sustainability expert who focuses on renewable energy and climate change. He has been involved in the environmental movement for over 20 years and believes that education is the key to creating a more sustainable future. Tony is the founder of Gie.eu.com, a website dedicated to providing information on renewables and sustainability. He lives in California with his wife and two children.

 

 

 

 

Activation energy is the amount of energy required to start a chemical reaction. It can be represented by a graph, and the activation energy can be determined by the slope of the graph. In this article, we will show you how to find the activation energy from a graph.

How to find activation energy from a graph:

finding the activation energy of a chemical reaction can be done by graphing the natural logarithm of the rate constant, ln(k), versus inverse temperature, 1/T.

For example, consider the following data for the decomposition of A at different temperatures.

  • T (K) ln(k)
  • 298 -11.700
  • 300 -11.631
  • 302 -11.562
  • 304 -11.494

A linear equation can be fitted to this data, which will have the form:

(y = mx + b), where:
y = ln(k), x= 1/T, and m = -Ea/R.

The activation energy, EA, can then be determined from the slope, m, using the following equation:

EA = -Rm

In our example above, the slope of the line is -0.0550 mol-1 K-1.

Therefore, the activation energy is:

(EA = -Rm) = (-8.314 J mol-1 K-1)(-0.0550 mol-1 K-1) = 0.4555 kJ mol-1.

How do you find the activation energy from an Arrhenius plot?

When a reaction is too slow to be observed easily, we can use the Arrhenius equation to determine the activation energy for the reaction. The Arrhenius equation is:

k = A e-Ea/RT

Where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature in Kelvin.

The activation energy is determined by plotting ln k (the natural log of the rate constant) versus 1/T. The resulting graph will be a straight line with a slope of -Ea/R:

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ln k = -Ea/R * (1/T) + ln A

  • A: Frequency factor
  • Ea: Activation energy
  • ln k: Natural log of rate constant
  • R: Gas constant
  • (1/T): Inverse of absolute temperature (Kelvin)

Determining Activation Energy. Notice that when the Arrhenius equation is rearranged as above it is a linear equation with the form y = mx + b; y is ln(k), x is 1/T, and m is -Ea/R. The activation energy for the reaction can be determined by finding the slope of the line.</p

What does an activation energy graph show?

An activation energy graph shows the minimum amount of energy required for a chemical reaction to take place. The activation energy is the energy required to overcome the activation barrier, which is the barrier separating the reactants and products in a potential energy diagram. The highest point of the curve between reactants and products in the potential energy diagram shows you the activation energy for a reaction.

When particles react, they must have enough energy to collide to overpower the barrier. Here, the activation energy is denoted by (Ea). The activation energy can be provided by either heat or light. For example, in order for a match to light, the activation energy must be supplied by friction. Once the match is lit, heat is produced and the reaction can continue on its own.

In order for reactions to occur, the particles must have enough energy to overcome the activation barrier. This is why reactions require a certain amount of heat or light. The higher the activation energy, the more heat or light is required. The activation energy can be thought of as a threshold that must be reached in order for a reaction to take place.

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An important thing to note about activation energies is that they are different for every reaction. The amount of energy required to overcome the activation barrier varies depending on the nature of the reaction. For example, some reactions may have a very high activation energy, while others may have a very low activation energy.

The activation energy can also be affected by catalysts. Catalysts are substances that increase the rate of a reaction by lowering the activation energy. This means that less heat or light is required for a reaction to take place in the presence of a catalyst.

How do you calculate activation energy?

Activation energy is the energy required to start a chemical reaction. It is typically measured in joules or kilojoules per mole (J/mol or kJ/mol).

There are a few steps involved in calculating activation energy:

  • Convert temperatures from degrees Celsius to Kelvin. T = degrees Celsius + 273.15. T1 = 3 + 273.15.
  • Find the value of ln(k2/k1). ln(k2/k1) = Ea/R x (1/T1 – 1/T2)
  • Plug in the values and solve for Ea. Ea = R x ln(k2/k1) / (1/T1 – 1/T2)

Here’s an example:

If the rate constant, k, at a temperature of 298 K is 2.5 x 10-3 mol/(L x s), and the rate constant, k, at a temperature of 303 K is 5.0 x 10-4 mol/(L x s), what is the activation energy for the reaction?

Step 1: Convert temperatures from degrees Celsius to Kelvin. T = degrees Celsius + 273.15. T1 = 298 + 273.15. T2 = 303 + 273.15.

Step 2: Find the value of ln(k2/k1). ln(k2/k1) = Ea/R x (1/T1 – 1/T2). ln(5.0 x 10-4 mol/(L x s) / 2.5 x 10-3) = Ea/8.31451 J/(mol x K) x (1/571.15 K – 1/578.15 K). ln(0.02) = Ea/8.31451 J/(mol x K) x (-0.001725835189309576)

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Step 3: Plug in the values and solve for Ea. Ea = 8.31451 J/(mol x K) x (-0.001725835189309576) / ln(0.02). Ea = 8.31451 J/(mol x K) x (-5779.614579055092). Ea = -47236191670764498 J/mol or -472 kJ/mol.

Answer: The activation energy for this reaction is 472 kJ/mol.

How do you determine the activation energy of a reaction experimentally?

The activation energy, Ea, can be determined graphically by measuring the rate constant, k, and different temperatures. The mathematical manipulation of Equation 7 leading to the determination of the activation energy is shown below.

Since, R is the universal gas constant whose value is known (8.314 J/mol-1K-1), the slope of the line is equal to -Ea/R. By measuring the rate constants at two different temperatures and using the equation above, the activation energy for the forward reaction can be determined.

Example

Consider the following reaction: A→B The rate constant, k, is measured at two different temperatures: 55°C and 85°C. The results are as follows:

  • k = 0.132 s-1 at 55°C
  • k = 1.14 s-1 at 85°C

Using Equation 7 and the value of R, the activation energy can be calculated to be: -(55-85)/(0.132-1.14) = 46 kJ/mol.

How do you find the activation energy of a Arrhenius equation?

The activation energy of a Arrhenius equation can be found using the Arrhenius Equation: k=AeEa/RT. k is the rate constant, A is the pre-exponential factor, T is temperature and R is gas constant (8.314 J/molK)

You can also use the equation: ln(k1k2)=−EaR(1/T1−1/T2) to calculate the activation energy.

Another way to find the activation energy is to use the equation ΔG,=Δ<em