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# Activation Energy

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Imagine if water boiled spontaneously at room temperature or if milk curdled the second you opened the carton. That would be a bit crazy, wouldn't it? These things don't happen because these reactions (and all reactions) require energy. Some reactions have a mountain of energy to climb, some have a small stump of a hill, but all need to climb some type of energy mountain to occur.

In this article, we will be covering activation energy, which is that metaphorical hill that all reactions have to climb.

• First, we will cover why activation energy is important.
• Next, we will cover the Arrhenius equation.
• Thereafter, we will cover the units for the variables in the Arrhenius equation.
• Lastly, we will look at graphs for activation energy and learn how to read them.

## Activation Energy Definition

Before we get into things, let's first look at the definition of our topic: activation energy.

Activation energy is the minimum amount of total energy required to for a reaction to occur

The amount of energy required is dependent on whether a reaction is endothermic or exothermic

An endothermic reaction is any reaction that requires an addition of energy to occur. It is a net absorption of heat.

An exothermic reaction is any reaction that releases heat; however, heat is still required for it to occur.

For endothermic reactions, you can think of activation energy like the electricity required to power a toaster. A toaster may require an outlet capable of 1200 Watts in the same way an endothermic reaction can require 100 Joules of energy to complete. The toaster doesn't release energy, just absorbs it.For an exothermic reaction, the reaction releases more energy than it requires (i.e. the activation energy).

A good example is lighting a match. Striking a match gives the system the initial energy it needs to ignite, and the heat released is much greater than what it took to light it.

Activation energy is the energy required to break bonds in reactants that prevent the reaction from taking place, some bonds are stronger than others, which is why it takes more energy to break them. This is why all reactions have an activation energy requirement! Forming bonds is what releases energy. If the bonds in the products are stronger than those in the reactants, there is a net release of heat (exothermic reaction). If these bonds are weaker, and therefore less stable, then the reaction is a net gain of heat (endothermic reaction).

Hint: While activation energy is just the required amount of energy to complete a reaction, a reaction can use an excess amount of energy which can help speed up a reaction. Think of boiling water: you don’t put your stove top at 100 °C to bring water to 100 °C, you use a higher temperature to bring water to 100 °C faster.

## Importance of Activation Energy

So, why is activation energy important in Chemistry? As discussed in the intro, activation energy is the hill that reactions have to climb to happen. It is very important to know how much energy will be needed, or else your reaction might never happen!

Take boiling water for an example again. If you put your stove at 90 °C, your water will never boil. If you were instead using a Bunsen burner to heat a flask with reactants, your reaction would similarly never happen. Knowing activation energy is critical to allow for reactions to even happen in the first place.

## Activation Energy Formula

When we calculate activation energy, we use the Arrhenius equation:

The Arrhenius equation shows how the rate of a reaction is dependent on its activation energy, temperature, and frequency factor $$k=Ae^{\frac{-E_A}{RT}}$$

Where: A is the frequency factor (constant) which is the fraction of molecule collisions that produce a reaction

EA is activation energy

R is the gas constant it is 8.314 J/mol*K (but can have different values depending on the units used)

T is the temperature

k is the rate constant that measures a reaction's relative speed

There is another form of this equation that we use: $$ln(k)=\frac{-E_A}{RT}+ln(A)$$

Look familiar? Here's the equation of a line: $$y=mx+b$$

The formula is set up this way, so we can easily determine the activation energy. When the inverse temperature (1/T) is graphed as a function of ln(k), the slope (m) of the graph will be $$\frac{-E_A}{R}$$, so we can easily solve for it.

## Activation Energy Units

Lastly, let’s take a brief look at relevant units:

• Activation energy is generally measured in Joules per mole (J/mol)

• Temperature is measured in Kelvin (K)

• R is our gas constant, and there are several constants with different units. Because temperature is generally measured in Kelvin and activation energy is often measured in Joules/mol, typically we’ll use the gas constant of 8.314 $$\frac{J}{molK}$$ which will cancel out our other units.

• k is the rate constant and its units depend on our order of the reaction. A zero-order reaction uses units of M/s, a first order-reaction uses units of 1/s, a second-order reaction uses units of 1/M*s, and so on. What units you use will depend on the reaction being looked at.

• The letter, A, in the Arrhenius equation is also a constant and will have units identical to the rate constant.

## Activation Energy Graph

There are two types of graphs you'll typically see when discussing activation energy. The first is an energy diagram.

An energy diagram shows the change in energy during a reaction as it goes from reactants to products.

Here is an example of two below:

Energy diagrams for exothermic and endothermic reactions. StudySmarter Original

The activation energy is measured from the reactants to the graph's peak. If the activation energy is the "hill" we have to climb to get to the other side, then the energy diagram is your "energy path". The activation energy for an endothermic reaction (right) is much greater than for an exothermic reaction (left).

This is because the products are higher in energy than the reactants for an endothermic reaction, and systems always want to be at the lowest energy as possible. This is why energy/heat needs to be added to the system for endothermic reactions to occur.

The activation energy can be lowered if a catalyst is added.

A catalyst is a species that is used (but not consumed), by the reaction to lower the activation energy.

A diagram for this phenomenon looks like this:

A catalyst lowers the activation energy of a reaction. StudySmarter Original

The top curve (in purple), shows the original reaction, while the bottom curve (in green), shows the reaction with a catalyst. As you can see, the catalyst greatly lowers the activation energy. It does this by giving the reaction a different pathway to follow. It is similar to taking a different route to get to your destination faster.The second type of graph is the plot of 1/T versus ln(k). Here is some example data:

Graph of the Arrhenius equation. StudySmarter Original.

As we saw before, the slope of this graph is equal to $$\frac{-E_A}{R}$$, so we can easily calculate the activation energy from this data:

Given the graph above, what is the activation energy of the reaction?

First, we can use the equation of the line to determine the slope:

$$y=-22333x+25.3$$

$$y=mx+b$$

$$m=-22333$$

Now we can solve for activation energy

$$m=\frac{-E_A}{R}$$

$$-22333 K=\frac{-E_A}{R}$$

$$-22333 K=\frac{-E_A}{\frac{8.314\,J}{molK}}$$

$$E_A=185,677\,\frac{J}{mol}\,\,\text{or}\,\,E_A=186\frac{kJ}{mol}$$

We can also calculate activation energy using two data points. Here's how we would do that:

A reaction was performed at two temperatures and the rate constant was recorded. The following data was measured: ln(k) = -0.693 for 1/T = 0.00336 K-1, and ln(k) = 0.182 for 1/T = 0.00251 K-1. What is the activation energy for this reaction?

We can use the equation for slope to calculate the activation energy: $$m=\frac{y_2-y_1}{x_2-x_1}$$

All we have to do is substitute in our values and solve for EA

$$(x_1,y_1)=(0.00336\,K^{-1},-0.693)$$

$$(x_2,y_2=(0.00251\,K^{-1},0.182)$$

$$\frac{-E_A}{R}=\frac{0.182+0.693}{0.00251\,K^{-1}-0.00336\,K^{-1}}$$

$$\frac{-E_A}{R}=-1,029\,K$$

$$E_A=(-1,029K)(-8.314\frac{J}{molK})$$

$$E_A=8,559\frac{J}{mol}\,\,\text{or}\,\,E_A=8.56\frac{kJ}{mol}$$

## Activation Energy - Key takeaways

• Activation energy is the minimum amount of total energy required to complete a reaction.
• The Arrhenius equation shows how the rate of a reaction is dependent on its activation energy, temperature, and frequency factor $$k=Ae^{\frac{-E_A}{RT}}$$
• An energy diagram shows the change in energy during a reaction as it goes from reactants to products.
• A catalyst is a species that is used (but not consumed), by the reaction to lower the activation energy.
• The other form of the Arrhenius equation is used for graphing, which is $$ln(k)=\frac{-E_A}{RT}+ln(A)$$

• When ln(k) versus 1/T is graphed, the slope is equal to $$\frac{-E_A}{R}$$

Activation energy is the total amount of energy required to complete an endothermic reaction

Activation energy is important because you must know that amount of energy you need to input into a reaction for it to complete.

Activation energy is based on the bonds between atoms that make up reactants, so activation energy increases the harder it is to break those bonds.

Activation energy can generally be calculated through the Arrhenius equation or using a graphed ln(k) and finding the slope of the graph.

An example of activation energy is the energy required for H2O2 to decompose, which is approximately 42 kJ / mol.

## Activation Energy Quiz - Teste dein Wissen

Question

What is activation energy?

Activation energy is the minimum amount of total energy required to for a reaction to occur

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Question

Fill in the blanks: A reaction that has a net release of heat is a ___, while a reaction that has a net gain of heat is a ___

exothermic reaction, endothermic reaction

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Question

True or False: Only endothermic reactions have an activation energy

False

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Question

Which has a larger activation energy, exothermic or endothermic reactions?

Endothermic

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Question

What is an energy diagram?

An energy diagram shows the change in energy during a reaction as it goes from reactants to products.

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Question

What two factors does the frequency factor measure? (Select two)

Rate of collisions

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Question

What is activation energy?

Activation energy (EAis the minimum energy needed for a reaction to proceed. This energy is dependent on the potential energy of the products and reactants.

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Question

True or False: Activation energy and the rate constant are directly proportional

False

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Question

How does an increase in temperature affect the frequency factor?

It increases it

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Question

What is the relationship between temperature and activation energy?

An increase in temperature means more molecules can pass the barrier; It has no direct effect

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Question

True or False: Temperature and the rate are directly proportional

True

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Question

True or False: The rate constant and rate are the same thing

False

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Question

What is collision theory?

The collision theory states that reactions are caused by collisions of molecules in the correct orientation and correct energy

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Question

Temperature is a measure of what kind of energy?

Kinetic energy

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Question

When we graph the Arrhenius equation, what variable are we usually solving for?

Activation energy

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Question

Besides the rate constant, what other variable is used to calculate the rate of reaction?

The concentration of the reactant(s)

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Question

The frequency factor and the rate constant are__

Directly proportional

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Question

What is the collision model?

The collision model or collision theory explains how chemical reactions occur. If atoms/molecules collide at the correct orientation and with the right energy, a chemical reaction will occur.

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Question

Which of the following variables affect the collision frequency?

All of the above

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Question

What is activation energy?

Activation energy (EAis the minimum energy required for a reaction to occur. This energy is required to break bonds to form new ones and to overcome the repulsion of each molecule's electrons. Collision model activation energy is referring to the minimum kinetic energy of the collision

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Question

How is activation energy related to the collision model?

Collisions need to have as much or more energy than the activation energy for a collision to be successful

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Question

Why do collisions need to have the correct orientation?

For new bonds to form, the proper elements need to be next to each other

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Question

True or False: If a collision has the correct orientation, it will succeed

False

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Question

If HBr is reacting with I2 to form HI, is a collision between the bromine side and iodine going to be successful?

No

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Question

What is the steric factor?

The fraction of collisions that will be successful

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Question

What is collision frequency?

The collision frequency (ZABis the average rate at which two reactants collide in a given system.

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Question

Temperature affects which of the following?

Collision frequency and energy of collision

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Question

True or False: An increase in activation energy leads to an increase in collisions

False

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Question

What happens to the molecules during an unsuccessful collision?

They bounce off each other

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Question

What are the three key factors of the collision model? (Select all that apply)

Orientation

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Question

True or False: The collision frequency and the rate of reaction are directly proportional

True

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Question

What is a multistep reaction?

A multistep reaction is a series of reactions that can be "summed up" by a net reaction. The reaction is made up of several steps called elementary reactions and may involve a catalyst.

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Question

What is the rate-determining step?

The rate-determining step is the step that is the slowest. The other reactions will be "halted" by this reaction and proceed at that rate. It is "rate-determining" since the rate is based on that reaction alone.

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Question

True or False: The rate-determining step has the highest activation energy

True

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Question

What is a catalyst?

A catalyst is a species that increases the rate of a reaction. It cancels itself out, but is not consumed during the reaction.

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Question

How does a catalyst lower the activation energy?

It provides an alternate reaction pathway that has a lower activation energy

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Question

How do you calculate the overall yield of a multistep reaction?

You multiply the percent yields of each step

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Question

True or False: A catalyst cannot be in the rate equation

False

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Question

What is an intermediate?

A species that is both created and consumed during the net reaction.

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Question

What is an elementary reaction?

An elementary reaction is a single-step reaction

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Question

What is the steady state approximation?

The steady-state approximation (also called the quasi-steady-state approximation or pseudo-steady-state approximation) is a way to simplify the derivation of the rate equation. It is based on the assumption that one intermediate in the mechanism will be produced as fast as it is consumed (i.e. it is at a steady state

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Question

Why do we use the steady-state approximation?

It makes the derivation of the rate law/concentration of the product simpler to calculate.

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Question

True or False: At a steady-state, the concentration of a species is 0

False

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Question

How is the steady-state approximation important for enzyme kinetics?

The steady-state approximation is used to derive the rate law equation for enzyme reactions

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Question

For an enzyme reaction, what is the intermediate?

ES

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Question

True or False: The steady-state approximation can be used for elementary (single-step) reactions

False

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Question

True or False: During a steady-state, the rate of consumption is equal to the rate of creation

True

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Question

What is an intermediate?

An intermediate is a species that isn't one of the initial reactants or final product. It is produced during the mechanism and will be completely consumed by the end.

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Question

True or False: reaction velocity is the same as reaction rate

True

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Question

What is an energy profile diagram?

An energy profile diagram shows the theoretical "energy pathway" of a reaction as it progresses from reactants to products.

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