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# Kinetics vs Thermodynamics

sKinetics and thermodynamics are related to one another in ways that can be explained by using chemical reactions. To understand kinetics and thermodynamics, however, we must first gain an understanding of the underlying relationships between the two, through application to chemical reactions and several examples from life in general.

### Introduction

Firstly, it is important to mention that a chemical reaction has kinetic and thermodynamic aspects. The quantity related to kinetics is the rate constant k; this constant is associated with the activation energy required for the reaction to move forward, that is, the reactivity of the reactants. The thermodynamic quantity is the energy difference resulting from the free energy (ΔG) given off during a chemical reaction, that is, the stability of the products relative to the reactants. While kinetics can tell us about the rates of reactions and how fast equilibrium is reached, they don't tell us anything about equilibrium conditions once the reaction equilibrates. In the same measure, thermodynamics only gives us information regarding the equilibrium conditions of products after the reaction takes place, but does not tell us the rate of reaction.

### Kinetics Overview

The rate constant k shows how fast a chemical reaction reaches equilibrium, which means the reactants were supplied with enough activation energy to enable the reaction to proceed in the forward direction-- turning reactants into products. This need for input of energy symbolizes the fact that the reactants are unreactive under certain conditions; meaning that the reaction must have some sort of energy input before it can proceed, otherwise, the reactants cannot reach the activation energy threshold and begin going in the downhill direction towards becoming products. Essentially, the reaction will be activated by the energy supplied to the reactants by different energy sources. The rate reaction k, and the kinetic energy required for activation of reaction tell us how fast this reaction will reach equilibrium-- reactants becoming fully converted to products. See Diagram #1.

Diagram #1: Depicted in the bottom graph are the main points talked about in the top paragraph. The transition state represents a threshold the reactants must pass before the reaction can proceed in the forward direction. The activation energy is the energy required to reach the transition state threshold. Once this threshold is reached, the reaction can begin to go downhill. It is important to remember that each reaction has a different transition state threshold, requiring different amounts of activation energies, and determined by the reactants reacting, and the conditions which the reaction is taking place in. The value of rate constant k is affected by these two aspects, and can be increased in the presence of a catalyst-- an enzyme, which speeds-up reactions, increasing their rate. In chemical reactions, specifically, the catalyst will both provide more energy to the reactants, and lower the transition state. The provider of activation energy can also be a spark, heat, or anything else that gives-off kinetic energy. Regardless of what provides the activation energy, a kinetic/nonspontaneous reaction is one in which the most stable state is that of the reactants. The change in energy between the reactants and products, also known as ΔG, relates to thermodynamics and will be discussed shortly.

 Example

#### Example #1: Gas in a Fuel Tank

This example will be a lot easier to understand. Have you ever wondered how gas in a fuel tank does not get "wasted" or burnt away while it's sitting in the parking lot? Fuel is unreactive under standard conditions, meaning that the spark you create while turning on the engine is what provides the activation energy to the reactants, beginning the process of fuel-burning-- which eventually enables your car to function. For more information about the way by which fuel-burning reactions are driven, visit 'outside link' number 1. For a video that shows why two elements don't spontaneously combust (as fuel would, had it not needed activation energy), go to 'outside link' number 5.

### Thermodynamics Overview

One can think of thermodynamics as the energy stored within a reaction, a reactant, or a product. Most often, we think of thermodynamics as the different forms of energy that are converted every time a reaction excretes energy or uses energy to initiate itself. With relation to Gibbs free energy (ΔG), thermodynamics is either (1) the energy released during a reaction, in which case ΔG will be negative and the reaction exothermic/spontaneous, or (2) the energy consumed during a reaction, in which case ΔG will be positive and the reaction endothermic/nonspontaneous. The thermodynamic reaction will favor the products, resulting in a spontaneous reaction that occurs without the need to input any sort of activation energy. This indicates that the reactions' most stable state is that of the products.

Thus, going back to Diagram #1, thermodynamics is what describes the free energy between the reactants and the products. Since thermodynamic values apply only after the reactants have turned into products, we can say that it describes the equilibrium state.

The way by which free energy (aka, Gibbs free energy) is related to thermodynamics is best expressed through the following equation:

Since "U" is the variable representing the internal energy of a system, we can indefinitely conclude that free energy and thermodynamics are closely correlated. Furthermore, as the equation shows, changes in internal energy will change the value of the free energy, which, in turn, affect our general reaction in several ways (affecting the rate of reaction k, whether the reaction is spontaneous, or nonspontaneous, and even whether or not activation energy will be needed to initiate the reaction).

 Example

#### Example #2: Thermodynamic Systems

The best way to understand thermodynamics is by realizing that anything that transfers, receives or contains heat can be described as a system. Heat can enter or leave a system, which affects the amount of thermal energy it contains. You can think of a kettle sitting on a stove. As you heat it up (and the water inside it), you are adding thermodynamic (thermal) energy to the system (the kettle with the water). As you turn off the stove, the kettle will cool down as the heat will diffuse back to the room and slowly equilibrate to room temperature. This is an example of the system losing thermal energy. To view an animated diagram of a thermodynamic system, click on 'Outside Link' number 2.

### Thermodynamics vs. Kinetics

Now that the overviews introduced you to kinetics and thermodynamics, their differences will be discussed. As mentioned above, the most stable states of a kinetic reaction are those of the reactants, in which an input of energy will be required to move the reaction from a state of stability, to that of reacting and converting itself to products. Kinetics is related to reactivity. On the other hand, the most stable state of a thermodynamic reaction is that of being in the state of products, because the reaction will happen spontaneously, without the need for energy to be added to make the reaction go forward. Thermodynamics is related to stability.

Therefore, something that is unreactive will desire to stay in the form of reactants, which will require an input of energy to cause the reaction to go forward, converting reactants into products. This is illustrated in example #3 below. Something that is thermodynamically stable will not need an input of energy to be converted from reactants to products, because its most stable and preferred state is that of being composed of products. Instead, a thermodynamically-stable reaction will require energy to be converted from products back to reactants. It's almost as if an unreactive reactant is stubborn and does not want to be converted into products-- it's too lazy. You have to induce it to become products by giving it kinetic energy, which MOVES the reaction forward (kinetics = movement). The same is for thermodynamically-stable reactions, except you'd be inducing the reaction to go back into reactants from a state of products.

 Example

#### Example #3: ATP- Reactivity

Adenosine triphosphate, also known as ATP, is the energy our cells produce and require in order to maintain metabolic pathways, DNA synthesis and repair, and any other cellular function we need in order to survive. ATP itself is a reactive molecule that has three phosphate groups. As we learned in the chemistry series, molecules in life desire to become as stable as possible, and do so by converting to states of lower energies. Thus, ATP, a high-energy molecule, wants to give off a phosphate group and become adenosine diphosphate, ADP. In order for this to happen, ATP needs to involve an enzyme that will strip one phosphate group off ATP, making it the more stable molecule ADP. This enzyme provides the energy of activation that enables ATP to become ADP, proving that ATP is kinetically stable.

 Example

#### Example#4: Water + Sugar - Thermodynamically-Stable

Solvents and polarity: A simple situation, a spoonful of sugar is added to a cup of water. If the two are left to be reacted, within a certain period of time the sugar will dissolve inside the water, becoming the product of sugar+water. The natural charges and polarity of water causes the sugar molecules to react with it, eventually dissolving within the water. There was no needed input of energy, meaning that this reaction was thermodynamically stable, and spontaneous. Clearly, the two reactants prefer to react and maintain stability as products.

Note: although this is a thermodynamically-stable/spontaneous reaction and does not require energy input, the use of kinetic energy will force this reaction to happen faster. Think of what would happen if you distributed the sugar into the cup of water, and then heated up the cup. The kinetic energy of the reactants will be increased by the thermal energy of the heat, which will cause the molecules to react with one another at a much faster rate had they been left alone at room temperature. This can give you an idea of how thermodynamics and kinetics are closely related, yet, how their stabilities differ.

1. Fuel Reactions and Kinetics: http://www.explainthatstuff.com/fuelcells.html
3. Nonspontaneous Reaction (compare with Diagram #1): http://www.biology.arizona.edu/biochemistry/problem_sets/energy_enzymes_catalysis/graphics/16t.gif
4. Thermodynamics: http://en.wikipedia.org/wiki/Thermodynamics#Thermodynamic_systems
5. Demonstration of two kinetically-stable elements in a mixture, after given enough energy of activation: http://www.metacafe.com/watch/908325/solid_rocket_fuel_ignition/

### References

1. Journal of Coordination Chemistry, Volume 62, Issue 1 Oct. 2009, pages 108-109
2. Thermodynamic stability and crystal structure of lanthanide complexes with di-2-pyridyl ketone. S. Domnguez a;  J. Torres b;  J. Gonzlez-Platas c;  M. Hummert d;  H. Schumann - e; C. Kremer b
3. Role of Solvation Barriers in Protein Kinetic Stability. RODRIGUEZ-LARREA David ; MINNING Stefan ; BORCHERT Torben V. ; SANCHEZ-RUIZ Jose M.

### Problems

1. Is it possible that graphite is thermodynamically stable and diamond is less reactive under standard conditions while they're practically the same thing?

2. Explain how kinetics relate to thermodynamics. Use the terms 'energy of motion', 'energy of heat', and an example from the module in your answer.
3. Why would it be beneficial for a thermodynamically-stable reaction to use an energy input in the form of an enzyme or a catalyst even if it does not require energy to proceed?
4. How come gas does not spontaneously combust inside a fuel tank?
5. How is the rate constant k related to equilibrium? How does the rate constant change if heat is added to the reaction?
6. If the difference in energy between the reactants and products is negative, is the reaction spontaneous/nonspontaneous?

1. Yes. Their different structures will differentiate their polarity and charge, and will cause the two compounds to act differently. Thus, one can be thermodynamically stable, while the other can be less reactive.
2. The energy of motion is related to kinetics, which determines how fast the reaction will reach equilibrium, related to thermodynamics. The energy of motion (kinetics) added to a reaction, will cause the reaction to happen faster, using energy of heat as a way by which to accelerate the reaction. An example of this is the cup of water with the sugar while it is being heated. The heat energy converts into kinetic energy (energy of motion), accelerating the reaction between the water molecules and the sugar crystals.
3. A catalyst or enzyme will still be beneficial in a thermodynamically-stable reaction because it will simply accelerate it.
4. Fuel is unreactive to standard conditions and regular atmosphere, which means it'll require an energy input in order to react. The energy inputed is the spark caused by the ignition of the car.
5. The rate constant k is related to equilibrium in that it tells us about how fast the reaction reaches equilibrium. If heat is added to a reaction, its rate will increase due to increased kinetic energy.
6. The reaction will be spontaneous, thermodynamically-stable. This is because the energy is given-off, not consumed by the reaction.

### Contributors

• Gal Ozery (UCD)

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