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# Reaction Thermodynamics

## Introduction

This doucument introduces the thermodynamics of chemical reactions. To start, imagine the following demonstration: Cold packs contain separate compartments of water and a salt such as ammonium nitrate. When you mix the salt and water the cold pack gets cold. Such a reaction is called an endothermic reaction.

NH4NO3 (s) NH4+(aq) + NO3-(aq)       Ho = +28.1 kJ/mol

This reaction is spontaneous even though thermal energy is needed to break the ionic bonds of the crystalline NH4NO3.

Why do endothermic reactions occur?

The driving force for the NH4NO3 reaction is the much greater disorder that is possible for the NH4+ and NO3- ions in solution compared to these ions arranged in a solid.

We describe the disorder or randomness of a system with the entropy, S, which has units of kJ/mol·K.

Qualitative examples:

Liquids are more disordered than solids and gases are more disordered than liquids.
At 0oC SH2O(l) > SH2O(s)
At 100oC SH2O(g) > SH2O(l)

As 90 people enter a 180-seat lecture hall, do they take seats beginning in the front row to completely fill the front half of the room and leaving the back half of the room empty? No, the probability of that arrangement is very, very small. The more likely arrangement is for the 90 people to more or less distribute themselves randomly in the room. This arrangement is more probable and we could quantitate this more probable arrangement in terms of entropy.

## Spontaneity and Gibbs Free Energy

The entropy must be included to predict if a reaction will be spontaneous. The total change in the available energy of a system is called the change in the Gibbs free energy, G:

G = H - TS
Where
G is the change in Gibbs free energy (kJ/mol)
H is the change in enthalpy (kJ/mol)
T is absolute temperature in K
S is the change in entropy (kJ/mol K)

The change in enthalpy is the amount of heat or work that is transferred when an reaction occurs.

A reaction is spontaneous if G is negative, that is, the products have a lower Gibbs free energy than the reactants.

Note that depending on the sign of H and S, the spontaneity of a reaction can be temperature dependent.

For standard conditions of 1 atm for gases and 1 M for solutes in solution, these energies are given an "o" superscript. The change in energy for any reaction (at standard conditions) can be found using tabulated standard energies of formation and standard entropies.

The f subscript for the Hfo and Gfo indicates standard heats of formation. I've used the rexn subscript to specify that the energy changes are of a reaction. This subscript is usually left off.

From tables of standard enthalpies and free energies we can calculate Ho and Go for this reaction.
NH4NO3 (s) NH4+(aq) + NO3-(aq)

Hfo (kJ/mol)Gfo (kJ/mol)
NH4NO3 (s)-365.6-184.0
NH4+(aq)-132.5-79.3
NO3-(aq)-205.0-108.7

Ho = -132.5 kJ/mol - 205.0 kJ/mol - (-365.6 kJ/mol)

Ho = +28.1 kJ/mol

Go = -79.3 kJ/mol - 108.7 kJ/mol - (-184 kJ/mol)

Go = -4.0 kJ/mol

Since Go is a negative number this reaction is spontaneous at standard concentrations. (We also observed that this reaction was spontaneous for the salt concentrations in the cold pack, which were probably higher than 1 M.)

## Activation Energy Diagram

Recall the activation energy diagram that was introduced in the kinetics document. The model is valid for both exothermic or endothermic reactions.

A diagram for an exothermic reaction:

```        ^
|                     ________
Energy  |                    /        \
|        reactants  /    Ea    \
|        __________/     __     \
|                                \
|                                 \
|                        G        \
|                                    \  products
|                        __           \_________
|
|
```

A diagram for an endothermic reaction:

```
^
|                     ________
Energy  |                    /        \
|                   /          \
|                  /            \
|                 /              \   products
|                /      Ea        \____________
|               /
|  reactants   /                      G
|  ___________/         ___           ___
|
|
```

Ea is the activation energy and G is the chagne in Gibbs free energy (in kJ/mol).

## Don't Forget the Really Big Concepts in Chemistry

Kinetics describes how quickly or slowly a reaction occurs.

Thermodynamics describes the changes in the form of energy when a reaction occurs, for example, converting chemical energy to heat.

Equilibrium describes reactions in which the reactants and products coexist.

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