• Basic Concepts
• Temperature changes within a phase
• Temperature changes between phases
• Calculating Enthalpy
• Gibbs Free Energy

#### Introduction

Thermodynamics explores the changes of energy within a system and how these changes in energy impact the temperature of the system and its surroundings. The basis of thermodynamics lies in the fact that forming bonds releases energy, while breaking bonds requires energy. Reactions can be endothermic or exothermic depending on the bonds broken or formed in the reaction’s mechanism.

## Basic Concepts

#### 4 Laws of Thermodynamics

0: Thermal equilibrium is always achieved between two substances that can exchange energy. If two substances are at thermal equilibrium with a third substance, they are also at thermal equilibrium with each other

1:Conservation of energy: energy can be converted from one form to another, but it can never be created or destroyed

2: The entropy of the universe is always increasing

3: At absolute zero (0 degrees Kelvin) a pure substance will have zero entropy

#### 4 Laws of Thermodynamics

Enthalpy (for practical purposes) is a measure of the energy contained within  a molecule (The differences between bond energy and enthalpy are beyond the scope of this resource). Enthalpy is denoted by ΔH

#### Endothermic Reactions

Entropy describes the universal concept that all matter progresses towards disorder. Solids increase in entropy as they become liquids and liquids increase in entropy as they become gases because individual particles have more freedom to move and become thus more disorderly. Entropy is denoted by ΔS

#### Endothermic Reactions A reaction is endothermic when heat is absorbed by the reaction, making its surroundings colder. As shown in the graph above, the products of an endothermic reaction have more potential energy stored within bonds than the reactants. This means that ΔH (enthalpy) is positive for all endothermic reactions.

#### Exothermic Reactions A reaction is exothermic when heat is released by the reaction, making its surroundings warmer. As shown in the graph above, the products of an exothermic reaction have less potential energy stored within the products as the reactants. This means that ΔH (enthalpy) is negative for all exothermic reactions.

## Temperature Changes within a Phase #### The Equation

q=mcΔt

This equation is most often used to calculate the energy absorbed or released by a reaction within a phase. Q is the energy absorbed or released by the reaction. M is the mass of the sample. C is the specific heat constant of the material. Δt is the change in temperature of the surroundings of the reaction.

#### More on Specific Heat

If a material’s specific heat is higher, it means that more energy is needed to change that material’s temperature a certain amount than it would take to change the temperature of a material with a lower specific heat the same amount. Therefore, heating up two samples of the same mass to the same temperature requires different amounts of energy depending on the material of each sample.

#### Change in temperature and change in Q

If the change in temperature is positive, q will also be positive, showing that heat was released from the reaction and into the surroundings, or that the reaction was exothermic. If the change in temperature is negative, q will also be negative, showing that heat was absorbed by the reaction from the surroundings, or that the reaction was endothermic.

## Changes Across Phases

#### Heat of Solution Melting, boiling, freezing, etc. are all phase changes. These reactions are endo- or exothermic depending on the direction of the change. Solid to liquid and liquid to gas are endothermic processes as energy is absorbed by the molecules as they break attractions and separate from the rest of the sample to become a liquid or gas. Contrastingly, gas to liquid and liquid to solid are exothermic processes as energy is released by molecules to form attractions and create a stronger structure within the liquid or solid.

The energy change of these reactions can be given by q=mHf where q is the energy change, m is mass, and Hf is the heat of fusion of the reaction. The heat of fusion is positive when the reaction is exothermic and negative when the reaction is endothermic. For a given phase change, the heat of fusion will be equal for both directions of the reaction, just the sign of Hf needs to be changed (positive or negative).

#### Heat of Solution The dissolution of a compound in water can be endothermic or exothermic. This is because dissolving in water requires breaking hydrogen bonds in the water and creating new ion-dipole attractions. Depending on the relative strengths and energies of these bonds, heat can be absorbed or released.

Within a reaction equation, changes in temperature can be denoted by a number of kilojoules per mole on either the reactants or products side of the reaction. If this number is added to the reactants side, the reaction is endothermic as heat needs to be absorbed by the reaction for it to proceed. If this number is added to the products side, the reaction is exothermic as heat is released by the reaction as it proceeds.

The number can be treated as if it has a stoichiometric ratio with the rest of the reactants and products. If the reaction is doubled, for example, the amount of heat, no matter what side of the reaction it is on, will also double. For any value of moles of reaction, the same ratio of heat will be absorbed or released.

## Calculating Enthalpy

#### Bond Enthalpy

Energy of bonds broken - Energy of bonds formed

Within every reaction, bonds of the reactants are broken and bonds of products are formed. Based on the fact that breaking bonds requires energy and forming bonds releases energy, the total energy change of a reaction can be found by subtracting the energy released from the energy used. Therefore, enthalpy of a reaction can be calculated by finding the overall change in energy before and after the reactions based on the bonds that are broken and formed.

A table of bond energy values is used for each of the bonds that are broken and formed. Make sure to include the coefficients of the bonds that are broken and formed. Bonds that appear on both the reactants and products side can be cancelled out.

#### Enthalpy of Formation

Enthalpy of formation of products - Enthalpy of formation of reactants

Another way to calculate overall enthalpy is using the enthalpies of formation of the reactants and products. Like bond energies, these values are listed in a table or are often included within a question when you are asked to use them. The enthalpy of formation of a compound is the enthalpy change associated with the formation of one mole of the compound from its elements. The enthalpy of formation for an element or compound as it is found in nature (such as O2 gas, N2 gas, Cu solid, etc.) is 0. Making sure to multiply by the coefficients of the equation, add up the enthalpy values of the products and reactants, then subtract the total enthalpy of the reactants from the total enthalpy of the products.

This same method can be used to calculate the entropy of a reaction given the entropies of the reactants and products in a table. Remember to multiply by reaction coefficients and use products - reactants.

#### Hess's Law

Hess’s Law states that reactions of known enthalpy can be added to find the enthalpy of the sum of the reactions. Reactions often need to be manipulated for this process to work. When a reaction is flipped, its delta H changes sign (positive or negative). Halving or doubling a reaction will also halve or double the enthalpy.

By manipulating given equations and adding them together, products and reactants can cancel out, yielding the desired equation. By manipulating enthalpies as the reactions are changed then adding them up, the desired enthalpy can be found.

## Gibbs Free Energy

#### ΔG = ΔH - TΔS

The calculation for enthalpy is important to see if a reaction will be spontaneous or nonspontaneous. The Gibbs free energy equation is used to numerically define a reaction as spontaneous or nonspontaneous. ΔG represents Gibbs free energy, while ΔH and ΔS represent enthalpy and entropy as described above, and T represents the temperature at which the reaction occurs. T must be in kelvin. Additionally, enthalpy values are often calculated in kilojoules while entropy values are calculated in joules, so be sure to perform the proper unit conversion (divide joules by 1000 to get kilojoules) to ensure that units match.

A reaction is spontaneous when delta G is negative and non spontaneous when delta G is positive. A reaction is entropy driven when a large entropy is able to overcome a positive enthalpy, and a reaction is enthalpy driven when a very negative enthalpy is able to overcome a negative entropy.

However, just because a reaction is spontaneous does not mean it will happen. This can be due to environmental conditions or a large activation energy that prevent a thermodynamically favorable reaction from occurring.

While it is important to remember the factors that contribute to spontaneity and why changes to entropy and enthalpy change spontaneity, the table can be memorized. 