Name: using formation data to find free energy
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 49 s
Channel: JoVE

K12 Standards

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New Jersey Student Learning Standards for Science

High School

Physical Science

Matter and Its Interactions

HS-PS1-4

Calculating Standard Free Energy Changes

The standard free energy change for a chemical reaction occurring under the standard condition can be calculated in one of three ways.
The first method uses the equation for the standard &#916;G of the reaction. Consider the formation of calcium carbonate from calcium oxide and carbon dioxide.
The standard enthalpy change of the reaction can be calculated from the heats of formation of the compounds in the reaction, and the standard entropy change can be calculated from their standard molar entropies.
Using the values from the reference tables, the standard enthalpy change and the standard entropy change for the reaction can be determined.
Substituting these values into the equation for the change in standard free energy, the standard &#916;G of the reaction at 298 K equals &#8722;130.7 &#215; 103 J.
In the second method, the change in standard free energy of a reaction is calculated from the difference between the sum of the free energies of formation of the products multiplied by their stoichiometric coefficients and the sum of the free energies of formation of the reactants multiplied by their stoichiometric coefficients.
Take, for example, the reaction between hydrogen and chlorine gases to form two moles of hydrogen chloride gas.
Like the enthalpy of formation, the standard free energy of formation of a pure element is zero.
Thus, the free energies of formation of hydrogen and chlorine gases are zero, while that of hydrogen chloride gas is &#8722;95.3 kilojoules.
So, the free energy of this reaction equals 2 times the free energy of formation of hydrogen chloride gas, or &#8722;190.6 kilojoules.
Recall from Hess&#8217;s law that for a stepwise reaction, the net enthalpy change can be calculated from the sum of the enthalpies of each step. The third method calculates the net free energy change for a reaction in a similar manner.
Consider the combustion of zinc sulfide to produce metallic zinc and sulfur dioxide gas, which can be carried out in two steps with known standard free energies.
Adding the free energy changes of the reactions gives an overall &#916;G of &#8722;98.8 kilojoules.
Note that step 1 is nonspontaneous. By coupling it with the spontaneous reaction in step 2, the net reaction has a negative &#916;G and is therefore spontaneous.

calculating standard free energy changes

The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the use of standard enthalpies and entropies to compute standard free energy changes, &#916;G&#176;, according to the following relation.
<img alt="Static equilibrium; &#931;Fx=0, &#931;Fy=0 equations; diagram of forces on a structure in equilibrium." src="/files/ftp_upload/11429/11429_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="HTML static equilibrium equations diagram with &#931;Fx=0, MA=0, physics concepts, analysis.
" />
The standard free energy change for a reaction may also be calculated from the standard free energy of formation &#916;Gf&#176; values of the reactants and products involved in the reaction. The standard free energy of formation is the free energy change that accompanies the formation of one mole of a substance from its elements in their standard states. Similar to the standard enthalpy of formation, &#916;Gf&#176; is by definition zero for elemental substances under standard state conditions. For the reaction
<img alt="Static equilibrium, &#931;Fx=0, &#931;Fy=0 diagram, free-body diagram analysis, force balancing method." src="/files/ftp_upload/11429/11429_Equation_2.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Chromatography method diagram, showing a liquid chromatography column setup for compound separation." />
the standard free energy change at room temperature may be calculated as
<img alt="Inclined plane inclined at angle &#952; with weights W1, W2; static equilibrium diagram &#931;Fx=0." src="/files/ftp_upload/11429/11429_Equation_3.png" style="text-align: center; height: 92px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium concept, &#931;Fx=0, &#931;Fy=0, diagram of forces at play, educational physics tool." />
The use of free energies of formation to compute free energy changes for reactions as described above is possible because &#916;G is a state function, and the approach is analogous to the use of Hess&#8217; Law in computing enthalpy changes. Consider the vaporization of water as an example:
<img alt="Chromatographic separation process; chromatography diagram; protein purification method." src="/files/ftp_upload/11429/11429_Equation_4.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Chemical equilibrium equation Kp=Kc(RT)^&#916;n, formula in a dynamic equilibrium diagram." />
An equation representing this process may be derived by adding the formation reactions for the two phases of water (necessarily reversing the reaction for the liquid phase). The free energy change for the sum reaction is the sum of free energy changes for the two added reactions:
<img alt="Quantum tunneling process, Schr&#246;dinger equation diagram, depicting potential barrier and wave function." src="/files/ftp_upload/11429/11429_Equation_5v2.png" style="text-align: center; height: 110px;" data-altupdatedat="1754904545000" data-alt="static equilibrium equation &#931;Fx=0, &#931;Fy=0, &#931;M=0 diagram; forces analysis method" />
This approach may also be used in cases where a nonspontaneous reaction is enabled by coupling it to a spontaneous reaction. For example, the production of elemental zinc from zinc sulfide is thermodynamically unfavorable, as indicated by a positive value for &#916;G&#176;1:
<img alt="Chemical equilibrium; reaction equation A&#8652;B; diagram with arrows indicating dynamic balance." src="/files/ftp_upload/11429/11429_Equation_6.png" style="text-align: center; height: 27px;" data-altupdatedat="1754904545000" data-alt="Four-bar linkage mechanism diagram illustrating static equilibrium principles with force vectors." />
The industrial process for the production of zinc from sulfidic ores involves coupling this decomposition reaction to the thermodynamically favorable oxidation of sulfur:
<img alt="Quantum energy levels diagram, particle in a 1D potential well, showing discrete states and transitions." src="/files/ftp_upload/11429/11429_Equation_7.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Chirality diagram showing enantiomers of a chiral molecule with three-dimensional bond structure." />
The coupled reaction exhibits a negative free energy change and is spontaneous:
<img alt="Thermodynamic cycle process diagram with heat exchange and work, illustrating system efficiency." src="/files/ftp_upload/11429/11429_Equation_8.png" style="text-align: center; height: 110px;" data-altupdatedat="1754904545000" data-alt="Chromatography process diagram showing mobile and stationary phases for compound separation." />
This process is typically carried out at elevated temperatures, so this result obtained using standard free energy values is just an estimate. The gist of the calculation, however, holds true.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/16-4-free-energy">Openstax, Chemistry 2e, Chapter 16.4: </a><a href="https://openstax.org/books/chemistry-2e/pages/16-4-free-energy">Free Energy</a>.

The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. ...

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KEY TERMS AND CONCEPTS

using formation data to find free energy

Standard free energy change is the free energy change for a reaction under standard conditions of 1 bar pressure and 298 K. Free energy is a state function, so its value depends only on the starting and ending states of the system. That makes it possible to calculate standard free energy changes from tabulated thermodynamic data.

One common method uses standard enthalpy and entropy values to find standard free energy change, ΔG°. Another method uses standard free energies of formation, ΔGf°, for the reactants and products. The standard free energy of formation is the free energy change when one mole of a substance forms from its elements in their standard states.

For elemental substances in their standard states, ΔGf° is defined as zero. That rule makes the calculations practical for many reactions at room temperature. It also shows why standard free energy values can be combined to find the free energy change of a larger reaction.

This approach works because ΔG is a state function, much like Hess’ law is used for enthalpy. For example, the vaporization of water can be built by adding the formation reactions for liquid water and water vapor, while reversing the liquid-phase reaction. The free energy change for the overall process is the sum of the free energy changes for the added reactions.

The same idea can also help with reactions that are not spontaneous on their own. The production of elemental zinc from zinc sulfide is thermodynamically unfavorable, which is shown by a positive ΔG°1. In industrial zinc production, that reaction is coupled to the favorable oxidation of sulfur, giving a coupled reaction with a negative free energy change.

That coupled process is spontaneous, although it is usually carried out at elevated temperatures. So the value calculated from standard free energy data is an estimate rather than an exact industrial condition. Even so, the calculation method still captures the main thermodynamic idea.

Using Formation Data to Find Free Energy

spontaneity

Spontaneous Change in Matter and Energy

Spontaneous change in matter and energy happens naturally under certain conditions. A nonspontaneous process will not occur unless it is driven by a continual input of energy from an outside source. Under a given set of conditions, processes also tend to move in one direction rather than the other. Water flows downhill on its own, so that is a spontaneous process. Water flowing uphill needs a pump, so that is nonspontaneous. Iron in the earth’s atmosphere will corrode, but rust does not turn...

entropy

Entropy in Matter and Energy Changes

Entropy describes how energy and matter are spread through a system. It is a thermodynamic state function, so it can change when a physical or chemical change occurs. When entropy increases, disorder increases. When entropy decreases, disorder decreases. A change in entropy is written as ΔS = Sf - Si. The concept is also linked to microstates, which are the specific arrangements of the locations and energies of all atoms or molecules in a system. Boltzmann’s relation, S = k ln W, connects...

second law of thermodynamics

Entropy and Spontaneous Change

Entropy and spontaneous change are linked through the entropy of the universe. Entropy is a thermodynamic property that helps predict whether a process will happen on its own. Processes with an increase in system entropy, or ΔS &gt; 0, are often spontaneous, but there are many exceptions. To make a better prediction, entropy changes must include both the system and the surroundings. In thermodynamics, the system plus the surroundings make up the universe. When heat moves between two objects,...

third law of thermodynamics

Entropy at Absolute Zero

The third law of thermodynamics links entropy to absolute zero. A pure, perfectly crystalline solid with no kinetic energy at 0 K has only one microstate. Because there is only one possible arrangement for its identical atoms or molecules, its entropy is zero. This limiting case sets the entropy scale for real substances. Careful calorimetric measurements can be used to find how entropy changes with temperature and to calculate absolute entropy values under specific conditions. Standard...

standard entropy change for a reaction

Calculating Entropy Change from Tables

Entropy is a state function, so the standard entropy change of a chemical reaction can be found from standard molar entropy values in a table. The reaction entropy, written as ΔS°rxn, is calculated by subtracting the total entropy of the reactants from the total entropy of the products. The balanced equation matters because the stoichiometric coefficients set how many moles of each substance are included. A table of standard entropies gives values in J/mol·K for substances such as graphite,...

gibbs free energy

Predicting Spontaneity with Gibbs Energy

Gibbs free energy helps predict whether a process is spontaneous under constant temperature and pressure. It is a thermodynamic property based on the system’s enthalpy and entropy. Chemists also call it free energy, and it is a state function. The idea was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. Unlike the second law approach, it uses system properties only. That makes it a useful shortcut when tracking both the system and the surroundings is...

effects of temperature on free energy

Temperature and Spontaneous Processes

Temperature can change whether a process is spontaneous. In chemistry, spontaneity means a process can happen on its own under a given set of conditions. Phase changes are one clear example, and some chemical reactions also change spontaneity as temperature changes. The relationship uses free energy change, enthalpy change, and entropy change. Entropy is a measure of disorder in the system. The key equation shows that the sign of free energy depends on the signs of enthalpy and entropy, and in...

Standard free energy change is the free energy change for a reaction under standard conditions of 1 bar pressure and 298 K. Free energy is a state function, so its value depends only on the starting and ending states of the system. That makes it possible to calculate standard free energy changes from tabulated thermodynamic data. One common method uses standard enthalpy and entropy values to find standard free energy change, ΔG°. Another method uses standard free energies of formation, ΔGf°,...

free energy changes for nonstandard states

free-energy-changes-for-nonstandard-states

Predicting Spontaneity with Reaction Quotient Q

Free energy under nonstandard conditions depends on the reaction quotient, Q, and the standard free energy change. Nonstandard conditions mean that concentrations are not 1 M or pressures are not 1 bar. The relation links the gas constant R, the absolute temperature T in kelvin, and Q. It can be used to predict whether a process is spontaneous under a given set of conditions. The reaction quotient, Q, helps show the status of a reversible reaction. It is based directly on the balanced chemical...

free energy and equilibrium

Predicting Reaction Direction with Free Energy

Free energy and equilibrium help predict which way a chemical reaction will move. A negative value of ΔG means the forward reaction is favored. A positive value means the reverse reaction is favored. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the system is at equilibrium. The reaction quotient, Q, helps show whether a reaction must move forward or backward to reach equilibrium. Q is the numerical value of the mass action expression for the system. If Q is less...

key terms and concepts

Learn how standard free energy change is calculated from enthalpy, entropy, and formation data, with examples like water vaporization and zinc production.

Using Formation Data to Find Free Energy | JoVE K12

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New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-12.

Next Generation Science Standards

Energy

HS-PS3-3

HS-PS3-4

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

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Electron Configuration of Multielectron Atoms

The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the ...

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Alkali Metals

Group 1 elements are soft and shiny metallic solids. They are malleable, ductile, and good conductors of heat and electricity. The melting points of the ...

Halogens

Group 17 elements, known as halogens, are nonmetals. At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine a solid. ...

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The Periodic Table and Organismal Elements

Elements are the smallest units of matter that cannot be broken down further by chemical processes. There are 118 known elements, but not all of these are ...

Electron Behavior

Electrons are negatively charged subatomic particles that are attracted to an orbit around the positively-charged nucleus of an atom. They reside in ...

Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms. 

Clarification statement: Examples of properties that could be predicted from patterns could include reactivity of metals, types of bonds formed, numbers of bonds formed, and reactions with oxygen. 

Assessment Boundary: Assessment is limited to main group elements. Assessment does not include quantitative understanding of ionization energy beyond relative trends.

HS-PS1-1

Lewis Symbols and the Octet Rule

Chemical bonds are complex interactions between two or more atoms or ions, which reduce the potential energy of the molecule. Gilbert N. Lewis developed a ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Chemical Equations

Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are ...

Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties. 

Clarification statement: Examples of chemical reactions could include the reaction of sodium and chlorine, of carbon and oxygen, or of carbon and hydrogen. 

Assessment Boundary: Assessment is limited to chemical reactions involving main group elements and combustion reactions.

HS-PS1-2

Intermolecular vs Intramolecular Forces

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular ...

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions ...

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Surface Tension, Capillary Action, and Viscosity

Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded ...

Plan and conduct an investigation to gather evidence to compare the structure of substances at the bulk scale to infer the strength of electrical forces between particles. 

Clarification statement: Emphasis is on understanding the strengths of forces between particles, not on naming specific intermolecular forces (such as dipole-dipole). Examples of particles could include ions, atoms, molecules, and networked materials (such as graphite). Examples of bulk properties of substances could include the melting point and boiling point, vapor pressure, and surface tension. 

Assessment Boundary: Assessment does not include Raoult's law calculations of vapor pressure.

HS-PS1-3

Enthalpy

Chemists ordinarily use a property known as enthalpy (H) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum ...

Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

bond-dissociation-energy-and-activation-energy

Bond Dissociation Energy and Activation Energy

Bond energy is the energy required to break a bond homolytically. These values are usually expressed in units of kcal/mol or kJ/mol and are referred to as ...

Develop a model to illustrate that the release or absorption of energy from a chemical reaction system depends upon the changes in total bond energy. 

Clarification statement: Emphasis is on the idea that a chemical reaction is a system that affects the energy change. Examples of models could include molecular-level drawings and diagrams of reactions, graphs showing the relative energies of reactants and products, and representations showing energy is conserved. 

Assessment Boundary: Assessment does not include calculating the total bond energy changes during a chemical reaction from the bond energies of reactants and products.

Reaction Rate

The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time ...

Temperature Dependence on Reaction Rate

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. ...

Temperature Dependence

Chemical Kinetics 
The reaction rate is the speed at which a chemical reaction occurs. The reaction rate is defined as the change in concentration of a ...

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Conducting Reactions Below Room Temperature

Source: Laboratory of Dr. Dana Lashley - College of William and Mary
Demonstration by: Matt Smith
When new bonds are formed in the course of a chemical ...

Apply scientific principles and evidence to provide an explanation about the effects of changing the temperature or concentration of the reacting particles on the rate at which a reaction occurs. 

Clarification statement: Emphasis is on student reasoning that focuses on the number and energy of collisions between molecules. 

Assessment Boundary: Assessment is limited to simple reactions in which there are only two reactants; evidence from temperature, concentration, and rate data; and qualitative relationships between rate and temperature.

HS-PS1-5

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Le Chatelier's Principle: Changing Concentration

A system at equilibrium is in a state of dynamic balance, with forward and reverse reactions taking place at equal rates. If an equilibrium system is ...

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Le Chatelier's Principle: Changing Volume (Pressure)

For gas-phase equilibria, changes in the concentrations of reactants and products can occur with altered volume and pressure. The partial pressure, P, of ...

le-chatelier-s-principle-changing-temperature

Le Chatelier's Principle: Changing Temperature

Consistent with the law of mass action, an equilibrium stressed by a change in concentration will shift to re-establish equilibrium without any change in ...

Le Ch&#226;telier's Principle

Source: Laboratory of Dr. Lynne O&#39;Connell &#8212; Boston College
When the conditions of a system at equilibrium are altered, the system responds in ...

Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium. 

Clarification statement: Emphasis is on the application of Le Chatelier's Principle and on refining designs of chemical reaction systems, including descriptions of the connection between changes made at the macroscopic level and what happens at the molecular level. Examples of designs could include different ways to increase product formation including adding reactants or removing products. 

Assessment Boundary: Assessment is limited to specifying the change in only one variable at a time. Assessment does not include calculating equilibrium constants and concentrations.

HS-PS1-6

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Formula Mass and Mole Concepts of Compounds

Formula Mass of Covalent Compounds

Chemical formulas represent the elemental makeup of substances. For covalent compounds, the formula represents the ...

Reaction Stoichiometry

A balanced chemical equation provides a great deal of information in a very succinct format. Chemical formulas provide the identities of the reactants and ...

The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

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Stoichiometry, Product Yield, and Limiting Reactants

Chemical equations represent how a chemical reaction proceeds from reactants to products through physical or chemical change using chemical formulas.
...

chemical-stoichiometry-gases-using-ideal-gas-law-to-determine

Chemical Stoichiometry and Gases: Using Ideal Gas Law to Determine Moles

Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions.

In addition to measuring quantities ...

Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction. 

Clarification statement: Emphasis is on using mathematical ideas to communicate the proportional relationships between masses of atoms in the reactants and the products, and the translation of these relationships to the macroscopic scale using the mole as the conversion from the atomic to the macroscopic scale. Emphasis is on assessing students' use of mathematical thinking and not on memorization and rote application of problem-solving techniques. 

Assessment Boundary: Assessment does not include complex chemical reactions.

HS-PS1-7

Radioactivity and Nuclear Equations

Nuclear chemistry is the study of reactions that involve changes in nuclear structure. The nucleus of an atom is composed of protons and, except for ...

Types of Radioactivity

The most common types of radioactivity are &#945; decay, &#946; decay, &#947; decay, neutron emission, and electron capture.
Alpha (&#945;) decay is the ...

Nuclear Fission

Many heavier elements with smaller binding energies per nucleon can decompose into more stable elements that have intermediate mass numbers and larger ...

Nuclear Power

Controlled nuclear fission reactions are used to generate electricity. Any nuclear reactor that produces power via the fission of uranium or plutonium by ...

Nuclear Fusion

The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process ...

Biological Effects of Radiation

All radioactive nuclides emit high-energy particles or electromagnetic waves. When this radiation encounters living cells, it can cause heating, break ...

Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay. 

Clarification statement: Emphasis is on simple qualitative models, such as pictures or diagrams, and on the scale of energy released in nuclear processes relative to other kinds of transformations. 

Assessment Boundary: Assessment does not include quantitative calculation of energy released. Assessment is limited to alpha, beta, and gamma radioactive decays.

HS-PS1-8

Using Formation Data to Find Free Energy

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