Name: predicting reaction direction with free energy
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 56 s
Channel: JoVE

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Free Energy and Equilibrium

Both the equilibrium constant and the standard free energy change can be used to determine whether a reaction is product or reactant favored.
For any reaction mixture composition, the &#916;G for the reaction is the sum of the standard free energy and RT times the natural log of the reaction quotient.
When the reactants and products are at equilibrium, the free energy change is zero, and the reaction quotient equals the equilibrium constant. So the standard free energy change equals &#8722;RT ln K.
If &#916;G naught is less than zero, ln K is positive, meaning K is greater than 1. In this case, product formation is favored at equilibrium. The larger the equilibrium constant, the more negative the free energy. 
Take, for example, the breakdown of dinitrogen tetroxide at 298 kelvin, in which K is 1.34 &#215; 1017. 
Substituting the known values into the equation, the standard free energy for the reaction equals &#8722;98 kJ/mole, and product formation is favored.
Conversely, if &#916;G naught is greater than zero, ln K is negative, meaning K is less than 1 and the reverse direction of the reaction is favored.
Consider the breakdown of sulfur trioxide gas at 298 kelvin, which has a &#916;G naught of 141.6 kJ/mole.
The equation can be rearranged so ln K equals negative &#916;G over RT.
Substituting the known values into the equation, and raising e to the power of the result, K is very small&#8212;indicating that the reactant is favored.
Notably, if the temperature varies, the equilibrium constant will also change.
The temperature dependence of the equilibrium constant can be derived from the equation that directly relates K to the &#916;G naught for the reaction.
The &#916;G naught can be replaced by the standard enthalpy minus temperature times the standard entropy. Dividing both sides by negative RT yields ln K equals negative &#916;H over RT plus &#916;S over R.
This equation is in the form of a straight line where the natural log of K can be plotted against the inverse of the temperature in kelvins with a slope of negative &#916;H over R and a y-intercept of &#916;S over R.
If the values of K are measured at two slightly different temperatures, then this graph can also be used to calculate the change in enthalpy, assuming it remains constant over a limited temperature range.

free energy and equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for &#916;G represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When &#916;Grxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
Recall that Q is the numerical value of the mass action expression for the system, and its value may be used to identify the direction in which a reaction will proceed in order to achieve equilibrium. When Q is lesser than the equilibrium constant, K, the reaction will proceed in the forward direction until equilibrium is reached and Q = K. Conversely, if Q &#62; K, the process will proceed in the reverse direction until equilibrium is achieved.
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
<img alt="Fishbone diagram for cause-effect analysis, identifying root causes in project management processes." src="/files/ftp_upload/11431/11431_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
R is the gas constant (8.314 J/K mol), T is the kelvin or absolute temperature, and Q is the reaction quotient. For gas-phase equilibria, the pressure-based reaction quotient, Qp, is used. The concentration-based reaction quotient, Qc, is used for condensed phase equilibria. This equation may be used to predict the spontaneity of a process under any given set of conditions
For a system at equilibrium, Q = K and &#916;Grxn = 0, and the previous equation may be written as
<img alt="static equilibrium &#931;Fx=0, &#931;Fy=0 diagram with forces labeled; vector components and directions shown" src="/files/ftp_upload/11431/11431_Equation_2.png" style="text-align: center; height: 75px;" data-altupdatedat="1761830439000" data-alt="Eq2" />
This form of the equation provides a useful link between these two essential thermodynamic properties, and it can be used to derive equilibrium constants from standard free energy changes and vice versa. The relations between standard free energy changes and equilibrium constants are summarized below.
If K &#62; 1, &#916;G&#186;rxn &#60; 0 and the products are more abundant in the reaction mixture.
If K &#60; 1, &#916;G&#186;rxn &#62; 0 and the reactants are more abundant in the reaction mixture.
 K = 1, &#916;G&#186;rxn = 0 and the reactants and products are comparably abundant in the reaction mixture.
The standard free energy for a reaction change depends on temperature:
<img alt="Centripetal force diagram with equations F=mv&#178;/r; analysis of circular motion dynamics." src="/files/ftp_upload/11431/11431_Equation_3.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
The standard free energy change for a reaction is related to the equilibrium constant for a reaction:
<img alt="Chromatography process, Van Deemter equation, factors affecting column efficiency, scientific diagram" src="/files/ftp_upload/11431/11431_Equation_4.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
Combining the two expressions:
<img alt="Chemical bonding: Covalent bond diagram showing electron sharing in a molecule." src="/files/ftp_upload/11431/11431_Equation_5.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq5" />
Dividing both sides by RT gives
<img alt="Kirchhoff's voltage law circuit diagram with loop equations, illustrating electrical circuit analysis." src="/files/ftp_upload/11431/11431_Equation_6v2.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq6" />
Rearranging gives
<img alt="Chromatography process: protein purification diagram, shows column flow and separation stages." src="/files/ftp_upload/11431/11431_Equation_7v2.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq7" />
The equation takes the form of a straight line y = mx + b. A plot of ln K plotted against 1/T yields a straight line with a slope of &#8722;&#916;H&#186;rxn/R and a y-intercept of &#916;S&#186;rxn/R. The equation can also be expressed in a two-point form:
<img alt="Titration setup diagram, showing acid-base reaction process with pH measurement." src="/files/ftp_upload/11431/11431_Equation_8v2.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq8" />
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 process may be viewed as a measure of its driving force. A negative value for &#916;G represents a driving force for the ...

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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 than the equilibrium constant, K, the reaction proceeds forward until Q = K. If Q is greater than K, the reaction proceeds in reverse until equilibrium is reached.

For conditions that are not standard, the free energy change is linked to the standard free energy change by ΔG = ΔG° + RT ln Q. In this equation, R is the gas constant, T is the absolute temperature in kelvin, and Q is the reaction quotient. For gas-phase equilibria, the pressure-based quotient Qp is used. For condensed-phase equilibria, the concentration-based quotient Qc is used. This relation helps predict whether a process is spontaneous under a given set of conditions.

At equilibrium, Q = K and ΔGrxn = 0, so the equation simplifies to a form that connects free energy and the equilibrium constant. This link lets chemists find equilibrium constants from standard free energy changes and also work backward from K to ΔG°. If K is greater than 1, ΔG°rxn is less than 0 and products are more abundant. If K is less than 1, ΔG°rxn is greater than 0 and reactants are more abundant. If K equals 1, ΔG°rxn is 0 and reactants and products are present in similar amounts.

Temperature also affects the standard free energy change. The relationship between ΔG° and K can be rearranged into a straight-line equation. A plot of ln K versus 1/T gives a line with slope −ΔH°rxn/R and y-intercept ΔS°rxn/R. The same relationship can also be written in a two-point form.

Predicting Reaction Direction with Free Energy

predicting-reaction-direction-with-free-energy

spontaneity

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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...

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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 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 ΔG, Q, and K predict reaction direction, equilibrium, and spontaneity. Explore standard free energy, temperature effects, and key chemistry relationships.

Predicting Reaction Direction with Free Energy | JoVE K12

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Predicting Reaction Direction with Free Energy

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