We can therefore solve this equation for the relationship between G o and K. This equation allows us to calculate the equilibrium constant for any reaction from the standard-state free energy of reaction, or vice versa. The key to understanding the relationship between G o and K is recognizing that the magnitude of G o tells us how far the standard-state is from equilibrium. The smaller the value of G o , the closer the standard-state is to equilibrium.
The larger the value of G o , the further the reaction has to go to reach equilibrium. The relationship between G o and the equilibrium constant for a chemical reaction is illustrated by the data in the table below. Use the value of G o obtained in Practice Problem 7 to calculate the equilibrium constant for the following reaction at 25C:.
Click here to check your answer to Practice Problem 9. Click here to see a solution to Practice Problem 9. The equilibrium constant for a reaction can be expressed in two ways: K c and K p. We can write equilibrium constant expressions in terms of the partial pressures of the reactants and products, or in terms of their concentrations in units of moles per liter.
For gas-phase reactions the equilibrium constant obtained from G o is based on the partial pressures of the gases K p. For reactions in solution, the equilibrium constant that comes from the calculation is based on concentrations K c.
Use the following standard-state free energy of formation data to calculate the acid-dissociation equilibrium constant K a at for formic acid:. HCO 2 aq HCO 2 - aq Click here to check your answer to Practice Problem Click here to see a solution to Practice Problem The Temperature Dependence of Equilibrium Constants. Equilibrium constants are not strictly constant because they change with temperature.
We are now ready to understand why. The standard-state free energy of reaction is a measure of how far the standard-state is from equilibrium. But the magnitude of G o depends on the temperature of the reaction. As a result, the equilibrium constant must depend on the temperature of the reaction. A good example of this phenomenon is the reaction in which NO 2 dimerizes to form N 2 O 4. This reaction is favored by enthalpy because it forms a new bond, which makes the system more stable.
The reaction is not favored by entropy because it leads to a decrease in the disorder of the system. NO 2 is a brown gas and N 2 O 4 is colorless. We can therefore monitor the extent to which NO 2 dimerizes to form N 2 O 4 by examining the intensity of the brown color in a sealed tube of this gas. What should happen to the equilibrium between NO 2 and N 2 O 4 as the temperature is lowered?
For the sake of argument, let's assume that there is no significant change in either H o or S o as the system is cooled. The contribution to the free energy of the reaction from the enthalpy term is therefore constant, but the contribution from the entropy term becomes smaller as the temperature is lowered. As the tube is cooled, and the entropy term becomes less important, the net effect is a shift in the equilibrium toward the right.
The figure below shows what happens to the intensity of the brown color when a sealed tube containing NO 2 gas is immersed in liquid nitrogen. There is a drastic decrease in the amount of NO 2 in the tube as it is cooled to o C. Use values of H o and S o for the following reaction at 25C to estimate the equilibrium constant for this reaction at the temperature of boiling water C , ice 0C , a dry ice-acetone bath C , and liquid nitrogen C :.
The value of G for a reaction at any moment in time tells us two things. The sign of G tells us in what direction the reaction has to shift to reach equilibrium. The magnitude of G tells us how far the reaction is from equilibrium at that moment. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system. Gibbs free energy equation : The Gibbs free energy equation is dependent on pressure. As such, it is a convenient criterion of spontaneity for processes with constant pressure and temperature.
Therefore, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure. Gibbs energy is the maximum useful work that a system can do on its surroundings when the process occurring within the system is reversible at constant temperature and pressure. As in mechanics, where potential energy is defined as capacity to do work, different potentials have different meanings. Energy that is not extracted as work is exchanged with the surroundings as heat.
Work Diagram : The reversible condition implies wmax and qmin. The impossibility of extracting all of the internal energy as work is essentially a statement of the Second Law. This is most commonly electrical work moving electric charge through a potential difference , but other forms of work are also possible. For instance, examples of useful, non-expansion work in biological organisms include muscle contraction and the transmission of nerve impulses.
Privacy Policy. Skip to main content. Search for:. Learning Objectives Calculate the change in standard free energy for a particular reaction. Key Takeaways Key Points The standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under standard conditions.
Combine the standard enthalpy of formation and the standard entropy of a substance to get its standard free energy of formation. Key Terms enthalpy : In thermodynamics, a measure of the heat content of a chemical or physical system. Learning Objectives Recall the possible free energy changes for chemical reactions.
Key Takeaways Key Points If the free energy of the reactants is greater than that of the products, the entropy of the world will increase when the reaction takes place as written, and so the reaction will tend to take place spontaneously. If the free energy of the products exceeds that of the reactants, then the reaction will not take place. Key Terms spontaneous change : A spontaneous process is the time-evolution of a system in which it releases free energy usually as heat and moves to a lower, more thermodynamically stable energy state.
Learning Objectives Differentiate between free changes for standard and nonstandard states. Non spontaneous - needs constant external energy applied to it in order for the process to continue and once you stop the external action the process will cease.
When solving for the equation, if change of G is negative, then it's spontaneous. If change of G if positive, then it's non spontaneous. In chemical reactions involving the changes in thermodynamic quantities, a variation on this equation is often encountered:. Since the changes of entropy of chemical reaction are not measured readily, thus, entropy is not typically used as a criterion.
The standard-state free energy of formation is the change in free energy that occurs when a compound is formed from its elements in their most thermodynamically stable states at standard-state conditions. In other words, it is the difference between the free energy of a substance and the free energies of its constituent elements at standard-state conditions:. This question is essentially asking if the following reaction is spontaneous at room temperature.
Will the reaction occur spontaneously? The following equation relates the standard-state free energy of reaction with the free energy at any point in a given reaction not necessarily at standard-state conditions :. This equation is particularly interesting as it relates the free energy difference under standard conditions to the properties of a system at equilibrium which is rarely at standard conditions. The Nernst equation relates the standard-state cell potential with the cell potential of the cell at any moment in time:.
Chem1 Virtual Textbook. Learning Objectives To get an overview of Gibbs energy and its general uses in chemistry.
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