Table of contents |
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Introduction |
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Gibbs Energy and Spontaneity |
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Enthalpically vs. Entropically Driving Reactions |
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The Relationship between ΔG and Work |
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Solved Examples |
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Summary |
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To further understand how the various components of ΔG dictate whether a process occurs spontaneously, we now look at a simple and familiar physical change: the conversion of liquid water to water vapor.
At Room Temperature (100 °C)
Above Room Temperature (110 °C)
Below Room Temperature (90 °C)
Equilibrium Temperature
Figure 13.7.1: Temperature Dependence of ΔH and TΔS for the Vaporization of Water. Both ΔH and TΔS are temperature dependent, but the lines have opposite slopes and cross at 373.15 K at 1 atm, where ΔH = TΔS. Because ΔG = ΔH − TΔS, at this temperature ΔG = 0, indicating that the liquid and vapor phases are in equilibrium. The normal boiling point of water is therefore 373.15 K. Above the normal boiling point, the TΔS term is greater than ΔH, making ΔG < 0; hence, liquid water evaporates spontaneously. Below the normal boiling point, the ΔH term is greater than TΔS , making ΔG > 0. Thus liquid water does not evaporate spontaneously, but water vapor spontaneously condenses to liquid.
Figure 13.7.2: An enthalpic favored reaction. (CC BY-NC; Ümit Kaya)
Figure 13.7.3: An entropically favored reaction.
This reaction as written, is entropically favorable, and enthalpically unfavorable; it is entropically driven. From Table 13.7.1, it would appear that we might be able to get the reaction to go to the right at high temperatures (high temperature would increase the energetic contribution of the entropic change).
Table 13.7.2: Approximate Thermodynamic Efficiencies of Various Devices
Standard Free-Energy Change
We have seen that there is no way to measure absolute enthalpies, although we can measure changes in enthalpy (ΔH) during a chemical reaction. Because enthalpy is one of the components of Gibbs free energy, we are consequently unable to measure absolute free energies; we can measure only changes in free energy. The standard free-energy change (ΔG°) is the change in free energy when one substance or a set of substances in their standard states is converted to one or more other substances, also in their standard states. The standard free-energy change can be calculated from the definition of free energy, if the standard enthalpy and entropy changes are known, using Equation 13.7.14:
ΔG° = ΔH° − TΔS° (13.7.14)
If ΔS° and ΔH° for a reaction have the same sign, then the sign of ΔGo depends on the relative magnitudes of the ΔH° and TΔS° terms. It is important to recognize that a positive value of ΔGo for a reaction does not mean that no products will form if the reactants in their standard states are mixed; it means only that at equilibrium the concentrations of the products will be less than the concentrations of the reactants.
A positive ΔG° means that the equilibrium constant is less than 1.
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The Gibbs Free Energy
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Example 1: Calculate the standard free-energy change (ΔG°) at 25°C for the reaction
H2(g) + O2(g)⇌H2O2(l)
At 25°C, the standard enthalpy change (ΔH°) is −187.78 kJ/mol, and the absolute entropies of the products and reactants are:
Is the reaction spontaneous as written?
Given: balanced chemical equation, ΔH° and S° for reactants and product
Asked for: spontaneity of reaction as written
Strategy: (a) Calculate ΔS° from the absolute molar entropy values given.
(b) Use Equation 13.7.14, the calculated value of ΔS°, and other data given to calculate ΔGo for the reaction.
(c) Use the value of ΔGo to determine whether the reaction is spontaneous as written.
Ans: (a) To calculate ΔGo for the reaction, we need to know ΔH°, ΔS°, and T. We are given ΔH°, and we know that T = 298.15 K. We can calculate ΔS° from the absolute molar entropy values provided using the “products minus reactants” rule:
As we might expect for a reaction in which 2 mol of gas is converted to 1 mol of a much more ordered liquid, ΔS° is very negative for this reaction.
(b) Substituting the appropriate quantities into Equation 13.7.14
The negative value of ΔGo indicates that the reaction is spontaneous as written. Because ΔS° and ΔH° for this reaction have the same sign, the sign of ΔGo depends on the relative magnitudes of the ΔH° and TΔS° terms. In this particular case, the enthalpy term dominates, indicating that the strength of the bonds formed in the product more than compensates for the unfavorable ΔS° term and for the energy needed to break bonds in the reactants.
Tabulated values of standard free energies of formation allow chemists to calculate the values of ΔGo for a wide variety of chemical reactions rather than having to measure them in the laboratory. The standard free energy of formation ( ΔG∘f) of a compound is the change in free energy that occurs when 1 mol of a substance in its standard state is formed from the component elements in their standard states. By definition, the standard free energy of formation of an element in its standard state is zero at 298.15 K. One mole of Cl2 gas at 298.15 K, for example, has ΔG∘f = 0. The standard free energy of formation of a compound can be calculated from the standard enthalpy of formation (ΔH∘f) and the standard entropy of formation (ΔS∘f) using the definition of free energy:(13.7.15)
Using standard free energies of formation to calculate the standard free energy of a reaction is analogous to calculating standard enthalpy changes from standard enthalpies of formation using the familiar “products minus reactants” rule:
(13.7.16)
where m and n are the stoichiometric coefficients of each product and reactant in the balanced chemical equation. A very large negative ΔGo indicates a strong tendency for products to form spontaneously from reactants; it does not, however, necessarily indicate that the reaction will occur rapidly. To make this determination, we need to evaluate the kinetics of the reaction.
"Products minus Reactants" Rule
The ΔGo of a reaction can be calculated from tabulated ΔGof values (Table T1) using the “products minus reactants” rule.
Example 2: Calculate ΔGo for the reaction of isooctane with oxygen gas to give carbon dioxide and water. Use the following data:
Is the reaction spontaneous as written?
Given: balanced chemical equation and values of ΔG°f for isooctane, CO2, and H2O
Asked for: spontaneity of reaction as written
Strategy: Use the “products minus reactants” rule to obtain ΔG∘rxn, remembering that ΔG°f for an element in its standard state is zero. From the calculated value, determine whether the reaction is spontaneous as written.
Ans: The balanced chemical equation for the reaction is as follows:
We are given ΔG∘f values for all the products and reactants except O2(g). Because oxygen gas is an element in its standard state, ΔG∘f (O2) is zero. Using the “products minus reactants” rule,
Because ΔGo is a large negative number, there is a strong tendency for the spontaneous formation of products from reactants (though not necessarily at a rapid rate). Also notice that the magnitude of ΔGo is largely determined by the ΔG∘f of the stable products: water and carbon dioxide.
Calculated values of ΔGo are extremely useful in predicting whether a reaction will occur spontaneously if the reactants and products are mixed under standard conditions. We should note, however, that very few reactions are actually carried out under standard conditions, and calculated values of ΔGo may not tell us whether a given reaction will occur spontaneously under nonstandard conditions. What determines whether a reaction will occur spontaneously is the free-energy change (ΔG) under the actual experimental conditions, which are usually different from ΔG°. If the ΔH and TΔS terms for a reaction have the same sign, for example, then it may be possible to reverse the sign of ΔG by changing the temperature, thereby converting a reaction that is not thermodynamically spontaneous, having Keq < 1, to one that is, having a Keq > 1, or vice versa. Because ΔH and ΔS usually do not vary greatly with temperature in the absence of a phase change, we can use tabulated values of ΔH° and ΔS° to calculate ΔGoat various temperatures, as long as no phase change occurs over the temperature range being considered.
In the absence of a phase change, neither ΔH nor ΔS vary greatly with temperature.
The change in Gibbs free energy, which is based solely on changes in state functions, is the criterion for predicting the spontaneity of a reaction.
We can predict whether a reaction will occur spontaneously by combining the entropy, enthalpy, and temperature of a system in a new state function called Gibbs free energy (G). The change in free energy (ΔG) is the difference between the heat released during a process and the heat released for the same process occurring in a reversible manner. If a system is at equilibrium, ΔG = 0. If the process is spontaneous, ΔG < 0. If the process is not spontaneous as written but is spontaneous in the reverse direction, ΔG > 0. At constant temperature and pressure, ΔG is equal to the maximum amount of work a system can perform on its surroundings while undergoing a spontaneous change. The standard free-energy change (ΔG°) is the change in free energy when one substance or a set of substances in their standard states is converted to one or more other substances, also in their standard states. The standard free energy of formation (ΔG∘f), is the change in free energy that occurs when 1 mol of a substance in its standard state is formed from the component elements in their standard states. Tabulated values of standard free energies of formation are used to calculate ΔGo for a reaction.
1. What is Gibbs energy and how is it related to spontaneity? | ![]() |
2. What is the difference between enthalpically and entropically driving reactions? | ![]() |
3. How is the relationship between ΔG and work defined? | ![]() |
4. Can you provide an example to illustrate the concept of Gibbs energy and spontaneity? | ![]() |
5. How is Gibbs energy related to the equilibrium of a reaction? | ![]() |