Chapter 18. Chemical Thermodynamics Show Jessie A. Key
In the Gibbs free energy change equation, the only part we as scientists can control is the temperature. We have seen how we can calculate the standard change in Gibbs free energy, ΔG°, but not all reactions we are interested in occur at exactly 298 K. The temperature plays an important role in determining the Gibbs free energy and spontaneity of a reaction.  If we examine the Gibbs free energy change equation, we can cluster the components to create two general terms, an enthalpy term, ΔH, and an entropy term, –TΔS. Depending on the sign and magnitude of each, the sum of these terms determines the sign of ΔG and therefore the spontaneity (Table 18.2 “Spontaneity and the Signs of Enthalpy and Entropy Terms”).
Since all temperature values are positive in the Kelvin scale, the temperature affects the magnitude of the entropy term. As shown in Table 18.2 “Spontaneity and the Signs of Enthalpy and Entropy Terms,” the temperature can be the deciding factor in spontaneity when the enthalpy and entropy terms have opposite signs. If ΔH is negative, and –TΔS positive, the reaction will be spontaneous at low temperatures (decreasing the magnitude of the entropy term). If ΔH is positive, and –TΔS negative, the reaction will be spontaneous at high temperatures (increasing the magnitude of the entropy term). Sometimes it can be helpful to determine the temperature when ΔG° = 0 and the process is at equilibrium. Knowing this value, we can adjust the temperature to drive the process to spontaneity or alternatively to prevent the process from occurring spontaneously. Remember that, at equilibrium: We can rearrange and solve for the temperature T:
Using the appendix table of standard thermodynamic quantities, determine the temperature at which the following process is at equilibrium: How does the value you calculated compare to the boiling point of chloroform given in the literature? Solution At equilibrium: We must estimate ΔH° and S° from their enthalpies of formation and standard molar entropies, respectively.
Now we can use these values to solve for the temperature:
The literature boiling point of chloroform is 61.2°C. The value we have calculated is very close but slightly lower due to the assumption that ΔH° and S° do not change with temperature when we estimate the ΔH° and S° from their enthalpies of formation and standard molar entropies.
According to the First Law of Thermodynamics, the total energy of an isolated system always remains constant. The first law explains the relationship between the work done by the system or by the system and the heat absorbed without putting any limitation on the direction of heat flow. However, all processes which occur naturally tend to proceed spontaneously in one direction only. What does spontaneity mean here? What factors determine the direction of a spontaneous change? Naturally, all processes have a tendency to occur in one direction under a given set of conditions. A spontaneous process is an irreversible process and it could only be reversed by some external agents. The entropy of any system is defined as the degree of randomness in it. Predicting the spontaneity of a reactionGenerally, the total entropy change is the essential parameter which defines the spontaneity of any process. Since most of the chemical reactions fall under the category of a closed system and open system; we can say there is a change in enthalpy too along with the change in entropy. Since, change in enthalpy also increases or decreases the randomness by affecting the molecular motions, entropy change alone cannot account for the spontaneity of such a process. Therefore, for explaining the spontaneity of a process we use the Gibbs energy change. Gibbs’ energy is a state function and an extensive property. The general expression for Gibbs energy change at constant temperature is expressed as: Gibbs Equation ⇒ΔGsys = ΔHsys – TΔSsys Where, ΔGsys = Gibbs energy change of the system ΔHsys = enthalpy change of the system ΔSsys = entropy change of the system T = Temperature of the system This is known as the Gibbs equation. For a spontaneous process, the total entropy change, ΔStotal is always greater than zero. ΔStotal=ΔSsys + ΔSsurr Where, ΔStotal= total entropy change for the process ΔSsys = entropy change of the system ΔSsurr = entropy change of the surrounding The change in temperature between the system and the surroundings in the case of thermal equilibrium between the system and surroundings is 0, i.e. ΔT= 0. Thus, enthalpy lost by the system is gained by the surrounding. Hence, the entropy change of the surrounding is given as, ΔHsurr = change in enthalpy of the surrounding ΔHsys = change in enthalpy of the system Also, for a spontaneous process, the total change in entropy is 0, i.e. ΔStotal> 0. Therefore; TΔSsys – ΔHsys>0 ΔHsys– TΔSsys<0 Using the Gibbs equation, it can be said that ΔGsys< 0 Thus, it can be inferred that any process is spontaneous if the change in Gibbs energy of the system is less than zero or else the process is not spontaneous. Therefore, with the help of the above relation, the spontaneity of a reaction can be easily predicted.
Reactions are favourable when they result in a decrease in enthalpy and an increase in entropy of the system. When both of these conditions are met, the reaction occurs naturally. A spontaneous reaction is a reaction that favours the formation of products at the conditions under which the reaction is occurring.
A reaction which is exothermic (ΔH negative) and results in an increase in the entropy of the system (ΔS positive) will always be spontaneous.
A spontaneous process is one that occurs on its own, without any energy input from the outside. For example, a ball will roll down an incline; water will flow downhill; ice will melt into water; radioisotopes will decay, and the iron will rust.
Enthalpy is the total heat content of the system. Entropy is the measurement of randomness of the system. change in enthalpy and change in entropy should be positive for a reaction to be spontaneous.
A spontaneous process is capable of proceeding in a given direction without needing to be driven by an outside source of energy. An endergonic reaction (also called a nonspontaneous reaction) is a chemical reaction in which the standard change in free energy is positive and energy is absorbed. To learn more about spontaneity and thermodynamics, register with BYJU’S and download our app – BYJU’S – The Learning App.
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