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Explain how the free energy changes as a spontaneous reaction occurs. Show by means of a diagram how \(G\) changes with the extent of reaction.

Short Answer

Expert verified
The free energy \( G \) decreases as a spontaneous reaction progresses, reaching a minimum at equilibrium where \( \Delta G = 0 \).

Step by step solution

01

Understand the Concept of Free Energy

Free energy, denoted as \(G\), is a thermodynamic potential that measures the maximum reversible work that can be performed by a thermodynamic system at constant temperature and pressure. In the context of chemical reactions, it helps to determine whether a process will occur spontaneously.
02

Recognize the Criteria for Spontaneity

A spontaneous reaction is one that occurs naturally without needing to be driven by external energy input. For such reactions, the change in Gibbs free energy (\( \Delta G \)) must be negative. This condition indicates that the process releases energy, making it spontaneous.
03

Sketch the Gibbs Free Energy vs. Extent of Reaction Diagram

On a graph, plot the Gibbs free energy \(G\) on the y-axis and the extent of reaction on the x-axis. In a spontaneous reaction, \(G\) starts at a higher value when the reaction is only beginning and decreases as the reaction proceeds. The curve slopes downward, reaching a minimum point at equilibrium, where \( \Delta G = 0 \).
04

Explain the Diagram

The downward slope of the graph indicates that \( \Delta G < 0 \) as the reaction progresses toward equilibrium, showing that the reaction loses free energy. The minimum on the graph represents the point of equilibrium, where no further net reaction occurs without external energy because \( \Delta G = 0 \). Beyond this point, any progression of the reaction in either direction would require the input of energy, making the reaction non-spontaneous in that direction.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Spontaneous Reaction
A spontaneous reaction is like an energy party that happens without needing anyone to bring extra energy to start it. In chemical terms, these reactions occur naturally and with ease. The key to determining if a reaction is spontaneous is the Gibbs free energy change, represented by \( \Delta G \). If \( \Delta G \) is negative, this indicates that the system is losing free energy, thus allowing the reaction to proceed on its own.
The negativity of \( \Delta G \) implies that energy is released during the reaction, and nature loves to move to more energy-efficient states. Spontaneity is a handy concept because it lets chemists predict if a reaction will happen without needing outside assistance, saving time and energy in experimental settings.
Thermodynamic Potential
Thermodynamic potential is a fancy term that refers to a kind of energy currency helpful in predicting the direction of chemical reactions. In simple terms, it's an energy measure that indicates how favorable a reaction or process is. Gibbs free energy \( G \), is one such potential, and it's particularly useful because it takes both entropy and enthalpy into account, thus providing a complete picture of energy changes at constant temperature and pressure.
Think of thermodynamic potential as a balance between chaos (entropy) and stability (enthalpy). This balance helps scientists ascertain if a reaction will proceed spontaneously. At constant conditions, a reaction is favorable when it leads to a decrease in Gibbs free energy.
Gibbs Free Energy Diagram
A Gibbs free energy diagram is a visual aide designed to clearly showcase how the free energy of a system changes during the course of a reaction. By plotting Gibbs free energy \( G \) on the y-axis and the extent of the reaction on the x-axis, one can easily track the progression of the reaction.
During a spontaneous reaction, the diagram will illustrate a downward slope, indicating that free energy is being lost as the reaction proceeds. This slope decreases until reaching a minimum point, signifying equilibrium where \( \Delta G = 0 \). Beyond this point, any further advancement in reaction would require extra energy, signaling the transition into non-spontaneity.
Equilibrium
Equilibrium is the zen state of chemical reactions where everything is balanced and no net change occurs over time. At this point, the Gibbs free energy has reached its minimum value, meaning \( \Delta G = 0 \). This balance indicates that the forward and reverse reactions happen at the same rate, and there's no free energy left to be harnessed without additional input.
  • At equilibrium, neither the reactants nor the products are favored.
  • The system remains unchanged if left undisturbed.
  • Equilibrium marks a point of stability in the reaction's energy landscape.
Understanding equilibrium is crucial in gauging the limits of spontaneous reactions and predicting when external energy might be necessary to shift the balance.

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Most popular questions from this chapter

a. Why are some reactions exothermic and others endothermic? b. Discuss the driving force in a spontaneous reaction that is highly exothermic and in one that is endothermic.

The direct reaction of iron(III) oxide, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\), to give iron and oxygen gas is a nonspontaneous reaction; normally, iron combines with oxygen to give rust (the oxide). Yet we do change iron(III) oxide, as iron ore, into iron metal. How is this possible? Explain.

The combustion of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), is a spontaneous reaction given by the equation $$ 2 \mathrm{C}_{2} \mathrm{H}_{2}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ As expected for a combustion, the reaction is exothermic. What is the sign of \(\Delta H^{\circ} ?\) What do you expect for the sign of \(\Delta S^{\circ}\) ? Explain the spontaneity of the reaction in terms of the enthalpy and entropy changes.

The reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ is spontaneous at room temperature but becomes nonspontaneous at a much higher temperature. From this fact alone, obtain the signs of \(\Delta H^{\circ}\), and \(\Delta S^{\circ}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change much with temperature. Explain your reasoning.

Consider a sample of water at \(25^{\circ} \mathrm{C}\) in a beaker in a room at \(50{ }^{\circ} \mathrm{C} .\) a. What change do you expect to observe in the water sample? Would this be a spontaneous process or not? b. What are the enthalpy and entropy changes for this change in the water sample? (Just indicate the sign of the changes.) Explain your answers. c. Does the entropy of the water increase or decrease during the change? How do you know? d. Is there a change in free energy for the water sample? If so, indicate the sign of the free-energy change and explain how you arrived at your answer. Consider the same sample of water, but starting at \(75^{\circ} \mathrm{C}\) in a room at \(50^{\circ} \mathrm{C}\). e. What change would you observe in the water sample? Would this change be a spontaneous process or not? f. What are the enthalpy and entropy changes for the water sample? (Just indicate the sign of the changes.) Explain your answers. g. Does the entropy of the water increase or decrease during the change? How do you know? h. Is there a change in free energy for the water sample? If so, indicate the sign of the free-energy change and explain how you arrived at your answer. Finally, consider the same sample of water, starting at \(50^{\circ} \mathrm{C}\) in a room at \(50^{\circ} \mathrm{C}\). i. What would you observe in the water sample? Is this a spontaneous process? j. What are the enthalpy and entropy changes for the water sample? (Just indicate the sign of the changes.) Be sure to justify your answer. k. Did the entropy of the water increase or decrease during the change? How do you know? I. Can you determine the exact free-energy change of the water in this case? If you can make this determination, what is the significance of this value?

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