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Chapter 18: Problem 9

Explain how \(\Delta G^{\circ}\) can be used to decide whether a chemical equation is spontaneous in the direction written.

Short Answer

Expert verified
Use \\(\Delta G^{\circ} < 0\\) for spontaneity; if positive, reaction is non-spontaneous. If zero, reaction is at equilibrium.

Step by step solution

01

Understanding the Concept

First, let's recognize what \(\Delta G^{\circ}\) represents. It is the standard Gibbs free energy change of a reaction and indicates whether a reaction is thermodynamically favorable under standard conditions: 1 atm pressure, 298K temperature, and 1 M concentration for all reactants and products.
02

Interpreting \\(\Delta G^{\circ}\\) Values

The sign of \(\Delta G^{\circ}\) helps us determine spontaneity. If \(\Delta G^{\circ} < 0\), the reaction is spontaneous in the direction written. If \(\Delta G^{\circ} > 0\), the reaction is non-spontaneous in the direction written and might proceed spontaneously in the reverse direction.
03

Zero Value Implication

If \(\Delta G^{\circ} = 0\), the reaction is at equilibrium under standard conditions, meaning neither the forward nor the reverse direction is favored, and the reaction will not proceed spontaneously in either direction.

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Key Concepts

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

Thermodynamics
Thermodynamics involves studying energy changes and transformations in a system. Within chemistry, this aspect focuses on how energy is transferred during chemical reactions.
In thermodynamics, Gibbs Free Energy (\( \Delta G \)) is a fundamental concept. It's used to predict whether a reaction will occur spontaneously. Spontaneity here means that a reaction will proceed without needing additional energy once started.
The equation to calculate Gibbs Free Energy is: \( \Delta G = \Delta H - T\Delta S \)\, where:
  • \( \Delta H \)\: Change in enthalpy (heat content of a system)
  • \( T \)\: Temperature in Kelvin
  • \( \Delta S \)\: Change in entropy (degree of disorder or randomness in the system)
Gibbs Free Energy integrates these thermodynamic concepts to help us understand if a process will naturally occur.
Reaction Spontaneity
Reaction spontaneity refers to whether a reaction can proceed on its own without external input.
The sign of the Gibbs Free Energy change (\( \Delta G \)) can predict this:
  • If \( \Delta G < 0 \)\, the reaction is spontaneous in the forward direction. This means the reaction releases energy and can proceed on its own.
  • If \( \Delta G > 0 \)\, the reaction is non-spontaneous. It requires more energy to proceed under the given conditions than it would release. Therefore, it might favor proceeding in the reverse direction.
  • If \( \Delta G = 0 \)\, the system is at equilibrium. Both forward and reverse reactions happen at the same rate, meaning there's no net change.
Understanding the spontaneity helps in predicting reaction behavior and is crucial in fields like chemistry and engineering.
Standard Conditions
Standard conditions provide a baseline to study reactions. They define a common ground for comparing different reactions.
The internationally agreed upon standard conditions include:
  • Pressure of 1 atmosphere (atm)
  • Temperature of 298.15 Kelvin (K) or 25掳C
  • Concentration of 1 Molar (M) for solutions
When measurements are under these conditions, scientists can easily compare data across various experiments and studies.
In terms of Gibbs Free Energy (\( \Delta G^{\circ} \)), these conditions allow for the calculation of standard Gibbs Free Energy change. This helps to predict whether reactions are spontaneous when all reactants and products start at these defined conditions. Reactions can behave differently if conditions aren't standard, which is why this baseline is so important in evaluating chemical behavior.

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Most popular questions from this chapter

Adenosine triphosphate (ATP) is often referred to as a biological "energy" source. What does this mean?

Find the sign of \(\Delta S^{\circ}\) for the reaction $$ 2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(g)+\mathrm{O}_{2}(g) $$ The reaction is endothermic and nonspontaneous at \(25^{\circ} \mathrm{C}\). Explain the spontaneity of the reaction in terms of enthalpy and entropy changes as the temperature increases.

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? l.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?

18.122 Coal is used as a fuel in some electric-generating plants. Coal is a complex material, but for simplicity we may consider it to be a form of carbon. The energy that can be derived from a fuel is sometimes compared with the enthalpy of the combustion reaction: $$ \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) $$ Calculate the standard enthalpy change for this reaction at \(25^{\circ} \mathrm{C}\). Actually, only a fraction of the heat from this reaction is available to produce electric energy. In electric generating plants, this reaction is used to generate heat for a steam engine, which turns the generator. Basically the steam engine is a type of heat engine in which steam enters the engine at high temperature \(\left(T_{h}\right),\) work is done, and the steam then exits at a lower temperature \(\left(T_{l}\right)\). The maximum fraction, \(f,\) of heat available to produce useful energy depends on the difference between these temperatures (expressed in kelvins), \(f=\left(T_{h}-T_{l}\right) / T_{h} .\) What is the maximum heat energy available for useful work from the combustion of \(1.00 \mathrm{~mol}\) of \(\mathrm{C}(s)\) to \(\mathrm{CO}_{2}(g)\) ? (Assume the value of \(\Delta H^{\circ}\) calculated at \(25^{\circ} \mathrm{C}\) for the heat obtained in the generator.) It is possible to consider more efficient ways to obtain useful energy from a fuel. For example, methane can be burned in a fuel cell to generate electricity directly. The maximum useful energy obtained in these cases is the maximum work, which equals the free-energy change. Calculate the standard free-energy change for the combustion of \(1.00 \mathrm{~mol}\) of \(\mathrm{C}(s)\) to \(\mathrm{CO}_{2}(g)\). Compare this value with the maximum obtained with the heat engine described here.

The following equation shows how nitrogen dioxide reacts with water to produce nitric acid: $$ 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(l)+\mathrm{NO}(g) $$ Predict the sign of \(\Delta S^{\circ}\) for this reaction.
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