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Chapter 16: Problem 41

Inferring Conclusions If both \(\Delta H\) and \(\Delta S\) are negative, how does temperature affect spontaneity?

Short Answer

Expert verified
Spontaneity increases at lower temperatures.

Step by step solution

01

Understand the Gibbs Free Energy Equation

Recall the Gibbs Free Energy equation: \[ \Delta G = \Delta H - T\Delta S \]Spontaneity of a reaction is determined by the sign of \(\Delta G\). If \(\Delta G\) is negative, the reaction is spontaneous.
02

Interpret Given Conditions

Given that both \(\Delta H\) and \(\Delta S\) are negative, this means:\[ \Delta H < 0 \ \Delta S < 0 \]
03

Analyze the Temperature Effect

The temperature \(T\) plays a significant role in the equation \[\Delta G = \Delta H - T\Delta S\]. Since \(\Delta S\) is negative, \(T\Delta S\) will be positive but subtracting it from \(\Delta H\). Higher temperatures will make the term \(T\Delta S\) larger, increasing \(\Delta G\). Conversely, lower temperatures will make \(T\Delta S\) smaller, potentially allowing \(\Delta G\) to be negative.
04

Conclusion on Spontaneity

For spontaneity (negative \(\Delta G\)), lower temperatures are favorable because they reduce the positive impact of \(T\Delta S\). Thus, the reaction is more likely to be spontaneous at low temperatures.

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Key Concepts

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

Thermodynamics
Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. It helps us understand how different physical quantities like temperature, energy, and entropy interact in systems. Key principles of thermodynamics include:
  • First Law of Thermodynamics (Law of Energy Conservation): Energy can neither be created nor destroyed, only transformed from one form to another.
  • Second Law of Thermodynamics: The total entropy (disorder) of an isolated system can never decrease over time.
  • Third Law of Thermodynamics: As the temperature approaches absolute zero, the entropy of a perfect crystal approaches a constant minimum.
In the context of chemical reactions, thermodynamics helps us predict whether a reaction will occur spontaneously or if it requires external energy.
Reaction Spontaneity
Reaction spontaneity is about understanding whether a chemical reaction will occur on its own without needing external energy. This is chiefly determined by the Gibbs Free Energy equation: \( \Delta G = \Delta H - T\Delta S \).
The signs of \Delta G \ (Gibbs Free Energy), \Delta H \ (enthalpy change), and \Delta S \ (entropy change) are crucial:
  • If \Delta G < 0 \, the reaction is spontaneous.
  • If \Delta G > 0 \, the reaction is non-spontaneous.
  • If \Delta G = 0 \, the reaction is at equilibrium.
By examining the values and signs of \Delta H \ and \Delta S \, we can deduce spontaneity. For instance, given \Delta H < 0 \ (exothermic reaction) and \Delta S < 0 \, the reaction's spontaneity will heavily depend on temperature.
Temperature Effect on Reactions
Temperature plays a significant role in determining the spontaneity of reactions. Let's consider the Gibbs Free Energy equation again: \( \Delta G = \Delta H - T\Delta S \).
If both \Delta H \ and \Delta S \ are negative:
  • At high temperatures, the term \( T\Delta S \) becomes more significant. Since \( \Delta S \) is negative, multiplying it by \( T \) results in a positive value. Subtracting a larger positive value from \( \Delta H \) can make \( \Delta G \) positive, which indicates non-spontaneity.
  • At lower temperatures, the impact of \( T\Delta S \) is reduced, potentially making \Delta G \ more negative. A negative \Delta G means the reaction is more likely to be spontaneous.
In summary, for reactions with both negative \Delta H \ and negative \Delta S \, lower temperatures generally favor spontaneity.

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Most popular questions from this chapter

A reaction has \(\Delta H=98 \mathrm{kJ}\) and \(\Delta S=292 \mathrm{JK}\) . Investigate the spontaneity of the reaction at room temperature. Would increasing the temperature have any effect on the spontaneity of the reaction?

Inferring Conclusions A reaction is endothermic and has a \(\Delta H=8 \mathrm{kJ}\) . This reaction occurs spontaneously at \(25^{\circ} \mathrm{C}\) . What must be true about the entropy change?

The standard enthalpy of formation for sulfur dioxide gas is \(-296.8 \mathrm{kJ} / \mathrm{mol}\) . Calculate the amount of energy given off in \(\mathrm{kJ}\) when 30.0 \(\mathrm{g}\) of \(\mathrm{SO}_{2}(g)\) is formed from its elements.

Performance Design a simple calorimeter investigation to determine the molar enthalpy of fusion of water. Use the following materials: a large plastic-foam cup with cover, a thermometer, a balance, water at room temperature, and an ice cube. Allow your teacher to review your design. Then carry out the investigation, and write a laboratory report including your calculations and a comparison of your quantitative results with known values. Try to account for any disagreements between the experimental and actual values.

A reaction has \(\Delta H=-76 \mathrm{kJ}\) and \(\Delta S=-117 \mathrm{J} / \mathrm{K}\) . Calculate \(\Delta G\) for the reaction at 298.15 \(\mathrm{K}\) . Is the reaction spontaneous?
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