Problem 21 - Chemistry in 30 days

Question

An endothermic reaction is spontaneous if (a) \(\Delta H>T \Delta S\) (b) \(\Delta H

Step-by-Step Solution

Answer

(b) \(\Delta H

Step 1: Understand Spontaneity Criterion

For a reaction to be spontaneous, the change in Gibbs free energy,  ight) to be negative.

Step 2: Identify the Gibbs Free Energy Equation

The Gibbs free energy equation is given by \[ \Delta G = \Delta H - T \Delta S \]where \( \Delta H \) is the change in enthalpy, \( \Delta S \) is the change in entropy, and \( T \) is the temperature in Kelvin.

Step 3: Express Condition for Spontaneous Reaction

For a reaction to be spontaneous ( ight) must be negative. This requires\[ \Delta H - T \Delta S < 0 \]Rearranging, we obtain:\[ \Delta H < T \Delta S \]

Step 4: Determine Corresponding Option

The condition for spontaneity \( \Delta H < T \Delta S \) corresponds to option (b). Hence, an endothermic reaction is spontaneous when \( \Delta H < T \Delta S \).

Key Concepts

Endothermic Reactions

Endothermic reactions are a category of chemical reactions that absorb energy from their surroundings. This energy is primarily in the form of heat. In these reactions, the products possess more energy than the reactants due to the absorbed energy.
A common example of an endothermic reaction is the melting of ice. In this process, heat energy from the surroundings is taken in to change ice into water.

• Endothermic reactions result in a temperature decrease of the surrounding area.
• They are significant in processes where energy input is necessary to bring about a change.

Understanding endothermic reactions can help us grasp how energy changes affect chemical processes and the conditions under which they occur.

Gibbs Free Energy

Gibbs free energy, denoted as \( \Delta G \), is a crucial thermodynamic quantity that helps predict whether a reaction will occur spontaneously. It is defined by the formula: \[ \Delta G = \Delta H - T \Delta S \]where:

• \( \Delta H \) is the change in enthalpy, representing the heat absorbed or released.
• \( T \) is the temperature in Kelvin.
• \( \Delta S \) is the change in entropy, indicating disorder or randomness.

A reaction is spontaneous when \( \Delta G \) is negative. This means the process will proceed on its own once started. Gibbs free energy bridges the concepts of energy and entropy, playing a crucial role in determining the direction and feasibility of reactions.

Enthalpy and Entropy

Enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) are vital concepts in understanding spontaneous reactions. Enthalpy measures the heat content in a system, and the change in enthalpy signifies whether heat is absorbed or released.

• Positive \( \Delta H \): Endothermic, energy absorbed.
• Negative \( \Delta H \): Exothermic, energy released.

Entropy, represented by \( \Delta S \), measures the degree of disorder in a system. Higher entropy means more disorder.

• Positive \( \Delta S \): Increase in disorder.
• Negative \( \Delta S \): Decrease in disorder.

Both these thermodynamic properties interplay to determine spontaneity. In essence, they dictate whether a process requires energy input or will proceed by itself, providing insight into the feasibility of reactions.

Temperature in Kelvin

Temperature is a measure of thermal energy within a system, and in chemistry, it's often expressed in Kelvin. The Kelvin scale is absolute, meaning it starts at absolute zero, the hypothetical point where molecular motion ceases.
The Kelvin scale is crucial in thermodynamics because it directly influences reaction spontaneity. It affects the \( T \Delta S \) part of the Gibbs free energy equation.

• Higher temperature can make non-spontaneous reactions spontaneous by affecting entropy.
• Temperatures in Kelvin remove negative values, simplifying calculations related to energy changes.

Understanding temperature's role is essential for comprehending how energy changes affect chemical reactions and why some reactions only proceed at certain temperatures.

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Problem 20

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Problem 25

Other exercises in this chapter

Problem 19

The molar enthalpy of fusion of water is \(6.01 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The entharps change of \(1 \mathrm{~mol}\) of water at its melting point will

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Problem 20

The heat of neutralisation of strong base and strong acid is \(57.0 \mathrm{~kJ}\); the heat released when \(0.5 \mathrm{~mol}\) of \(\mathrm{HNO}_{3}\) solutio

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Problem 25

If an endothermic reaction is non-spontaneous at freezing point of water and becomes feasible at its boiling point, then (a) \(\Delta H\) is \(-v e, \Delta S\)

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Problem 26

Assuming that water vapour is an ideal gas, the internal energy change \((\Delta U)\) when 1 mol of water is vapourized at 1 bar pressure and \(100^{\circ} \mat

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Key Concepts

Endothermic Reactions

Endothermic reactions are a category of chemical reactions that absorb energy from their surroundings. This energy is primarily in the form of heat. In these reactions, the products possess more energy than the reactants due to the absorbed energy.
A common example of an endothermic reaction is the melting of ice. In this process, heat energy from the surroundings is taken in to change ice into water.

• Endothermic reactions result in a temperature decrease of the surrounding area.
• They are significant in processes where energy input is necessary to bring about a change.

Understanding endothermic reactions can help us grasp how energy changes affect chemical processes and the conditions under which they occur.

Gibbs Free Energy

Gibbs free energy, denoted as \( \Delta G \), is a crucial thermodynamic quantity that helps predict whether a reaction will occur spontaneously. It is defined by the formula: \[ \Delta G = \Delta H - T \Delta S \]where:

• \( \Delta H \) is the change in enthalpy, representing the heat absorbed or released.
• \( T \) is the temperature in Kelvin.
• \( \Delta S \) is the change in entropy, indicating disorder or randomness.

A reaction is spontaneous when \( \Delta G \) is negative. This means the process will proceed on its own once started. Gibbs free energy bridges the concepts of energy and entropy, playing a crucial role in determining the direction and feasibility of reactions.

Enthalpy and Entropy

Enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) are vital concepts in understanding spontaneous reactions. Enthalpy measures the heat content in a system, and the change in enthalpy signifies whether heat is absorbed or released.

• Positive \( \Delta H \): Endothermic, energy absorbed.
• Negative \( \Delta H \): Exothermic, energy released.

Entropy, represented by \( \Delta S \), measures the degree of disorder in a system. Higher entropy means more disorder.

• Positive \( \Delta S \): Increase in disorder.
• Negative \( \Delta S \): Decrease in disorder.

Both these thermodynamic properties interplay to determine spontaneity. In essence, they dictate whether a process requires energy input or will proceed by itself, providing insight into the feasibility of reactions.

Temperature in Kelvin

Temperature is a measure of thermal energy within a system, and in chemistry, it's often expressed in Kelvin. The Kelvin scale is absolute, meaning it starts at absolute zero, the hypothetical point where molecular motion ceases.
The Kelvin scale is crucial in thermodynamics because it directly influences reaction spontaneity. It affects the \( T \Delta S \) part of the Gibbs free energy equation.

• Higher temperature can make non-spontaneous reactions spontaneous by affecting entropy.
• Temperatures in Kelvin remove negative values, simplifying calculations related to energy changes.

Understanding temperature's role is essential for comprehending how energy changes affect chemical reactions and why some reactions only proceed at certain temperatures.