Problem 84 - Chemistry: Principles and Reactions

Question

Determine whether each of the following statements is true or false. If false, modify it to make it true. (a) An exothermic reaction is spontaneous. (b) When \(\Delta G^{\circ}\) is positive, the reaction cannot occur under any conditions. (c) \(\Delta S^{\circ}\) is positive for a reaction in which there is an increase in the number of moles. (d) If \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are both negative, \(\Delta G^{\circ}\) will be negative.

Step-by-Step Solution

Answer

Question: Determine if the following statement is true or false. If false, modify the statement to make it true: "An exothermic reaction is always spontaneous." Answer: False. Correct statement: An exothermic reaction can be spontaneous.

Step 1: Understanding exothermic and spontaneous reactions

An exothermic reaction is a reaction that releases heat, which means the change in enthalpy, \(\Delta H\), is negative. However, spontaneity of a reaction is determined by its Gibbs free energy change, \(\Delta G\). Remember that \(\Delta G = \Delta H - T\Delta S\) where T is the absolute temperature and \(\Delta S\) is the change in entropy.

Step 2: Identifying the Correct Statement

An exothermic reaction (∆H < 0) can be spontaneous depending on the value of ∆S and the given temperature. Therefore, the statement is not always true. To make it true, we can modify the statement as: The correct statement is: An exothermic reaction can be spontaneous. (b) When \(\Delta G^{\circ}\) is positive, the reaction cannot occur under any conditions.

Step 1: Understanding the meaning of positive \(\Delta G^{\circ}\)

The value of \(\Delta G^{\circ}\) indicates the spontaneity of a reaction under standard conditions. If \(\Delta G^{\circ}\) is positive, the reaction is non-spontaneous under standard conditions, but it does not mean that the reaction cannot occur under any conditions.

Step 2: Identifying the Correct Statement

To make the statement true, we can modify it as: The correct statement is: When \(\Delta G^{\circ}\) is positive, the reaction is non-spontaneous under standard conditions. (c) \(\Delta S^{\circ}\) is positive for a reaction in which there is an increase in the number of moles.

Step 1: Understanding the meaning of positive \(\Delta S^{\circ}\)

A positive change in entropy, \(\Delta S^{\circ}\), means that the randomness or disorder of the system increases. In general, when the number of moles of products is greater than the number of moles of reactants, an increase in disorder is observed, resulting in a positive entropy change.

Step 2: Verifying the Statement

The statement is true, as an increase in the number of moles generally corresponds to an increase in entropy. (d) If \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are both negative, \(\Delta G^{\circ}\) will be negative.

Step 1: Understanding the relationship between \(\Delta H^{\circ}\), \(\Delta S^{\circ}\), and \(\Delta G^{\circ}\)

As mentioned earlier, \(\Delta G = \Delta H - T\Delta S\), so we need to examine the values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) to determine the sign of \(\Delta G^{\circ}\).

Step 2: Identifying the Correct Statement

If \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are both negative, then the \(\Delta H^{\circ}\) term is negative but the \(T\Delta S^{\circ}\) term is positive (since both T and \(\Delta S^{\circ}\) are negative). Therefore, the subtraction will result in a positive \(\Delta G^{\circ}\). The statement is false. To make it true, we can modify it as: The correct statement is: If \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are both negative, \(\Delta G^{\circ}\) will be positive.

Key Concepts

Exothermic Reactions

An exothermic reaction is a chemical reaction that releases heat into the surroundings. This means that the change in enthalpy, represented as \( \Delta H \), is negative. These reactions can often be observed when you feel warmth coming from a chemical process, like a burning candle or mixing certain chemicals.
Many students assume that because heat is released, exothermic reactions are always spontaneous. However, spontaneity is not just about heat release; it involves Gibbs Free Energy \( \Delta G \), which takes into account both enthalpy and entropy effects. The formula \( \Delta G = \Delta H - T\Delta S \), where \( T \) is temperature and \( \Delta S \) is entropy change, determines spontaneity.

• Exothermic reactions can be spontaneous if the entropy change and temperature conditions favor it.
• Thus, not all exothermic reactions are spontaneous; it depends on the balance of entropy and temperature.

Spontaneity

Spontaneity in a chemical reaction relates to the ability of the reaction to occur without additional energy input. This is primarily determined by the Gibbs Free Energy change, \( \Delta G \). If \( \Delta G \) is negative, the reaction is spontaneous under given conditions.
The formula \( \Delta G = \Delta H - T\Delta S \) combines both enthalpy and entropy to assess spontaneity. This means:

• A reaction can be spontaneous even if it absorbs heat (endothermic) if the entropy increase sufficiently compensates for the heat absorbed.
• A positive \( \Delta G \) under standard conditions means non-spontaneity, but changes in temperature, pressure, or concentrations can alter this.

Thus, spontaneity is not a one-size-fits-all condition but depends on multiple thermodynamic variables.

Entropy

Entropy, symbolized as \( \Delta S \), is the measure of disorder or randomness in a system. In chemistry, when a reaction results in greater randomness, the change in entropy is positive.

• A positive \( \Delta S \) often occurs when the number of gas molecules increases in a reaction.
• This increase in molecular randomness often leads to increased entropy and can make a reaction more likely to be spontaneous.

Entropy speaks to the natural tendency of systems to move toward disorder or equilibrium, which is a fascinating and fundamental concept in thermodynamics.

Enthalpy

Enthalpy, represented by \( \Delta H \), is the total heat content of a system. It includes both internal energy and the product of pressure and volume.

• Exothermic reactions have a negative \( \Delta H \), signifying heat release.
• Endothermic reactions have a positive \( \Delta H \), indicating heat absorption.

Understanding enthalpy changes helps us comprehend how energy transformations occur during chemical reactions. Combining this with entropy through Gibbs Free Energy provides a complete picture of a reaction's thermodynamics and potential spontaneity.