Problem 88 - Chemistry: The Central Science

Question

Indicate whether each of the following statements is true or false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of \(\Delta H\) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\). (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Step-by-Step Solution

Answer

(a) False. The feasibility depends on the Gibbs free energy (ΔG), not just the change in enthalpy (ΔH). (b) True, the reaction between sodium (Na) and chlorine gas (Cl2) to form sodium chloride (NaCl) is spontaneous. (c) False, a spontaneous process is generally irreversible. (d) False, spontaneous processes do not require external work to proceed. (e) False, not all exothermic reactions are spontaneous, and spontaneous processes typically increase disorder or entropy.

Step 1: (a) Statement Analysis

The statement says that the feasibility of manufacturing ammonia (NH3) from nitrogen (N2) and hydrogen (H2) depends entirely on the value of the change in enthalpy (ΔH) for the process N2(g) + 3 H2(g) → 2 NH3(g). This statement is false. While the value of ΔH plays an important role in determining the feasibility of a reaction, it is not the sole determinant. The Gibbs free energy (ΔG), which also considers the change in entropy (ΔS) and temperature (T), is a better indicator of the feasibility of a reaction. #b# Determining the truth of the statement regarding the reaction between Na and Cl2

Step 2: (b) Statement Analysis

The statement says that the reaction between sodium (Na) and chlorine gas (Cl2) to form sodium chloride (NaCl) is spontaneous. This statement is true. When a metal reacts with a non-metal, the reaction generally results in an ionic compound formation, which is an exothermic process. With the release of energy as heat and the formation of a more stable compound, the reaction is spontaneous. #c# Determine the truth of the statement regarding the reversibility of spontaneous processes

Step 3: (c) Statement Analysis

The statement says that a spontaneous process can, in principle, be conducted reversibly. This statement is false. In fact, a spontaneous process is generally irreversible. The reason for this is that a spontaneous process occurs under certain conditions that lead to a decrease in the system's free energy, making it difficult for the process to return to its original state without inputting external energy or altering the conditions in which it occurs. #d# Determine the truth of the statement regarding the need for work in spontaneous reactions

Step 4: (d) Statement Analysis

The statement says that spontaneous processes, in general, require work to be done to force them to proceed. This statement is false. A spontaneous process occurs without any external intervention, which means that it does not require external work to proceed. Instead, it occurs due to the inherent tendency of the system to reach a state of lower free energy. #e# Determine the truth of the statement linking exothermic reactions to order

Step 5: (e) Statement Analysis

The statement claims that spontaneous processes are those that are exothermic and lead to a higher degree of order in the system. This statement is false. Although many spontaneous processes are exothermic, not all exothermic reactions are spontaneous. Moreover, spontaneous processes typically lead to an increase in disorder or entropy in the system, rather than leading to a higher degree of order. The Gibbs free energy, which considers both enthalpy change (ΔH) and entropy change (ΔS), is the best indicator of the spontaneity of a process.

Key Concepts

What is Gibbs Free Energy?

Gibbs free energy (G) is a concept in chemistry that predicts whether a process will occur spontaneously under constant pressure and temperature. It's a way to balance the books of a reaction's energy account. The formula for Gibbs free energy is \[ G = H - TS \] where \(H\) represents enthalpy change, \(T\) temperature in Kelvin, and \(S\) entropy change. A negative value of \(\Delta G\), the change in free energy, signifies a spontaneous process. It's essentially the currency of energy that a reaction has at its disposal to do work. The concept is critical because it goes beyond heat alone (enthalpy) to include the concept of disorder (entropy) in determining the spontaneity of a reaction.

For a more intuitive understanding, imagine a ball at the top of a hill. Without being pushed, it will spontaneously roll down because it has excess energy (lower Gibbs energy at the bottom). Chemical reactions work similarly; substances will undergo change to reach a state of lower free energy naturally, just like the ball rolling downhill.

Understanding Enthalpy Change (ΔH)

Enthalpy change (\(\Delta H\)) is the difference in heat content between products and reactants at constant pressure. Think of it as the heat exchanged with the surroundings during a reaction. If the reaction gives off heat, it is exothermic and \(\Delta H\) is negative. Conversely, if the reaction absorbs heat, it is endothermic and \(\Delta H\) is positive.

Since enthalpy is part of the Gibbs free energy equation, it has a significant impact on a reaction’s spontaneity. However, it’s not the sole factor; the change in entropy (\(\Delta S\)) and temperature also play crucial roles. To conceptualize this, picture a bonfire. The release of heat is comparable to enthalpy change in a chemical reaction. A large release of heat may suggest a process could be spontaneous, but we can't be certain without considering entropy and temperature as well.

Entropy Change (ΔS) in Chemical Reactions

Entropy change (\(\Delta S\)) refers to the change in disorder or randomness associated with a chemical reaction. In general, nature favors an increase in entropy. A positive \(\Delta S\) indicates that the disorder increases from reactants to products, which can drive a reaction to be spontaneous. Thus, if a process results in more spread out energy (higher entropy), it's like cleaning your room by pushing everything under the bed; it seems more disorganized but reaches a state that nature ultimately prefers.

An increase in entropy could mean more molecules being produced, gases being formed from liquids or solids, or a solid dissolving in a solution. In the context of the entire universe, every spontaneous process increases the universe’s total entropy. So, entropy is as pivotal as enthalpy in determining a reaction's direction and spontaneity but must be balanced against other factors encapsulated in the Gibbs free energy equation.

Reversibility of Chemical Reactions

The reversibility of chemical reactions involves the concept that reactions can go in both forward and reverse directions. However, spontaneity and reversibility are not the same. A spontaneous process tends to occur naturally in one direction under a given set of conditions and leads to a lower Gibb's free energy state. But it's often irreversible without altering those conditions or supplying additional energy.

Think about melting ice. Under normal conditions, ice melts spontaneously at temperatures above 0°C, but to reverse it—to refreeze water into ice—you'd need a freezer. That's a classic example of how a spontaneous process (melting) isn’t easily reversed because it requires a change in conditions (lower temperature) or an input of energy (freezer's power). Therefore, while reversibility is important in understanding reaction dynamics, a spontaneous process is inherently unidirectional unless external interventions are made.

Exothermic Reactions

Exothermic reactions release energy, usually in the form of heat, during the course of the reaction. This release makes the surroundings warmer, and the reaction may occur spontaneously because it lowers the system's enthalpy (\(\Delta H < 0\)). Many spontaneous reactions are exothermic, like the combustion of gasoline in a car engine or the rusting of iron.

However, it's not a given that all exothermic reactions are spontaneous, as the total change in the Gibbs free energy considering both enthalpy and entropy dictates spontaneity. For example, even though a bonfire is exothermic, it doesn't start on its own without a spark. So, while exothermic reactions often trend towards spontaneity due to a favorable enthalpy change, the full picture of spontaneity requires the inclusion of entropy and temperature considerations.