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 \(\mathrm{Na}(\mathrm{s})\) with \(\mathrm{Cl}_{2}(\mathrm{~g})\) to form \(\mathrm{NaCl}(\mathrm{s})\) 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.

Short answer

(a) False. Correct statement: The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends on the Gibbs free energy change (\(\Delta G\)) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\). (b) True. (c) False. Correct statement: A spontaneous process, in principle, is irreversible. (d) False. Correct statement: Spontaneous processes in general do not require work to be done to force them to proceed. (e) False. Correct statement: Spontaneous processes are those for which the Gibbs free energy change (\(\Delta G\)) is negative.

Step-by-step solution

Statement (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 \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\). This statement is false. The feasibility of a reaction depends not only on the enthalpy change (\(\Delta H\)), but also on the entropy change (\(\Delta S\)) and temperature (T). The Gibbs free energy change (\(\Delta G\)) determines the spontaneity of a reaction: if \(\Delta G < 0\), the reaction is spontaneous, and if \(\Delta G > 0\), the reaction is non-spontaneous. The correct statement should be: The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends on the Gibbs free energy change (\(\Delta G\)) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\).

Statement (b)

The reaction of \(\mathrm{Na}(\mathrm{s})\) with \(\mathrm{Cl}_{2}(\mathrm{~g})\) to form \(\mathrm{NaCl}(\mathrm{s})\) is a spontaneous process. This statement is true because the reaction between sodium metal and chlorine gas is exothermic and highly favorable, leading to the formation of a stable ionic compound, sodium chloride.

Statement (c)

A spontaneous process can in principle be conducted reversibly. This statement is false. In principle, a spontaneous process is irreversible, meaning it proceeds in one direction and is not easily reversed. The correct statement should be: A spontaneous process, in principle, is irreversible.

Statement (d)

Spontaneous processes in general require that work be done to force them to proceed. This statement is false. Spontaneous processes occur without the need for external work to be done. The correct statement should be: Spontaneous processes in general do not require work to be done to force them to proceed.

Statement (e)

Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system. This statement is false. Spontaneous processes can be exothermic or endothermic, and they can lead to a higher or lower degree of order in the system, depending on the change in entropy (\(\Delta S\)). The correct statement should be: Spontaneous processes are those for which the Gibbs free energy change (\(\Delta G\)) is negative.

Key concepts

Gibbs Free Energy

At the heart of predicting and understanding chemical reactions lies a powerful concept known as Gibbs free energy (\( \text{Delta} G \)). In simple terms, the Gibbs free energy is the amount of energy available to do work during a reaction at constant temperature and pressure. It's a decisive factor in determining whether a process is spontaneous—that is, whether it will occur without the need for external energy.

Gibbs free energy incorporates both enthalpy (\( \text{Delta} H \)), which reflects the heat absorbed or released, and entropy (\( \text{Delta} S \)), which measures the disorder or randomness within a system. The relationship is given by the formula \(\text{Delta} G = \text{Delta} H - T\text{Delta} S\), where \(T\) is the temperature in Kelvin. A negative \( \text{Delta} G \) means the reaction is spontaneous; a positive value indicates it's non-spontaneous.

For instance, the manufacturing of ammonia (\( \text{NH}_3 \)) from nitrogen (\( \text{N}_2 \) and hydrogen (\( \text{H}_2 \) is spontaneous at certain temperatures and pressures because \( \text{Delta} G \) is negative. However, it's crucial to note that spontaneity doesn't imply that the reaction occurs rapidly; it simply means the reaction is thermodynamically favorable.

Enthalpy Change

The concept of enthalpy change (\( \text{Delta} H \) represents the heat exchange in a system under constant pressure. This thermodynamic quantity helps us understand whether a process absorbs heat (endothermic) or releases heat (exothermic).

For example, the reaction of sodium (\( \text{Na}_\text{(s)} \) with chlorine gas (\( \text{Cl}_2 \) to form sodium chloride (\( \text{NaCl}_\text{(s)} \) is exothermic, as the process releases a large amount of heat. Though enthalpy is a crucial factor, it isn't the sole determinant of a reaction's spontaneity, as it doesn't account for changes in disorder or randomness—the role that entropy plays.

Entropy Change

Entropy change (\( \text{Delta} S \) is a measure of the change in disorder or randomness within a system during a chemical process. In general, the greater the disorder, the higher the entropy.

An increase in entropy tends to favor the spontaneity of a process, and this is essential for understanding why not all spontaneous reactions are exothermic or lead to a more ordered system. For instance, a block of ice (\( \text{H}_2\text{O}_\text{(s)} \) melting into water (\( \text{H}_2\text{O}_\text{(l)} \) is endothermic and increases disorder, illustrating that entropy can drive a process to be spontaneous even when it absorbs heat. Ultimately, when combined with enthalpy, entropy helps determine the overall spontaneity of a process through the Gibbs free energy equation.