Question

Is each statement true or false? If false, correct it. (a) All spontaneous reactions occur quickly. (b) The reverse of a spontaneous reaction is nonspontaneous. (c) All spontaneous processes release heat. (d) The boiling of water at \(100^{\circ} \mathrm{C}\) and 1 atm is spontaneous. (e) If a process increases the freedom of motion of the particles of a system, the entropy of the system decreases. (f) The energy of the universe is constant; the entropy of the universe decreases toward a minimum. (g) All systems disperse their energy spontaneously. (h) Both \(\Delta S_{\text {sys }}\) and \(\Delta S_{\text {surr }}\) equal zero at equilibrium.

Short answer

(a) False(b) True(c) False(d) True(e) False(f) False(g) True(h) True

Step-by-step solution

- Analyze Statement (a)

Statement: All spontaneous reactions occur quickly.Evaluate: This is false. Spontaneity does not imply the speed of the reaction. A spontaneous reaction can occur either quickly or slowly.

- Analyze Statement (b)

Statement: The reverse of a spontaneous reaction is nonspontaneous.Evaluate: This is true. If a reaction is spontaneous in one direction, it means it naturally occurs without external input. Therefore, the reverse reaction will not occur under the same conditions and is nonspontaneous.

- Analyze Statement (c)

Statement: All spontaneous processes release heat.Evaluate: This is false. Spontaneous processes can either release heat (exothermic) or absorb heat (endothermic). The key factor for spontaneity is the change in Gibbs free energy, not just heat.

- Analyze Statement (d)

Statement: The boiling of water at \(100^{\circ} \mathrm{C}\) and 1 atm is spontaneous.Evaluate: This is true. At \(100^{\circ} \mathrm{C}\) and 1 atm pressure, water boils spontaneously because the vapor pressure equals the surrounding pressure.

- Analyze Statement (e)

Statement: If a process increases the freedom of motion of the particles of a system, the entropy of the system decreases.Evaluate: This is false. Increasing the freedom of motion of particles generally increases the entropy of the system.

- Analyze Statement (f)

Statement: The energy of the universe is constant; the entropy of the universe decreases toward a minimum.Evaluate: This is false. While the energy of the universe is constant (law of conservation of energy), the entropy of the universe tends to increase toward a maximum, not decrease.

- Analyze Statement (g)

Statement: All systems disperse their energy spontaneously.Evaluate: This is true. Systems tend to disperse energy spontaneously to increase entropy, according to the second law of thermodynamics.

- Analyze Statement (h)

Statement: Both \(\Delta S_{\text {sys }}\) and \(\Delta S_{\text {surr }}\) equal zero at equilibrium.Evaluate: This is true. At equilibrium, the total entropy of the system and the surroundings does not change, so \(\Delta S_{\text {sys }} = 0\) and \(\Delta S_{\text {surr }} = 0\).

Key concepts

Gibbs Free Energy

Gibbs Free Energy, denoted as \( \Delta G \), is a measure of the maximum reversible work that a thermodynamic system can perform. It helps us determine whether a reaction is spontaneous. When \( \Delta G < 0 \), the reaction is spontaneous. This means it can occur without any additional energy input. For example, the boiling of water at 100\(^{\circ} \mathrm{C} \) and 1 atm pressure is spontaneous because it occurs naturally under these conditions. However, it's essential to understand that spontaneity does not imply the speed of a reaction. A spontaneous reaction could be slow or fast. The key takeaway is that a negative \Delta G indicates that the process can proceed without outside help.
Spontaneity relates to the free energy change rather than the heat or speed of the process.

Entropy

Entropy, symbolized as \( S \), is a measure of the disorder or randomness in a system. The second law of thermodynamics tells us that for any spontaneous process, the total entropy of a system and its surroundings always increases. For instance, when a process increases the freedom of motion of the particles in a system, such as the melting of ice into water, the entropy of the system increases. This is contrary to the false statement that entropy decreases.
Importantly, at equilibrium, the change in entropy of the system (\( \Delta S_{\text {sys }} \)) and the surroundings (\( \Delta S_{\text {surr }} \)) is zero, meaning there's no net change in disorder. This balance allows the system to maintain a steady state.

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and the forms of energy involved in chemical processes. It encompasses several important laws:

• The first law states that energy cannot be created or destroyed, only transformed (the law of conservation of energy).
• The second law of thermodynamics tells us that the total entropy of an isolated system always increases over time. Therefore, the idea that the entropy of the universe decreases is incorrect; it actually increases toward a maximum.
• The third law states that the entropy of a perfect crystal at absolute zero is zero.

In spontaneous processes, systems tend to disperse their energy to maximize entropy, which aligns with the false statement that all spontaneous processes release heat; they instead aim for increased entropy, which can involve either absorption or release of heat, depending on the process.