Problem 11 - Chemistry: The Central Science

Question

Which of the following processes are spontaneous and which are nonspontaneous: (a) the ripening of a banana, (b) dissolution of sugar in a cup of het coffee, (c) the reaction of nitrogen atoms to form \(\mathrm{N}_{2}\) molecules at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), (d) lightning. (c) formation of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) molecules from \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) at room temperature and \(1 \mathrm{~atm}\) of pressure?

Step-by-Step Solution

Answer

Based on the given processes, the following are spontaneous: (a) the ripening of a banana, (b) dissolution of sugar in a cup of hot coffee, (c) the reaction of nitrogen atoms to form N2 molecules at $25^{\circ} \mathrm{C}$ and $1\mathrm{~atm}$, and (d) lightning. The formation of CH4 and O2 molecules from CO2 and H2O at room temperature and $1\mathrm{~atm}$ pressure (e) is a nonspontaneous process, as it requires external energy input to occur.

Step 1: (a) Ripening of a banana

The ripening of a banana involves the conversion of starch into simpler sugars like glucose and fructose. This process is a natural phenomenon and takes place over time without any external influence. Therefore, the ripening of a banana is a spontaneous process.

Step 2: (b) Dissolution of sugar in hot coffee

The dissolution of sugar in hot coffee occurs due to the molecular interactions between sugar (solute) and coffee (solvent) molecules. The increase in temperature makes these interactions stronger; hence, sugar dissolves more effectively in hot coffee compared to cold coffee. This process takes place without any external influence, making it a spontaneous process.

Step 3: (c) Reaction of nitrogen atoms to form N2 molecules at 25°C and 1 atm

Nitrogen atoms readily combine to form N2 molecules through a chemical reaction governed by the bond formation between these atoms. This process occurs without any external influence, such as energy input, at 25°C and 1 atm pressure. Hence, the reaction of nitrogen atoms to form N2 molecules is a spontaneous process.

Step 4: (d) Lightning

Lightning is a natural process that occurs due to the discharge of electrical energy in the atmosphere. This process happens without any external influence and is driven by the movement of charged particles in the atmosphere. Hence, lightning is a spontaneous process.

Step 5: (e) Formation of CH4 and O2 molecules from CO2 and H2O at room temperature and 1 atm pressure

The formation of CH4 and O2 molecules from CO2 and H2O is an endothermic process, which means it requires an input of energy to proceed. Additionally, this process involves the conversion of a more stable molecule (CO2) to a less stable molecule (CH4). Thus, the formation of CH4 and O2 molecules from CO2 and H2O at room temperature and 1 atm pressure is a nonspontaneous process, as it requires external energy input to occur.

Key Concepts

Chemical Spontaneity

Chemical spontaneity fundamentally refers to the natural tendency of a process to occur without the need for additional energy from an external source. It provides a key insight into whether a chemical reaction or physical process can proceed on its own. The ripening of bananas, for instance, is an example of a spontaneous process—it happens automatically as bananas mature, breaking down complex starches into simpler sugars.

In thermodynamics, this spontaneity is often analyzed through the concept of free energy, with processes having a decrease in Gibbs free energy (\( \triangle G < 0 \) being considered spontaneous. Factors like enthalpy, entropy, and temperature play a critical role in this determination. For instance, the dissolution of sugar in hot coffee is spontaneous because it leads to an increase in entropy, or disorder, which is energetically favored. In contrast, the formation of methane (\( \text{CH}_4 \) and oxygen (\( \text{O}_2 \) from carbon dioxide (\( \text{CO}_2 \) and water (\( \text{H}_2O \) requires energy input, making it nonspontaneous at room temperature and pressure.

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In the context of chemical reactions, it helps us understand energy transfer, the direction in which a reaction will proceed, and whether that reaction will be spontaneous.

The foundation of thermodynamics is built on laws, such as the law of conservation of energy and the concept of entropy. When solving problems related to spontaneity, scientists consider the first and second laws of thermodynamics. The first law, also known as the law of energy conservation, states that the total energy of an isolated system is constant. The second law introduces the concept of entropy, indicating that systems naturally progress towards a state of maximum disorder. For example, lightning is a spontaneous event that aligns with the principles of thermodynamics, converting electrical potential energy into other energy forms following the conservation of energy, while increasing the overall entropy of the system.

Endothermic and Exothermic Reactions

Reactions that release heat into their surroundings are termed exothermic, while those that absorb heat are called endothermic. In an exothermic reaction, such as the formation of nitrogen molecules (\( \text{N}_2 \) from nitrogen atoms, the energy required to break the original bonds is less than the energy released from forming new bonds, which often makes them spontaneous.

In contrast, endothermic reactions, like the synthesis of methane (\( \text{CH}_4 \) and oxygen (\( \text{O}_2 \) from carbon dioxide (\( \text{CO}_2 \) and water (\( \text{H}_2O \) at room temperature, are nonspontaneous. They absorb energy from their surroundings to proceed, which is why an external energy source is necessary. Understanding whether a reaction is endothermic or exothermic helps in predicting the energy flow during the reaction and, in many cases, its spontaneity or lack thereof.