Problem 11 - Chemistry: The Central Science in SI Units, Global Edition

Question

Which of the following processes are spontaneous and which are nonspontaneous: (a) mixing of water and ethanol, \((\mathbf{b})\) dissolution of sugar in a cup of hot coffee, (c) formation of oxygen atoms from \(\mathrm{O}_{2}\) molecules at \(\mathrm{STP}\), (d) rusting of iron, (e) formation of glucose from \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) at \(\mathrm{STP} ?\)

Step-by-Step Solution

Answer

(a) Mixing of water and ethanol is spontaneous because it has an increase in entropy and an exothermic reaction. (b) Dissolution of sugar in hot coffee is spontaneous due to an increase in entropy and an exothermic reaction. (c) Formation of oxygen atoms from O2 molecules at STP is nonspontaneous because it involves a positive enthalpy change and a decrease in entropy. (d) Rusting of iron is spontaneous because it is an exothermic reaction and has an increase in entropy. (e) Formation of glucose from CO2 and H2O at STP is nonspontaneous since it is endothermic with a positive enthalpy change and a decrease in entropy, and requires sunlight to occur.

Step 1: Process (a): Mixing of water and ethanol

In a mixing process, both entropy and enthalpy changes are important factors. When water and ethanol mix, the overall entropy increases due to the formation of a more homogeneous and disordered mixture. The enthalpy change in the system is slightly negative (exothermic) because new hydrogen bonds are formed between water and ethanol molecules. Both these factors (increased entropy and negative enthalpy change) make this process spontaneous.

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

When sugar is dissolved in hot coffee, the solid sugar molecules separate into individual molecules, resulting in an increase in entropy (greater disorder). Moreover, the dissolution process is usually exothermic, which releases heat to the surroundings. The combination of increased entropy and an exothermic reaction indicates a spontaneous process at constant temperature and pressure.

Step 3: Process (c): Formation of oxygen atoms from O2 molecules at STP

The formation of oxygen atoms from O2 molecules requires an input of energy to break the oxygen-oxygen double bond. This makes the process endothermic (positive enthalpy change). Additionally, the process involves a decrease in entropy as the molecules transform into individual atoms that occupy less volume. Given these factors (positive enthalpy change and decreased entropy), the process is nonspontaneous under standard temperature and pressure.

Step 4: Process (d): Rusting of iron

The rusting of iron is an oxidation process involving iron atoms reacting with oxygen molecules to form Fe2O3 (iron oxide), which is commonly known as rust. This process is exothermic, releasing energy in the form of heat and light. Also, the process results in increased entropy, as the solid iron molecules are transformed into solid rust molecules and occupy a larger volume. Therefore, the rusting of iron is a spontaneous process.

Step 5: Process (e): Formation of glucose from CO2 and H2O at STP

The formation of glucose from CO2 and H2O is a complex process occurring in plants via photosynthesis. This process requires an input of energy (sunlight), which makes it endothermic (positive enthalpy change). Also, the process leads to a decrease in entropy as individual CO2 and H2O molecules form a more ordered glucose molecule. Overall, the formation of glucose from CO2 and H2O at STP is found to be nonspontaneous since it requires an external source of energy (sunlight) to occur.

Key Concepts

Entropy in Chemistry

Entropy in chemistry is a measure of the disorder or randomness of a system. When substances interact or change states, their entropy invariably changes. A system with higher entropy is more disordered.

For example, when you mix water and ethanol, they form a more homogeneous mixture. This homogeneity increases the system's disorder, thus increasing its entropy. Processes that result in an increase in entropy are generally spontaneous because nature tends to favor disorder.

Besides, the dissolution of sugar into hot coffee also showcases an increase in entropy. The sugar molecules spread out into the liquid, leading to greater disorder. These examples clearly illustrate how increased entropy in a system contributes to the spontaneity of a process.

The spontaneity of mixing and dissolution processes is largely driven by a system's preference for achieving maximum randomness.

Enthalpy Changes

Enthalpy refers to the total heat content of a system. Changes in enthalpy during a reaction can influence whether a process is spontaneous or not. Exothermic reactions, which release heat, typically increase spontaneity.

Take the mixing of water and ethanol, for example. It is slightly exothermic because it releases a small amount of heat due to the formation of new hydrogen bonds. This negative enthalpy change, in conjunction with an increase in entropy, further supports its spontaneity.

Dissolution processes, such as sugar dissolving in hot coffee, are also generally exothermic. The release of heat to the surroundings aids in making such processes spontaneous.

However, not all reactions align with this trend. The formation of oxygen atoms from O2 molecules is endothermic—requiring heat. Coupled with a decrease in entropy, this results in a nonspontaneous reaction under the same conditions.

Chemical Reactions at STP

Chemical reactions at standard temperature and pressure (STP, 0°C and 1 atm) are essential benchmarks in chemistry. Understanding reactions at STP is crucial as it provides a consistent condition to predict spontaneity and reaction feasibility.

The rusting of iron at STP, for example, is a spontaneous exothermic oxidation process. Here, iron atoms react with oxygen, releasing heat and forming iron oxide (rust). The increase in entropy as solid iron becomes a different solid compound consolidates its spontaneity.

Conversely, processes like the decomposition of O2 into individual oxygen atoms require energy input, making them nonspontaneous at STP. This highlights that spontaneity isn't just about temperature but also the inherent properties of the reactants and products.

• Reactions that release energy and increase entropy at STP are typically spontaneous.
• Reactions that require energy input and decrease entropy are generally nonspontaneous.

Photosynthesis in Plants

Photosynthesis is a vital natural process where plants convert carbon dioxide and water into glucose and oxygen using sunlight. However, this transformation at STP is not naturally spontaneous.

The process requires an input of energy—in this case, sunlight—making it endothermic. The formation of glucose represents a decrease in entropy because it involves creating a structured molecule from simpler ones.

In essence, the nonspontaneous nature of photosynthesis at STP demonstrates well how life overcomes natural thermodynamic tendencies using external energy sources.

• Allows plants to convert solar energy into chemical energy.
• Crucial for the sustenance of life on Earth, providing glucose as a source of energy.

While this synthesis isn't spontaneous at STP, the process remains fundamental, highlighting the intricate balance between energy, entropy, and life.