Chemical Thermodynamics: Entropy: Videos & Practice Problems

Entropy is a fundamental concept in thermodynamics, closely linked to the second law, which states that molecular systems naturally progress towards a state of maximum disorder or randomness. This principle implies that the total entropy of the universe is always increasing, indicating a trend towards chaos and degradation. As galaxies evolve, stars may explode into supernovas, ultimately leading to black holes, illustrating the universe's tendency towards disorder.

The change in entropy, denoted as ΔS, can be expressed mathematically as:

ΔS_universe = ΔS_system + ΔS_surroundings

This equation emphasizes that the total change in entropy is always greater than zero, reflecting the second law of thermodynamics.

Entropy can also be analyzed in terms of phase changes. For instance, when a substance transitions from solid to liquid (melting or fusion) or from liquid to gas (vaporization), the distance between molecules increases, leading to greater disorder. Consequently, these processes result in a positive change in entropy (ΔS > 0). Conversely, when a substance transitions from gas to liquid to solid, the molecules become more ordered, resulting in a decrease in entropy (ΔS < 0).

It is important to note that while entropy typically increases, it can theoretically reach zero at absolute zero temperature (0 Kelvin), as stated in the third law of thermodynamics. At this temperature, all molecular motion ceases, and the entropy of a substance is exactly zero. However, achieving 0 Kelvin is highly theoretical, as the average temperature of the universe is approximately 2 Kelvin.

Understanding these principles of entropy lays the groundwork for comparing the entropies of different compounds, which will be explored further in subsequent discussions.

Covalent compounds, which consist solely of nonmetals bonded together, exhibit varying degrees of entropy based on specific criteria. When comparing the entropies of different covalent compounds, it is essential to follow a systematic approach that considers their phases, microstates, and masses.

The first criterion is the phase of the compounds. Gases, with their molecules widely spaced apart, possess the highest entropy. This is followed by aqueous compounds, which are dissolved in a solvent, typically water. Liquids, such as water or organic solvents like hexane or methylene chloride, come next, while solids, where molecules are closely packed, exhibit the lowest entropy. Thus, as one moves from gases to solids, the organization of molecules increases, leading to a decrease in entropy.

If the compounds being compared are in the same phase, the next factor to consider is the number of microstates. Microstates refer to the various ways a molecule can orient and bend while maintaining similar energy levels. The complexity of a compound, determined by the number of different elements it contains, directly correlates with its microstates. For instance, when comparing nitrogen dioxide (NO₂) and nitrogen trioxide (NO₃), NO₂ has three elements (1 nitrogen and 2 oxygens), while NO₃ has four elements (1 nitrogen and 3 oxygens). Consequently, NO₃ has greater complexity, more microstates, and thus higher entropy.

In cases where the covalent compounds share the same phase and number of elements, the final consideration is their masses. Generally, a greater mass corresponds to higher entropy. For example, comparing xenon gas (approximately 131 grams) to helium gas (approximately 4 grams), xenon, being significantly heavier, would exhibit greater entropy.

In summary, when evaluating the entropies of covalent compounds, one should first assess their phases, then their microstates based on complexity, and finally their masses. This structured approach ensures a comprehensive understanding of the entropy differences among various covalent compounds.

When analyzing the entropies of various ionic compounds, lattice energy plays a crucial role. An ionic compound consists of a positively charged ion, known as a cation, and a negatively charged ion, called an anion. Lattice energy is defined as the energy released when one mole of an ionic crystal is formed from its gaseous ions. For instance, in the formation of sodium chloride (NaCl), gaseous sodium ions combine with gaseous chloride ions to create solid sodium chloride, releasing an entropy value of -787 kilojoules per mole. This process is exothermic, indicating that energy is released during bond formation, which is why the change in enthalpy (ΔH) is negative.

To estimate lattice energy quantitatively, we can use the following equation:

Lattice Energy = \(\frac{|q_1 \cdot q_2|}{r_1 + r_2}\)

In this equation, \(q_1\) and \(q_2\) represent the absolute values of the cation and anion charges, while \(r_1\) and \(r_2\) denote the radii of the cation and anion, respectively. For simplification, the radius can be approximated based on the period number of the elements in the periodic table. For sodium chloride, sodium (Na⁺) has a charge of +1 and chloride (Cl^-) has a charge of -1. Both ions are in period 3, leading to an estimated radius of 3 for each.

When comparing sodium chloride to barium oxide (BaO), which consists of Ba²⁺ and O^2-, the lattice energy can be calculated as follows:

Lattice Energy (BaO) = \(\frac{|2 \cdot (-2)|}{6 + 2} = \frac{4}{8} = \frac{1}{2}\)

This calculation shows that barium oxide has a larger estimated lattice energy than sodium chloride, indicating a stronger ionic bond between the barium and oxide ions compared to the sodium and chloride ions. Consequently, barium oxide exhibits higher boiling and melting points, as well as lower entropies.

Furthermore, a trend can be observed in the periodic table: as one moves towards the top right corner, lattice energy tends to increase. This trend is significant for understanding the relative strengths of ionic bonds and the properties of ionic compounds.

Understanding the concept of entropy is crucial in thermodynamics, particularly when predicting the sign of entropy changes (ΔS) during various processes. Entropy, a measure of disorder or randomness in a system, can either increase or decrease based on the changes in temperature, pressure, and the state of matter.

In the first example, we analyze the transition of iodine (I₂) from 90 degrees Celsius and 5.0 atmospheres of pressure to 50 degrees Celsius and 10 atmospheres of pressure. The decrease in temperature indicates that the molecules lose energy and move closer together, which typically results in a decrease in entropy. Additionally, the increase in pressure further compresses the molecules, reinforcing the idea that the system's disorder is diminishing. Therefore, the entropy change for this process is negative (ΔS < 0).

Next, we consider the decomposition of solid ammonium chloride into hydrogen chloride gas and ammonia gas. Here, one reactant breaks down into two gaseous products, leading to an increase in disorder as more particles are formed. This process results in a positive change in entropy (ΔS > 0) due to the increase in the number of gas molecules, which have higher entropy compared to solids.

Finally, we examine the combustion reaction of methane (CH₄) with oxygen (O₂). Initially, there are three moles of gas (1 mole of CH₄ and 2 moles of O₂), which produce one mole of carbon dioxide (CO₂) gas and two moles of liquid water (H₂O). The transition from three moles of gas to one mole of gas and two moles of liquid indicates a significant decrease in entropy, as gases possess higher entropy than liquids. Thus, the entropy change for this reaction is also negative (ΔS < 0).

In summary, when predicting the sign of entropy changes, consider whether the process involves breaking bonds (which typically increases entropy) or forming bonds (which usually decreases entropy). Additionally, the states of matter and the number of moles of gas versus liquid play a significant role in determining the overall change in disorder within the system.

When an aqueous solution containing aluminum ions is mixed with an aqueous solution of hydroxide ions at 25 degrees Celsius, an immediate precipitate of insoluble aluminum hydroxide forms. The balanced chemical equation for this reaction is:

1 mole of Al³⁺ + 3 moles of OH^- → 1 mole of Al(OH)₃

In this context, it is important to understand the concept of entropy, which is a measure of disorder in a system. All compounds and elements have an entropy greater than zero, except at absolute zero (0 Kelvin), where the entropy is defined as zero. The entropies of formation for the involved species are crucial for calculating the change in entropy for the reaction.

The standard reaction enthalpy (ΔH) for this process is given as -61.33 kJ/mol. To find the total entropy change (ΔS_total), we apply the second law of thermodynamics, which states that:

ΔS_universe = ΔS_reaction + ΔS_surroundings

First, we calculate the change in entropy for the reaction (ΔS_reaction). This is done using the formula:

ΔS_reaction = ΣS_products - ΣS_reactants

Using the provided entropies of formation, we find:

ΔS_reaction = S_Al(OH)3 - (S_Al³⁺ + 3 × S_OH^-)

Substituting the values, we have:

ΔS_reaction = 216 J/(mol·K) - (-325 J/(mol·K) + 3 × -10.90 J/(mol·K))

This simplifies to:

ΔS_reaction = 216 J/(mol·K) + 357.7 J/(mol·K) = 573.7 J/(mol·K)

Next, we calculate the change in entropy of the surroundings (ΔS_surroundings) using the formula:

ΔS_surroundings = -ΔH / T

Here, T is the temperature in Kelvin, which is 298.15 K (25 degrees Celsius + 273.15). Thus:

ΔS_surroundings = -(-61.33 kJ/mol) / 298.15 K

Converting kJ to J gives:

ΔS_surroundings = 61,330 J/mol / 298.15 K ≈ 205.7 J/(mol·K)

Finally, we can find the total entropy change:

ΔS_total = ΔS_reaction + ΔS_surroundings

ΔS_total = 573.7 J/(mol·K) + 205.7 J/(mol·K) ≈ 779.4 J/(mol·K)

Since ΔS_total is greater than zero, this indicates that the process is spontaneous according to the second law of thermodynamics. Understanding these principles allows for a deeper insight into the thermodynamic behavior of chemical reactions.