6.2 Standard molar entropies
5 min read•july 30, 2024
The Third Law of Thermodynamics sets the stage for understanding entropy, a measure of disorder in systems. Standard molar entropies quantify this disorder for substances at specific conditions, providing a foundation for comparing and analyzing different materials.
Standard molar entropies help us predict and calculate entropy changes in chemical processes. By examining trends and factors affecting entropy, we gain insights into the behavior of substances and the driving forces behind chemical reactions.
Standard Molar Entropy
Definition and Relation to the Third Law of Thermodynamics
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- (S°) the entropy of one mole of a substance in its standard state at a specified temperature, usually 298 K (25°C)
- The Third Law of Thermodynamics states the entropy of a perfect crystal at absolute zero (0 K) is zero, providing a reference point for measuring absolute entropies
- Entropy a measure of the disorder or randomness of a system, with indicating greater disorder
- Standard molar entropies always positive values, as all substances have some degree of disorder at temperatures above absolute zero
- The entropy of a substance increases with increasing temperature, as higher temperatures lead to greater molecular motion and disorder
Properties and Trends
- Standard molar entropies depend on the physical state of the substance (solid, liquid, or gas), with gases having the highest entropies and solids having the lowest
- Entropy also depends on the complexity of the substance, with more complex molecules generally having higher entropies than simpler ones
- For elements, the standard molar entropy can vary based on the allotropic form (graphite vs. diamond for carbon)
- Entropy increases during phase transitions from solid to liquid to gas, as the increased molecular motion leads to greater disorder
- Entropy also increases with increasing molar mass, as larger molecules have more vibrational and rotational modes that contribute to disorder
Calculating Standard Molar Entropy
Using Tabulated Data
- Standard molar entropies for elements and compounds can be found in reference tables, usually at a temperature of 298 K (25°C) and a pressure of 1 atm
- For elements, the standard molar entropy depends on the physical state (solid, liquid, or gas) and the allotropic form (graphite vs. diamond for carbon)
- The standard molar entropy of a compound can be calculated by summing the standard molar entropies of its constituent elements, taking into account their stoichiometric coefficients
- When using tabulated data, it is essential to ensure that the values are given in the same units (J mol⁻¹ K⁻¹) and at the same temperature and pressure
Calculating Standard Molar Entropy of Compounds
- To calculate the standard molar entropy of a compound, use the formula:
- stoichiometric coefficient of each element in the compound
- standard molar entropy of each element in the compound
- Example: Calculate the standard molar entropy of water (H2O) given that and
- This method assumes that the entropy of a compound is the sum of the entropies of its constituent elements, which is an approximation but often provides reasonable estimates
Entropy Change for Reactions
Calculating Standard Entropy Change
- The standard (ΔS°) for a chemical reaction can be calculated using the standard molar entropies of the reactants and products
- , where stoichiometric coefficient and standard molar entropy of each species
- A positive ΔS° indicates an increase in entropy during the reaction, while a negative ΔS° indicates a decrease in entropy
- The magnitude of ΔS° depends on the physical states of the reactants and products, as well as the stoichiometry of the reaction
- Reactions that involve an increase in the number of gas molecules typically have a positive ΔS°, as gases have higher entropies than liquids or solids
- Reactions that involve a decrease in the number of gas molecules or the formation of a more ordered structure (crystallization) typically have a negative ΔS°
Factors Affecting Entropy Change
- Phase changes
- Entropy increases during phase transitions from solid to liquid to gas (melting, vaporization)
- Entropy decreases during phase transitions from gas to liquid to solid (condensation, freezing)
- Changes in the number of molecules
- Reactions that produce more molecules than reactants have a positive ΔS° (decomposition reactions)
- Reactions that produce fewer molecules than reactants have a negative ΔS° (synthesis reactions)
- Temperature changes
- Entropy increases with increasing temperature, as higher temperatures lead to greater molecular motion and disorder
- Exothermic reactions (negative ΔH°) tend to have a smaller ΔS° than endothermic reactions (positive ΔH°) at the same temperature
Spontaneity and Standard Molar Entropy
Gibbs Free Energy and Spontaneity
- The spontaneity of a chemical process depends on both the enthalpy change (ΔH°) and the entropy change (ΔS°) of the system
- The change (ΔG°) combines these factors to determine the spontaneity of a process at constant temperature and pressure:
- A negative ΔG° indicates a spontaneous process, while a positive ΔG° indicates a non-spontaneous process. A ΔG° of zero indicates a system at equilibrium
- The entropy change (ΔS°) can be the determining factor for the spontaneity of a process, particularly when the enthalpy change (ΔH°) is small or close to zero
- If ΔS° is positive and ΔH° is negative, the process will be spontaneous at all temperatures
- If ΔS° is positive and ΔH° is positive, the process will be spontaneous at high temperatures ()
- If ΔS° is negative and ΔH° is negative, the process will be spontaneous at low temperatures ()
Entropy-Driven Processes
- Some processes are spontaneous primarily due to a large increase in entropy, even if the enthalpy change is unfavorable (positive ΔH°)
- Examples of entropy-driven processes:
- Mixing of gases or liquids: The increased randomness of the mixed state leads to a positive ΔS°, even if no chemical reaction occurs
- Dissolution of salts in water: The increased disorder of the dissolved ions in solution leads to a positive ΔS°, which can overcome the positive ΔH° of breaking the ionic bonds in the salt crystal
- Evaporation of liquids: The transition from liquid to gas increases entropy, making evaporation spontaneous even though it requires energy input (positive ΔH°)
- Understanding the interplay between entropy and enthalpy changes is crucial for predicting the spontaneity and feasibility of chemical reactions and processes
Key Terms to Review (18)
Absolute entropy: Absolute entropy is a measure of the disorder or randomness of a system at a specific temperature, typically defined at absolute zero. It reflects the total energy dispersion within a system and is quantified in units of joules per mole per kelvin (J/mol·K). Understanding absolute entropy is essential for thermodynamic calculations, as it connects to the Third Law of Thermodynamics and standard molar entropies, which help quantify the entropy changes in chemical reactions and physical processes.
Cal/(mol·k): The unit cal/(mol·k) refers to the amount of heat energy in calories associated with one mole of a substance per unit change in temperature in Kelvin. This unit is critical for expressing standard molar entropy, which quantifies the disorder or randomness in a system. Understanding this unit helps relate energy changes to the thermodynamic behavior of substances and their respective entropies at standard conditions.
Calorimetry: Calorimetry is the science of measuring heat transfer in physical and chemical processes. It involves determining the amount of energy absorbed or released during reactions or phase changes, providing essential insights into thermodynamics and energy changes. This method connects to various concepts including temperature measurement, heat capacity, reaction enthalpy, and entropy changes in reactions.
Entropy at absolute zero: Entropy at absolute zero refers to the state where a system's entropy theoretically approaches zero as temperature reaches 0 Kelvin. This concept is tied to the Third Law of Thermodynamics, which states that as a system approaches absolute zero, the entropy of a perfect crystal becomes constant and minimal, leading to implications for the calculation of absolute entropy and standard molar entropies.
Entropy change: Entropy change refers to the measure of the disorder or randomness in a system and how it varies during a process. It is crucial for determining whether a process is spontaneous or non-spontaneous, as spontaneous processes generally result in an increase in entropy of the universe. Understanding entropy change also plays a significant role in thermodynamic cycles and helps to quantify the efficiency of heat engines.
Gibbs Free Energy: Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. This concept is vital for predicting the spontaneity of processes, as it combines the system's enthalpy and entropy to determine whether a reaction or process can occur naturally without external input.
Higher entropy: Higher entropy refers to a state of increased disorder or randomness in a system, which is associated with the number of possible microstates available to that system. In physical chemistry, higher entropy indicates that a system has more accessible arrangements of its particles, leading to a greater degree of randomness and energy dispersal. This concept is crucial in understanding thermodynamic processes and the direction of spontaneous reactions.
J/(mol·k): The unit 'j/(mol·k)' represents the amount of energy in joules associated with a change in temperature per mole of a substance, specifically in the context of entropy. This unit is crucial for understanding how energy disperses at a molecular level as temperature changes. It connects thermodynamic principles with molecular behavior, illustrating how the entropy of a substance can be quantified and compared under standard conditions.
Josiah Willard Gibbs: Josiah Willard Gibbs was an American scientist renowned for his contributions to physical chemistry, particularly in the fields of thermodynamics and statistical mechanics. He formulated the concept of free energy and introduced the statistical interpretation of entropy, which links microscopic particle behavior to macroscopic thermodynamic properties, paving the way for advancements in understanding chemical systems and their spontaneity.
Lower entropy: Lower entropy refers to a state of reduced disorder or randomness in a system, indicating that the system has a higher degree of organization. In thermodynamics, it signifies a state where the energy of the system is more concentrated and less dispersed, which often corresponds to a decrease in the number of accessible microstates. This concept is crucial for understanding the behavior of substances at a molecular level, especially when discussing standard molar entropies.
Ludwig Boltzmann: Ludwig Boltzmann was an Austrian physicist and philosopher known for his foundational work in statistical mechanics and thermodynamics, particularly in understanding entropy and its relation to the microscopic behavior of particles. His theories help explain how macroscopic properties of materials emerge from the collective behavior of microscopic entities, connecting concepts of spontaneity and entropy to the statistical nature of physical systems.
Reaction spontaneity: Reaction spontaneity refers to the natural tendency of a chemical reaction to occur without external influence. This concept is closely linked to thermodynamics, where a spontaneous reaction is one that can proceed in the direction of products under given conditions, often indicated by a decrease in free energy and an increase in entropy. The balance between enthalpy and entropy changes during a reaction determines whether the process is spontaneous at a specific temperature.
S° = s(products) - s(reactants): This equation represents the calculation of standard entropy change for a chemical reaction, where s° is the standard entropy change, and it is determined by subtracting the standard molar entropies of the reactants from those of the products. Standard molar entropy, denoted as s°, provides a measure of the randomness or disorder in a system at standard conditions. The equation emphasizes that the change in entropy during a reaction is crucial for understanding the thermodynamic favorability of processes.
Second Law of Thermodynamics: The Second Law of Thermodynamics states that in any energy transfer or transformation, the total entropy of an isolated system can never decrease over time, and is often expressed in terms of the irreversibility of natural processes. This law highlights the tendency of systems to evolve towards a state of maximum entropy, which has important implications for energy, heat, work, and spontaneity in various processes.
Standard molar entropy: Standard molar entropy is a measure of the degree of disorder or randomness in a substance at standard conditions, typically defined as 1 bar of pressure and a specified temperature, often 298.15 K (25°C). This concept is deeply linked to the Third Law of Thermodynamics, which states that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero. Standard molar entropies provide a way to quantify the entropy associated with one mole of a substance, reflecting its microscopic configurations and the energy dispersal among those configurations.
Statistical Mechanics: Statistical mechanics is a branch of theoretical physics that applies statistical methods to describe the behavior of systems with a large number of particles. It connects macroscopic thermodynamic properties to microscopic behaviors, allowing us to understand how the collective behavior of individual particles results in observable phenomena like temperature and pressure. This approach is crucial for linking concepts such as entropy and energy distributions in various contexts.
Temperature Dependence: Temperature dependence refers to the way in which a physical or chemical property of a substance changes with temperature. This concept is crucial in understanding various processes, such as heat capacity, phase changes, and reaction rates, which all exhibit different behaviors as temperature varies.
δs° = σs°(products) - σs°(reactants): This equation represents the change in standard molar entropy for a chemical reaction at standard conditions. It quantifies the difference in the total standard molar entropies of the products and the reactants, reflecting how disorder and randomness change during the reaction. Understanding this change helps predict the spontaneity of a reaction and its thermodynamic feasibility.