The provided source materials focus exclusively on educational resources for understanding and calculating Gibbs free energy (ΔG) in chemical thermodynamics. These resources are designed for students and educators, offering practice problems, theoretical explanations, and calculation methods related to spontaneity, equilibrium constants, and the effects of temperature on reactions. The documents do not contain any information about free samples, promotional offers, product trials, brand freebies, or mail-in sample programmes. Consequently, it is not possible to write a 2000-word article on the requested consumer topics based on the provided data. Below is a factual summary of the information available in the source documents.
Key Concepts in Gibbs Free Energy
Gibbs free energy is a thermodynamic potential that measures the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It is central to predicting the spontaneity of chemical reactions. The fundamental equation is:
ΔG = ΔH - TΔS
Where: - ΔG is the change in Gibbs free energy. - ΔH is the change in enthalpy. - T is the absolute temperature in Kelvin. - ΔS is the change in entropy.
A reaction is spontaneous if ΔG is negative, non-spontaneous if ΔG is positive, and at equilibrium if ΔG is zero. The relationship between ΔG and the equilibrium constant (K) is given by:
ΔG° = -RT ln K
Where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin. This equation shows that a large positive ΔG° corresponds to a small K, and a large negative ΔG° corresponds to a large K.
Practice Problems and Applications
The source documents contain several practice problems that illustrate these principles. For example, one problem involves the reaction CO(g) + 2H₂(g) → CH₃OH(g) at 444 K. The equilibrium constant (K_eq) is calculated as 12.8, leading to ΔG° = -9.4 kJ/mol, indicating spontaneity under standard conditions.
Another problem examines the reaction Fe₃O₄(s) → 3Fe(s) + 2O₂(g) at 298 K. Using standard enthalpy and entropy values, ΔH° is calculated as +1118.4 kJ and ΔS° as 347.2 J/K. The resulting ΔG° is +1015 kJ, showing the reaction is non-spontaneous.
Temperature dependence is a critical theme. For a reaction with ΔH = 158 kJ and ΔS = 411 J/K, spontaneity (ΔG < 0) occurs above 384 K. This highlights how entropy becomes more influential at higher temperatures.
Equilibrium Constants and Reaction Quotients
The documents also cover the calculation of equilibrium constants from standard Gibbs energy changes. For instance, for the reaction CO(g) + O₂(g) → CO₂(g) at 298 K, using standard formation energies (ΔGf° for CO = -137.2 kJ/mol, for CO₂ = -394.4 kJ/mol), ΔG° is -257.2 kJ/mol. This yields Kp ≈ 1.11.
The reaction quotient (Q) is used to determine the direction of a reaction under non-standard conditions. For NH₃(aq) + H₂O(l) → NH₄⁺(aq) + OH⁻(aq) with specific concentrations, Q_c is calculated as 1.0 × 10⁻⁵. Using ΔG° = 29.05 kJ/mol, the actual ΔG is found to be positive (525.9 kJ/mol), indicating the reaction is not spontaneous in the forward direction under those conditions.
Temperature and Spontaneity
The interplay between enthalpy and entropy dictates how temperature affects spontaneity. For an exothermic reaction (ΔH < 0) with a negative entropy change (ΔS < 0), increasing temperature makes the reaction less spontaneous. Conversely, for an endothermic reaction (ΔH > 0) with a positive entropy change (ΔS > 0), increasing temperature can drive spontaneity. This is illustrated with the dimerization of NO₂ to N₂O₄, which is enthalpy-favoured but entropy-disfavoured.
Conclusion
The provided sources offer a solid foundation for understanding Gibbs free energy through theoretical explanations and practical problem-solving. They cover essential calculations for spontaneity, equilibrium constants, and the temperature dependence of reactions. These resources are valuable for UK students studying chemistry, particularly at the A-level or undergraduate level, seeking to master thermodynamic principles. However, they do not provide information on consumer-oriented topics such as free samples or promotional offers.