The free energy of a system is a crucial concept in thermodynamics, as it determines the spontaneity and feasibility of a process. To calculate the free energy of a system, we can use the formula ΔG = ΔH – TΔS, where ΔG is the change in free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. This formula allows us to quantify the balance between the energy released or absorbed (enthalpy) and the disorder or randomness (entropy) of a system, providing a comprehensive understanding of its spontaneity and thermodynamic behavior.
Calculating Enthalpy Change (ΔH)
The change in enthalpy (ΔH) for a chemical reaction can be measured using calorimetry techniques. Calorimetry is the experimental method used to determine the heat absorbed or released during a chemical or physical process.
Bomb Calorimetry
Bomb calorimetry is a technique used to measure the heat of combustion of a substance. In a bomb calorimeter, the sample is placed in a sealed, pressurized container (the “bomb”) and ignited, causing the sample to undergo complete combustion. The heat released during the combustion is measured by the temperature increase of a known mass of water surrounding the bomb. The change in enthalpy (ΔH) can then be calculated using the formula:
ΔH = -q / n
Where:
– q is the heat absorbed or released by the system (in Joules)
– n is the number of moles of the reactant or product
Coffee Cup Calorimetry
Coffee cup calorimetry is a simpler and more accessible technique for measuring the heat of reaction between two substances. In this method, the reactants are mixed in a coffee cup or similar insulated container, and the temperature change of the mixture is measured. The change in enthalpy (ΔH) can then be calculated using the formula:
ΔH = -m × c × ΔT / n
Where:
– m is the mass of the solution (in grams)
– c is the specific heat capacity of the solution (in J/g·°C)
– ΔT is the change in temperature (in °C)
– n is the number of moles of the reactant or product
Calculating Entropy Change (ΔS)
The change in entropy (ΔS) for a reaction can be calculated using the formula:
ΔS = (S2 – S1) / n
Where:
– S1 and S2 are the entropies of the reactants and products, respectively
– n is the number of moles of reactants or products
The entropy of a substance can be found in tables of thermodynamic properties or calculated using the formula:
S = k ln W
Where:
– k is the Boltzmann constant (1.38 × 10^-23 J/K)
– W is the number of microstates of the substance
Calculating Free Energy Change (ΔG)
Once we have calculated the values of ΔH and ΔS, we can plug them into the formula for ΔG and solve for the change in free energy:
ΔG = ΔH – TΔS
Where:
– ΔG is the change in free energy
– ΔH is the change in enthalpy
– T is the absolute temperature in Kelvin
– ΔS is the change in entropy
The sign of ΔG determines the spontaneity of the reaction:
– If ΔG is negative, the reaction is spontaneous.
– If ΔG is positive, the reaction is non-spontaneous.
– If ΔG is zero, the system is at equilibrium.
Example Calculation
Let’s calculate the change in free energy for the reaction between hydrogen gas and oxygen gas to form water vapor:
2H2(g) + O2(g) → 2H2O(g)
From tables of thermodynamic properties, we find that the standard enthalpy change (ΔH°) for this reaction is -241.8 kJ/mol, and the standard entropy change (ΔS°) is 169.1 J/(mol·K). Plugging these values into the formula for ΔG° at 298 K (25°C), we get:
ΔG° = ΔH° – TΔS°
ΔG° = -241.8 kJ/mol – (298 K)(0.1691 kJ/mol·K)
ΔG° = -237.1 kJ/mol
Since ΔG° is negative, this reaction is spontaneous under standard conditions.
Conclusion
In summary, to calculate the free energy of a system, we need to measure or calculate the changes in enthalpy and entropy for the reaction, and then plug these values into the formula for ΔG. A negative value of ΔG indicates a spontaneous reaction, while a positive value indicates a non-spontaneous reaction. By understanding the relationship between enthalpy, entropy, and free energy, we can gain valuable insights into the thermodynamic behavior of chemical and physical systems.
References
- Schwartz, R. N. (2014). Lecture 8: Free energy. Retrieved from https://scholar.harvard.edu/files/schwartz/files/8-freeenergy_0.pdf
- Schwartz, R. N. (2014). Lecture 8: Free energy. Retrieved from https://scholar.harvard.edu/files/schwartz/files/8-freeenergy.pdf
- Chem.libretexts.org. (2023). Gibbs Free Energy – Chemistry LibreTexts. Retrieved from https://chem.libretexts.org/Bookshelves/General_Chemistry/Map:_Chemistry_-_The_Central_Science_%28Brown_et_al.%29/19:_Chemical_Thermodynamics/19.05:_Gibbs_Free_Energy
- Chem.libretexts.org. (2023). The Gibbs Free Energy – Chemistry LibreTexts. Retrieved from https://chem.libretexts.org/Bookshelves/General_Chemistry/Map:_Principles_of_Modern_Chemistry_%28Oxtoby_et_al.%29/Unit_4:_Equilibrium_in_Chemical_Reactions/13:_Spontaneous_Processes_and_Thermodynamic_Equilibrium/13.7:_The_Gibbs_Free_Energy
- Openstax.org. (2019). Free Energy – Chemistry 2e | OpenStax. Retrieved from https://openstax.org/books/chemistry-2e/pages/16-4-free-energy
The lambdageeks.com Core SME Team is a group of experienced subject matter experts from diverse scientific and technical fields including Physics, Chemistry, Technology,Electronics & Electrical Engineering, Automotive, Mechanical Engineering. Our team collaborates to create high-quality, well-researched articles on a wide range of science and technology topics for the lambdageeks.com website.
All Our Senior SME are having more than 7 Years of experience in the respective fields . They are either Working Industry Professionals or assocaited With different Universities. Refer Our Authors Page to get to know About our Core SMEs.