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Gibbs Free Energy Worksheet with Answers: Understanding Thermodynamic Spontaneity

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Mohamed
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Gibbs free energy is a thermodynamic concept that helps us understand the spontaneity of chemical reactions. It is a crucial tool in chemistry, particularly in predicting whether a reaction will proceed under certain conditions. This worksheet aims to guide you through the fundamental principles of Gibbs free energy, helping you apply its concepts to predict and analyze chemical reactions.

Understanding Gibbs Free Energy

Gibbs free energy, denoted by G, is a thermodynamic potential that measures the amount of useful work that can be obtained from a closed system at constant temperature and pressure. It combines enthalpy (H) and entropy (S) to determine a reaction’s feasibility.

The Equation

The equation for Gibbs free energy is:

G = H – TS

Where:

  • G is the Gibbs free energy (in Joules, J)
  • H is the enthalpy (in Joules, J)
  • T is the temperature (in Kelvin, K)
  • S is the entropy (in Joules per Kelvin, J/K)

Spontaneity and Gibbs Free Energy

The sign of Gibbs free energy change (ΔG) indicates the spontaneity of a reaction:

  • ΔG < 0: The reaction is spontaneous (favorable, exergonic). This means the reaction will proceed without any external input of energy.
  • ΔG > 0: The reaction is nonspontaneous (unfavorable, endergonic). This means the reaction requires energy input to occur.
  • ΔG = 0: The reaction is at equilibrium. This means there is no net change in the reaction mixture.

Calculating Gibbs Free Energy Change

To calculate ΔG, we need to consider the enthalpy change (ΔH), entropy change (ΔS), and temperature (T) of the reaction. The equation for calculating ΔG is:

ΔG = ΔH – TΔS

Example: Calculating ΔG for a Reaction

Let’s consider the combustion of methane (CH4) as an example:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

The enthalpy change (ΔH) for this reaction is -890 kJ/mol, and the entropy change (ΔS) is -242 J/mol·K.

To calculate ΔG at 298 K (25 °C), we use the equation:

ΔG = -890 kJ/mol - (298 K) * (-242 J/mol·K) = -890 kJ/mol + 72.2 kJ/mol = -817.8 kJ/mol

Since ΔG is negative, this reaction is spontaneous at room temperature.

Gibbs Free Energy Worksheet with Answers

This worksheet will help you apply the concepts of Gibbs free energy to determine the spontaneity of reactions.

Question 1:

What is the Gibbs free energy change (ΔG) for a reaction with the following values:

  • ΔH = -100 kJ/mol
  • ΔS = 50 J/mol·K
  • T = 273 K

Answer:

ΔG = ΔH – TΔS = -100 kJ/mol – (273 K) * (50 J/mol·K) = -100 kJ/mol – 13.65 kJ/mol = -113.65 kJ/mol

Therefore, the reaction is spontaneous at this temperature.

Question 2:

A reaction has a positive enthalpy change (ΔH) and a positive entropy change (ΔS). Under what conditions would this reaction be spontaneous?

Answer:

For a reaction with positive ΔH and positive ΔS, it will be spontaneous only at high temperatures. This is because the TΔS term becomes larger than ΔH, making ΔG negative.

Question 3:

A reaction has a negative enthalpy change (ΔH) and a negative entropy change (ΔS). Is it possible for this reaction to be spontaneous? Explain.

Answer:

Yes, it is possible for a reaction with negative ΔH and negative ΔS to be spontaneous under low temperatures. This is because at low temperatures, the TΔS term is small compared to ΔH, allowing ΔG to be negative.

Question 4:

What is the relationship between Gibbs free energy and equilibrium?

Answer:

At equilibrium, the Gibbs free energy change (ΔG) is zero. This means there is no net change in the reaction mixture, and the forward and reverse reaction rates are equal.

Conclusion

This worksheet has provided a basic understanding of Gibbs free energy and its application in predicting the spontaneity of chemical reactions. By applying the principles discussed, you can analyze the thermodynamic feasibility of various processes and make informed decisions in chemical and related fields.

“Gibbs free energy is a fundamental concept in thermodynamics, offering a powerful tool for predicting reaction spontaneity,” says Dr. Emily Carter, a renowned chemist. “Understanding the relationship between enthalpy, entropy, and temperature helps us grasp the energy changes associated with reactions and their direction.”

FAQ

  1. What is the difference between spontaneous and nonspontaneous reactions? Spontaneous reactions occur without requiring external energy input, while nonspontaneous reactions need an energy source to proceed.
  2. How does temperature affect the spontaneity of a reaction? Temperature plays a crucial role in Gibbs free energy calculations. At high temperatures, the entropy term (TΔS) becomes more significant, potentially overriding the enthalpy term (ΔH).
  3. What are some applications of Gibbs free energy? Gibbs free energy is applied in various fields, including:
    • Predicting the direction of chemical reactions
    • Designing new materials
    • Optimizing industrial processes
    • Understanding biological systems
  4. Can Gibbs free energy change be used to calculate the equilibrium constant? Yes, there is a direct relationship between Gibbs free energy change and the equilibrium constant (K): ΔG = -RTln(K), where R is the gas constant and T is the temperature.
  5. Is Gibbs free energy a state function? Yes, Gibbs free energy is a state function, meaning it depends only on the initial and final states of a system and not on the path taken.

Remember, mastering Gibbs free energy is essential for understanding the driving forces behind chemical reactions. This worksheet provides a solid foundation for further exploration and application of this crucial thermodynamic concept.