Gibbs Free Energy Worksheet With Answers

Gibbs Free Energy Worksheet with Answers: A Comprehensive Guide

Understanding Gibbs Free Energy is crucial in chemistry and thermodynamics. This comprehensive guide provides a Gibbs Free Energy worksheet with answers, covering various aspects of this important concept. We'll delve into the equation, its applications, and practical examples to help you master this subject. This worksheet is suitable for high school, undergraduate, and even graduate students looking to reinforce their understanding of Gibbs Free Energy.

What is Gibbs Free Energy?

Gibbs Free Energy (ΔG), named after Josiah Willard Gibbs, predicts the spontaneity of a reaction under constant temperature and pressure conditions. It's a thermodynamic potential that measures the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The significance of ΔG lies in its ability to determine whether a process will occur spontaneously or require external energy input.

Key Concepts:

• Spontaneity: A spontaneous process occurs naturally without external intervention. A non-spontaneous process requires energy input to proceed.
• Equilibrium: A state where the forward and reverse reaction rates are equal, resulting in no net change in the concentrations of reactants and products.

The Gibbs Free Energy Equation

The core equation for Gibbs Free Energy is:

ΔG = ΔH - TΔS

Where:

• ΔG is the change in Gibbs Free Energy (in Joules or Kilojoules)
• ΔH is the change in enthalpy (heat content) (in Joules or Kilojoules)
• T is the absolute temperature (in Kelvin)
• ΔS is the change in entropy (disorder) (in Joules/Kelvin)

Understanding the terms:

• ΔH (Enthalpy): Represents the heat absorbed or released during a reaction. A negative ΔH indicates an exothermic reaction (heat released), while a positive ΔH indicates an endothermic reaction (heat absorbed).
• T (Temperature): Temperature influences the spontaneity of a reaction. Higher temperatures can favor reactions with positive ΔS.
• ΔS (Entropy): Measures the disorder or randomness of a system. A positive ΔS indicates an increase in disorder (more randomness), while a negative ΔS indicates a decrease in disorder (more order).

Interpreting ΔG Values

The value of ΔG dictates the spontaneity of a reaction:

• ΔG < 0 (Negative): The reaction is spontaneous under the given conditions. It will proceed without external input.
• ΔG > 0 (Positive): The reaction is non-spontaneous under the given conditions. It requires external energy input to proceed.
• ΔG = 0: The reaction is at equilibrium. There is no net change in the concentrations of reactants and products.

Gibbs Free Energy Worksheet: Problems and Solutions

Now let's work through some example problems to solidify your understanding of Gibbs Free Energy.

Problem 1:

A chemical reaction has a ΔH of -50 kJ/mol and a ΔS of +100 J/mol·K. Calculate the Gibbs Free Energy change (ΔG) at 298 K. Is the reaction spontaneous at this temperature?

Solution 1:

1. Convert units: Ensure all units are consistent. Convert ΔS to kJ/mol·K: 100 J/mol·K * (1 kJ/1000 J) = 0.1 kJ/mol·K

2. Apply the equation: ΔG = ΔH - TΔS = -50 kJ/mol - (298 K)(0.1 kJ/mol·K) = -50 kJ/mol - 29.8 kJ/mol = -79.8 kJ/mol

3. Interpret the result: Since ΔG is negative (-79.8 kJ/mol), the reaction is spontaneous at 298 K.

Problem 2:

A reaction has a ΔH of +25 kJ/mol and a ΔS of -50 J/mol·K. Determine if the reaction is spontaneous at 25°C (298 K).

Solution 2:

1. Convert units: Convert ΔS to kJ/mol·K: -50 J/mol·K * (1 kJ/1000 J) = -0.05 kJ/mol·K

2. Apply the equation: ΔG = ΔH - TΔS = +25 kJ/mol - (298 K)(-0.05 kJ/mol·K) = +25 kJ/mol + 14.9 kJ/mol = +39.9 kJ/mol

3. Interpret the result: Since ΔG is positive (+39.9 kJ/mol), the reaction is non-spontaneous at 298 K.

Problem 3:

Calculate the temperature at which the following reaction becomes spontaneous: ΔH = +50 kJ/mol and ΔS = +150 J/mol·K

Solution 3:

1. Set ΔG to zero: At the point where a reaction becomes spontaneous, ΔG = 0.

2. Solve for T: 0 = ΔH - TΔS => T = ΔH/ΔS

3. Convert units: Convert ΔS to kJ/mol·K: 150 J/mol·K * (1 kJ/1000 J) = 0.15 kJ/mol·K

4. Calculate T: T = (50 kJ/mol) / (0.15 kJ/mol·K) = 333.33 K

5. Interpret the result: The reaction becomes spontaneous above 333.33 K (approximately 60°C).

Problem 4:

A reaction has ΔG = -10 kJ/mol. What can you conclude about the spontaneity and equilibrium of the reaction?

Solution 4:

Since ΔG is negative (-10 kJ/mol), the reaction is spontaneous under the given conditions. The reaction will proceed in the forward direction until it reaches equilibrium. At equilibrium, ΔG will be 0.

Problem 5:

Consider two reactions: Reaction A (ΔG = -20 kJ/mol) and Reaction B (ΔG = +15 kJ/mol). Which reaction is more favorable under standard conditions?

Solution 5:

Reaction A is more favorable because it has a more negative ΔG value. A more negative ΔG indicates a greater driving force towards product formation.

Problem 6 (Advanced):

A reaction has a ΔH of -40 kJ/mol and a ΔS of -100 J/mol·K. At what temperature will the reaction be at equilibrium?

Solution 6:

At equilibrium, ΔG = 0. Therefore, 0 = ΔH - TΔS. Solving for T, we get:

T = ΔH/ΔS = (-40 kJ/mol) / (-0.1 kJ/mol·K) = 400 K. The reaction will be at equilibrium at 400 K.

Applications of Gibbs Free Energy

Gibbs Free Energy has widespread applications across various fields, including:

• Chemistry: Predicting reaction spontaneity, determining equilibrium constants, and understanding phase transitions.
• Biochemistry: Studying metabolic processes, enzyme kinetics, and protein folding.
• Materials Science: Designing new materials with desired properties and understanding material stability.
• Environmental Science: Assessing the feasibility of environmental remediation processes.

Conclusion

This comprehensive guide and accompanying Gibbs Free Energy worksheet with answers provide a solid foundation for understanding this critical thermodynamic concept. Remember to always pay close attention to units and correctly interpret the sign of ΔG to determine reaction spontaneity. By mastering Gibbs Free Energy, you'll gain a deeper understanding of chemical reactions and their behavior under various conditions. Continue practicing with different problems to enhance your comprehension and problem-solving skills. This will prove invaluable in your academic pursuits and beyond.